characteristics of a causal hypothesis

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Causal research: definition, examples and how to use it.

16 min read Causal research enables market researchers to predict hypothetical occurrences & outcomes while improving existing strategies. Discover how this research can decrease employee retention & increase customer success for your business.

What is causal research?

Causal research, also known as explanatory research or causal-comparative research, identifies the extent and nature of cause-and-effect relationships between two or more variables.

It’s often used by companies to determine the impact of changes in products, features, or services process on critical company metrics. Some examples:

• How does rebranding of a product influence intent to purchase?
• How would expansion to a new market segment affect projected sales?
• What would be the impact of a price increase or decrease on customer loyalty?

To maintain the accuracy of causal research, ‘confounding variables’ or influences — e.g. those that could distort the results — are controlled. This is done either by keeping them constant in the creation of data, or by using statistical methods. These variables are identified before the start of the research experiment.

As well as the above, research teams will outline several other variables and principles in causal research:

• Independent variables

The variables that may cause direct changes in another variable. For example, the effect of truancy on a student’s grade point average. The independent variable is therefore class attendance.

• Control variables

These are the components that remain unchanged during the experiment so researchers can better understand what conditions create a cause-and-effect relationship.  

This describes the cause-and-effect relationship. When researchers find causation (or the cause), they’ve conducted all the processes necessary to prove it exists.

• Correlation

Any relationship between two variables in the experiment. It’s important to note that correlation doesn’t automatically mean causation. Researchers will typically establish correlation before proving cause-and-effect.

• Experimental design

Researchers use experimental design to define the parameters of the experiment — e.g. categorizing participants into different groups.

• Dependent variables

These are measurable variables that may change or are influenced by the independent variable. For example, in an experiment about whether or not terrain influences running speed, your dependent variable is the terrain.  

Why is causal research useful?

It’s useful because it enables market researchers to predict hypothetical occurrences and outcomes while improving existing strategies. This allows businesses to create plans that benefit the company. It’s also a great research method because researchers can immediately see how variables affect each other and under what circumstances.

Also, once the first experiment has been completed, researchers can use the learnings from the analysis to repeat the experiment or apply the findings to other scenarios. Because of this, it’s widely used to help understand the impact of changes in internal or commercial strategy to the business bottom line.

Some examples include:

• Understanding how overall training levels are improved by introducing new courses
• Examining which variations in wording make potential customers more interested in buying a product
• Testing a market’s response to a brand-new line of products and/or services

So, how does causal research compare and differ from other research types?

Well, there are a few research types that are used to find answers to some of the examples above:

1. Exploratory research

As its name suggests, exploratory research involves assessing a situation (or situations) where the problem isn’t clear. Through this approach, researchers can test different avenues and ideas to establish facts and gain a better understanding.

Researchers can also use it to first navigate a topic and identify which variables are important. Because no area is off-limits, the research is flexible and adapts to the investigations as it progresses.

Finally, this approach is unstructured and often involves gathering qualitative data, giving the researcher freedom to progress the research according to their thoughts and assessment. However, this may make results susceptible to researcher bias and may limit the extent to which a topic is explored.

2. Descriptive research

Descriptive research is all about describing the characteristics of the population, phenomenon or scenario studied. It focuses more on the “what” of the research subject than the “why”.

For example, a clothing brand wants to understand the fashion purchasing trends amongst buyers in California — so they conduct a demographic survey of the region, gather population data and then run descriptive research. The study will help them to uncover purchasing patterns amongst fashion buyers in California, but not necessarily why those patterns exist.

As the research happens in a natural setting, variables can cross-contaminate other variables, making it harder to isolate cause and effect relationships. Therefore, further research will be required if more causal information is needed.

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How is causal research different from the other two methods above?

Well, causal research looks at what variables are involved in a problem and ‘why’ they act a certain way. As the experiment takes place in a controlled setting (thanks to controlled variables) it’s easier to identify cause-and-effect amongst variables.

Furthermore, researchers can carry out causal research at any stage in the process, though it’s usually carried out in the later stages once more is known about a particular topic or situation.

Finally, compared to the other two methods, causal research is more structured, and researchers can combine it with exploratory and descriptive research to assist with research goals.

Summary of three research types

What are the advantages of causal research?

• Improve experiences

By understanding which variables have positive impacts on target variables (like sales revenue or customer loyalty), businesses can improve their processes, return on investment, and the experiences they offer customers and employees.

• Help companies improve internally

By conducting causal research, management can make informed decisions about improving their employee experience and internal operations. For example, understanding which variables led to an increase in staff turnover.

• Repeat experiments to enhance reliability and accuracy of results

When variables are identified, researchers can replicate cause-and-effect with ease, providing them with reliable data and results to draw insights from.

• Test out new theories or ideas

If causal research is able to pinpoint the exact outcome of mixing together different variables, research teams have the ability to test out ideas in the same way to create viable proof of concepts.

• Fix issues quickly

Once an undesirable effect’s cause is identified, researchers and management can take action to reduce the impact of it or remove it entirely, resulting in better outcomes.

What are the disadvantages of causal research?

• Provides information to competitors

If you plan to publish your research, it provides information about your plans to your competitors. For example, they might use your research outcomes to identify what you are up to and enter the market before you.

• Difficult to administer

Causal research is often difficult to administer because it’s not possible to control the effects of extraneous variables.

• Time and money constraints

Budgetary and time constraints can make this type of research expensive to conduct and repeat. Also, if an initial attempt doesn’t provide a cause and effect relationship, the ROI is wasted and could impact the appetite for future repeat experiments.

• Requires additional research to ensure validity

You can’t rely on just the outcomes of causal research as it’s inaccurate. It’s best to conduct other types of research alongside it to confirm its output.

• Trouble establishing cause and effect

Researchers might identify that two variables are connected, but struggle to determine which is the cause and which variable is the effect.

• Risk of contamination

There’s always the risk that people outside your market or area of study could affect the results of your research. For example, if you’re conducting a retail store study, shoppers outside your ‘test parameters’ shop at your store and skew the results.

How can you use causal research effectively?

To better highlight how you can use causal research across functions or markets, here are a few examples:

Market and advertising research

A company might want to know if their new advertising campaign or marketing campaign is having a positive impact. So, their research team can carry out a causal research project to see which variables cause a positive or negative effect on the campaign.

For example, a cold-weather apparel company in a winter ski-resort town may see an increase in sales generated after a targeted campaign to skiers. To see if one caused the other, the research team could set up a duplicate experiment to see if the same campaign would generate sales from non-skiers. If the results reduce or change, then it’s likely that the campaign had a direct effect on skiers to encourage them to purchase products.

Improving customer experiences and loyalty levels

Customers enjoy shopping with brands that align with their own values, and they’re more likely to buy and present the brand positively to other potential shoppers as a result. So, it’s in your best interest to deliver great experiences and retain your customers.

For example, the Harvard Business Review found that an increase in customer retention rates by 5% increased profits by 25% to 95%. But let’s say you want to increase your own, how can you identify which variables contribute to it?Using causal research, you can test hypotheses about which processes, strategies or changes influence customer retention. For example, is it the streamlined checkout? What about the personalized product suggestions? Or maybe it was a new solution that solved their problem? Causal research will help you find out.

Improving problematic employee turnover rates

If your company has a high attrition rate, causal research can help you narrow down the variables or reasons which have the greatest impact on people leaving. This allows you to prioritize your efforts on tackling the issues in the right order, for the best positive outcomes.

For example, through causal research, you might find that employee dissatisfaction due to a lack of communication and transparency from upper management leads to poor morale, which in turn influences employee retention.

To rectify the problem, you could implement a routine feedback loop or session that enables your people to talk to your company’s C-level executives so that they feel heard and understood.

How to conduct causal research first steps to getting started are:

1. Define the purpose of your research

What questions do you have? What do you expect to come out of your research? Think about which variables you need to test out the theory.

2. Pick a random sampling if participants are needed

Using a technology solution to support your sampling, like a database, can help you define who you want your target audience to be, and how random or representative they should be.

3. Set up the controlled experiment

Once you’ve defined which variables you’d like to measure to see if they interact, think about how best to set up the experiment. This could be in-person or in-house via interviews, or it could be done remotely using online surveys.

4. Carry out the experiment

Make sure to keep all irrelevant variables the same, and only change the causal variable (the one that causes the effect) to gather the correct data. Depending on your method, you could be collecting qualitative or quantitative data, so make sure you note your findings across each regularly.

5. Analyze your findings

Either manually or using technology, analyze your data to see if any trends, patterns or correlations emerge. By looking at the data, you’ll be able to see what changes you might need to do next time, or if there are questions that require further research.

6. Verify your findings

Your first attempt gives you the baseline figures to compare the new results to. You can then run another experiment to verify your findings.

7. Do follow-up or supplemental research

You can supplement your original findings by carrying out research that goes deeper into causes or explores the topic in more detail. One of the best ways to do this is to use a survey. See ‘Use surveys to help your experiment’.

Identifying causal relationships between variables

To verify if a causal relationship exists, you have to satisfy the following criteria:

• Nonspurious association

A clear correlation exists between one cause and the effect. In other words, no ‘third’ that relates to both (cause and effect) should exist.

• Temporal sequence

The cause occurs before the effect. For example, increased ad spend on product marketing would contribute to higher product sales.

• Concomitant variation

The variation between the two variables is systematic. For example, if a company doesn’t change its IT policies and technology stack, then changes in employee productivity were not caused by IT policies or technology.

How surveys help your causal research experiments?

There are some surveys that are perfect for assisting researchers with understanding cause and effect. These include:

• Employee Satisfaction Survey – An introductory employee satisfaction survey that provides you with an overview of your current employee experience.
• Manager Feedback Survey – An introductory manager feedback survey geared toward improving your skills as a leader with valuable feedback from your team.
• Net Promoter Score (NPS) Survey – Measure customer loyalty and understand how your customers feel about your product or service using one of the world’s best-recognized metrics.
• Employee Engagement Survey – An entry-level employee engagement survey that provides you with an overview of your current employee experience.
• Customer Satisfaction Survey – Evaluate how satisfied your customers are with your company, including the products and services you provide and how they are treated when they buy from you.
• Employee Exit Interview Survey – Understand why your employees are leaving and how they’ll speak about your company once they’re gone.
• Product Research Survey – Evaluate your consumers’ reaction to a new product or product feature across every stage of the product development journey.
• Brand Awareness Survey – Track the level of brand awareness in your target market, including current and potential future customers.
• Online Purchase Feedback Survey – Find out how well your online shopping experience performs against customer needs and expectations.

That covers the fundamentals of causal research and should give you a foundation for ongoing studies to assess opportunities, problems, and risks across your market, product, customer, and employee segments.

If you want to transform your research, empower your teams and get insights on tap to get ahead of the competition, maybe it’s time to leverage Qualtrics CoreXM.

Qualtrics CoreXM provides a single platform for data collection and analysis across every part of your business — from customer feedback to product concept testing. What’s more, you can integrate it with your existing tools and services thanks to a flexible API.

Qualtrics CoreXM offers you as much or as little power and complexity as you need, so whether you’re running simple surveys or more advanced forms of research, it can deliver every time.

Get started on your market research journey with CoreXM

Related resources

Market intelligence 10 min read, marketing insights 11 min read, ethnographic research 11 min read, qualitative vs quantitative research 13 min read, qualitative research questions 11 min read, qualitative research design 12 min read, primary vs secondary research 14 min read, request demo.

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What is a Research Hypothesis: How to Write it, Types, and Examples

Any research begins with a research question and a research hypothesis . A research question alone may not suffice to design the experiment(s) needed to answer it. A hypothesis is central to the scientific method. But what is a hypothesis ? A hypothesis is a testable statement that proposes a possible explanation to a phenomenon, and it may include a prediction. Next, you may ask what is a research hypothesis ? Simply put, a research hypothesis is a prediction or educated guess about the relationship between the variables that you want to investigate.  

It is important to be thorough when developing your research hypothesis. Shortcomings in the framing of a hypothesis can affect the study design and the results. A better understanding of the research hypothesis definition and characteristics of a good hypothesis will make it easier for you to develop your own hypothesis for your research. Let’s dive in to know more about the types of research hypothesis , how to write a research hypothesis , and some research hypothesis examples .  

Table of Contents

What is a hypothesis ?  

A hypothesis is based on the existing body of knowledge in a study area. Framed before the data are collected, a hypothesis states the tentative relationship between independent and dependent variables, along with a prediction of the outcome.  

What is a research hypothesis ?  

Young researchers starting out their journey are usually brimming with questions like “ What is a hypothesis ?” “ What is a research hypothesis ?” “How can I write a good research hypothesis ?”   

A research hypothesis is a statement that proposes a possible explanation for an observable phenomenon or pattern. It guides the direction of a study and predicts the outcome of the investigation. A research hypothesis is testable, i.e., it can be supported or disproven through experimentation or observation.     

Characteristics of a good hypothesis  

Here are the characteristics of a good hypothesis :  

• Clearly formulated and free of language errors and ambiguity  
• Concise and not unnecessarily verbose  
• Has clearly defined variables  
• Testable and stated in a way that allows for it to be disproven  
• Can be tested using a research design that is feasible, ethical, and practical   
• Specific and relevant to the research problem  
• Rooted in a thorough literature search  
• Can generate new knowledge or understanding.  

How to create an effective research hypothesis  

A study begins with the formulation of a research question. A researcher then performs background research. This background information forms the basis for building a good research hypothesis . The researcher then performs experiments, collects, and analyzes the data, interprets the findings, and ultimately, determines if the findings support or negate the original hypothesis.  

Let’s look at each step for creating an effective, testable, and good research hypothesis :  

• Identify a research problem or question: Start by identifying a specific research problem.   
• Review the literature: Conduct an in-depth review of the existing literature related to the research problem to grasp the current knowledge and gaps in the field.   
• Formulate a clear and testable hypothesis : Based on the research question, use existing knowledge to form a clear and testable hypothesis . The hypothesis should state a predicted relationship between two or more variables that can be measured and manipulated. Improve the original draft till it is clear and meaningful.  
• State the null hypothesis: The null hypothesis is a statement that there is no relationship between the variables you are studying.   
• Define the population and sample: Clearly define the population you are studying and the sample you will be using for your research.  
• Select appropriate methods for testing the hypothesis: Select appropriate research methods, such as experiments, surveys, or observational studies, which will allow you to test your research hypothesis .  

Remember that creating a research hypothesis is an iterative process, i.e., you might have to revise it based on the data you collect. You may need to test and reject several hypotheses before answering the research problem.  

How to write a research hypothesis  

When you start writing a research hypothesis , you use an “if–then” statement format, which states the predicted relationship between two or more variables. Clearly identify the independent variables (the variables being changed) and the dependent variables (the variables being measured), as well as the population you are studying. Review and revise your hypothesis as needed.  

An example of a research hypothesis in this format is as follows:  

“ If [athletes] follow [cold water showers daily], then their [endurance] increases.”  

Population: athletes  

Independent variable: daily cold water showers  

Dependent variable: endurance  

You may have understood the characteristics of a good hypothesis . But note that a research hypothesis is not always confirmed; a researcher should be prepared to accept or reject the hypothesis based on the study findings.  

Research hypothesis checklist  

Following from above, here is a 10-point checklist for a good research hypothesis :  

• Testable: A research hypothesis should be able to be tested via experimentation or observation.  
• Specific: A research hypothesis should clearly state the relationship between the variables being studied.  
• Based on prior research: A research hypothesis should be based on existing knowledge and previous research in the field.  
• Falsifiable: A research hypothesis should be able to be disproven through testing.  
• Clear and concise: A research hypothesis should be stated in a clear and concise manner.  
• Logical: A research hypothesis should be logical and consistent with current understanding of the subject.  
• Relevant: A research hypothesis should be relevant to the research question and objectives.  
• Feasible: A research hypothesis should be feasible to test within the scope of the study.  
• Reflects the population: A research hypothesis should consider the population or sample being studied.  
• Uncomplicated: A good research hypothesis is written in a way that is easy for the target audience to understand.  

By following this research hypothesis checklist , you will be able to create a research hypothesis that is strong, well-constructed, and more likely to yield meaningful results.  

Types of research hypothesis  

Different types of research hypothesis are used in scientific research:  

1. Null hypothesis:

A null hypothesis states that there is no change in the dependent variable due to changes to the independent variable. This means that the results are due to chance and are not significant. A null hypothesis is denoted as H0 and is stated as the opposite of what the alternative hypothesis states.   

Example: “ The newly identified virus is not zoonotic .”  

2. Alternative hypothesis:

This states that there is a significant difference or relationship between the variables being studied. It is denoted as H1 or Ha and is usually accepted or rejected in favor of the null hypothesis.  

Example: “ The newly identified virus is zoonotic .”  

3. Directional hypothesis :

This specifies the direction of the relationship or difference between variables; therefore, it tends to use terms like increase, decrease, positive, negative, more, or less.   

Example: “ The inclusion of intervention X decreases infant mortality compared to the original treatment .”   

4. Non-directional hypothesis:

While it does not predict the exact direction or nature of the relationship between the two variables, a non-directional hypothesis states the existence of a relationship or difference between variables but not the direction, nature, or magnitude of the relationship. A non-directional hypothesis may be used when there is no underlying theory or when findings contradict previous research.  

Example, “ Cats and dogs differ in the amount of affection they express .”  

5. Simple hypothesis :

A simple hypothesis only predicts the relationship between one independent and another independent variable.  

Example: “ Applying sunscreen every day slows skin aging .”  

6 . Complex hypothesis :

A complex hypothesis states the relationship or difference between two or more independent and dependent variables.   

Example: “ Applying sunscreen every day slows skin aging, reduces sun burn, and reduces the chances of skin cancer .” (Here, the three dependent variables are slowing skin aging, reducing sun burn, and reducing the chances of skin cancer.)  

7. Associative hypothesis:  

An associative hypothesis states that a change in one variable results in the change of the other variable. The associative hypothesis defines interdependency between variables.  

Example: “ There is a positive association between physical activity levels and overall health .”  

8 . Causal hypothesis:

A causal hypothesis proposes a cause-and-effect interaction between variables.  

Example: “ Long-term alcohol use causes liver damage .”  

Note that some of the types of research hypothesis mentioned above might overlap. The types of hypothesis chosen will depend on the research question and the objective of the study.  

Research hypothesis examples  

Here are some good research hypothesis examples :  

“The use of a specific type of therapy will lead to a reduction in symptoms of depression in individuals with a history of major depressive disorder.”  

“Providing educational interventions on healthy eating habits will result in weight loss in overweight individuals.”  

“Plants that are exposed to certain types of music will grow taller than those that are not exposed to music.”  

“The use of the plant growth regulator X will lead to an increase in the number of flowers produced by plants.”  

Characteristics that make a research hypothesis weak are unclear variables, unoriginality, being too general or too vague, and being untestable. A weak hypothesis leads to weak research and improper methods.   

Some bad research hypothesis examples (and the reasons why they are “bad”) are as follows:  

“This study will show that treatment X is better than any other treatment . ” (This statement is not testable, too broad, and does not consider other treatments that may be effective.)  

“This study will prove that this type of therapy is effective for all mental disorders . ” (This statement is too broad and not testable as mental disorders are complex and different disorders may respond differently to different types of therapy.)  

“Plants can communicate with each other through telepathy . ” (This statement is not testable and lacks a scientific basis.)  

Importance of testable hypothesis  

If a research hypothesis is not testable, the results will not prove or disprove anything meaningful. The conclusions will be vague at best. A testable hypothesis helps a researcher focus on the study outcome and understand the implication of the question and the different variables involved. A testable hypothesis helps a researcher make precise predictions based on prior research.  

To be considered testable, there must be a way to prove that the hypothesis is true or false; further, the results of the hypothesis must be reproducible.  

Frequently Asked Questions (FAQs) on research hypothesis  

1. What is the difference between research question and research hypothesis ?  

A research question defines the problem and helps outline the study objective(s). It is an open-ended statement that is exploratory or probing in nature. Therefore, it does not make predictions or assumptions. It helps a researcher identify what information to collect. A research hypothesis , however, is a specific, testable prediction about the relationship between variables. Accordingly, it guides the study design and data analysis approach.

2. When to reject null hypothesis ?

A null hypothesis should be rejected when the evidence from a statistical test shows that it is unlikely to be true. This happens when the test statistic (e.g., p -value) is less than the defined significance level (e.g., 0.05). Rejecting the null hypothesis does not necessarily mean that the alternative hypothesis is true; it simply means that the evidence found is not compatible with the null hypothesis.  

3. How can I be sure my hypothesis is testable?  

A testable hypothesis should be specific and measurable, and it should state a clear relationship between variables that can be tested with data. To ensure that your hypothesis is testable, consider the following:  

• Clearly define the key variables in your hypothesis. You should be able to measure and manipulate these variables in a way that allows you to test the hypothesis.  
• The hypothesis should predict a specific outcome or relationship between variables that can be measured or quantified.   
• You should be able to collect the necessary data within the constraints of your study.  
• It should be possible for other researchers to replicate your study, using the same methods and variables.   
• Your hypothesis should be testable by using appropriate statistical analysis techniques, so you can draw conclusions, and make inferences about the population from the sample data.  
• The hypothesis should be able to be disproven or rejected through the collection of data.  

4. How do I revise my research hypothesis if my data does not support it?  

If your data does not support your research hypothesis , you will need to revise it or develop a new one. You should examine your data carefully and identify any patterns or anomalies, re-examine your research question, and/or revisit your theory to look for any alternative explanations for your results. Based on your review of the data, literature, and theories, modify your research hypothesis to better align it with the results you obtained. Use your revised hypothesis to guide your research design and data collection. It is important to remain objective throughout the process.  

5. I am performing exploratory research. Do I need to formulate a research hypothesis?  

As opposed to “confirmatory” research, where a researcher has some idea about the relationship between the variables under investigation, exploratory research (or hypothesis-generating research) looks into a completely new topic about which limited information is available. Therefore, the researcher will not have any prior hypotheses. In such cases, a researcher will need to develop a post-hoc hypothesis. A post-hoc research hypothesis is generated after these results are known.  

6. How is a research hypothesis different from a research question?

A research question is an inquiry about a specific topic or phenomenon, typically expressed as a question. It seeks to explore and understand a particular aspect of the research subject. In contrast, a research hypothesis is a specific statement or prediction that suggests an expected relationship between variables. It is formulated based on existing knowledge or theories and guides the research design and data analysis.

7. Can a research hypothesis change during the research process?

Yes, research hypotheses can change during the research process. As researchers collect and analyze data, new insights and information may emerge that require modification or refinement of the initial hypotheses. This can be due to unexpected findings, limitations in the original hypotheses, or the need to explore additional dimensions of the research topic. Flexibility is crucial in research, allowing for adaptation and adjustment of hypotheses to align with the evolving understanding of the subject matter.

8. How many hypotheses should be included in a research study?

The number of research hypotheses in a research study varies depending on the nature and scope of the research. It is not necessary to have multiple hypotheses in every study. Some studies may have only one primary hypothesis, while others may have several related hypotheses. The number of hypotheses should be determined based on the research objectives, research questions, and the complexity of the research topic. It is important to ensure that the hypotheses are focused, testable, and directly related to the research aims.

9. Can research hypotheses be used in qualitative research?

Yes, research hypotheses can be used in qualitative research, although they are more commonly associated with quantitative research. In qualitative research, hypotheses may be formulated as tentative or exploratory statements that guide the investigation. Instead of testing hypotheses through statistical analysis, qualitative researchers may use the hypotheses to guide data collection and analysis, seeking to uncover patterns, themes, or relationships within the qualitative data. The emphasis in qualitative research is often on generating insights and understanding rather than confirming or rejecting specific research hypotheses through statistical testing.

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What is causal research design?

Last updated

14 May 2023

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Examining these relationships gives researchers valuable insights into the mechanisms that drive the phenomena they are investigating.

Organizations primarily use causal research design to identify, determine, and explore the impact of changes within an organization and the market. You can use a causal research design to evaluate the effects of certain changes on existing procedures, norms, and more.

This article explores causal research design, including its elements, advantages, and disadvantages.

Analyze your causal research

Dovetail streamlines causal research analysis to help you uncover and share actionable insights

• Components of causal research

You can demonstrate the existence of cause-and-effect relationships between two factors or variables using specific causal information, allowing you to produce more meaningful results and research implications.

These are the key inputs for causal research:

The timeline of events

Ideally, the cause must occur before the effect. You should review the timeline of two or more separate events to determine the independent variables (cause) from the dependent variables (effect) before developing a hypothesis. 

If the cause occurs before the effect, you can link cause and effect and develop a hypothesis .

For instance, an organization may notice a sales increase. Determining the cause would help them reproduce these results. 

Upon review, the business realizes that the sales boost occurred right after an advertising campaign. The business can leverage this time-based data to determine whether the advertising campaign is the independent variable that caused a change in sales. 

Evaluation of confounding variables

In most cases, you need to pinpoint the variables that comprise a cause-and-effect relationship when using a causal research design. This uncovers a more accurate conclusion. 

Co-variations between a cause and effect must be accurate, and a third factor shouldn’t relate to cause and effect. 

Observing changes

Variation links between two variables must be clear. A quantitative change in effect must happen solely due to a quantitative change in the cause. 

You can test whether the independent variable changes the dependent variable to evaluate the validity of a cause-and-effect relationship. A steady change between the two variables must occur to back up your hypothesis of a genuine causal effect. 

• Why is causal research useful?

Causal research allows market researchers to predict hypothetical occurrences and outcomes while enhancing existing strategies. Organizations can use this concept to develop beneficial plans. 

Causal research is also useful as market researchers can immediately deduce the effect of the variables on each other under real-world conditions. 

Once researchers complete their first experiment, they can use their findings. Applying them to alternative scenarios or repeating the experiment to confirm its validity can produce further insights. 

Businesses widely use causal research to identify and comprehend the effect of strategic changes on their profits. 

• How does causal research compare and differ from other research types?

Other research types that identify relationships between variables include exploratory and descriptive research . 

Here’s how they compare and differ from causal research designs:

Exploratory research

An exploratory research design evaluates situations where a problem or opportunity's boundaries are unclear. You can use this research type to test various hypotheses and assumptions to establish facts and understand a situation more clearly.

You can also use exploratory research design to navigate a topic and discover the relevant variables. This research type allows flexibility and adaptability as the experiment progresses, particularly since no area is off-limits.

It’s worth noting that exploratory research is unstructured and typically involves collecting qualitative data . This provides the freedom to tweak and amend the research approach according to your ongoing thoughts and assessments. 

Unfortunately, this exposes the findings to the risk of bias and may limit the extent to which a researcher can explore a topic. 

This table compares the key characteristics of causal and exploratory research:

Descriptive research

This research design involves capturing and describing the traits of a population, situation, or phenomenon. Descriptive research focuses more on the " what " of the research subject and less on the " why ."

Since descriptive research typically happens in a real-world setting, variables can cross-contaminate others. This increases the challenge of isolating cause-and-effect relationships. 

You may require further research if you need more causal links. 

This table compares the key characteristics of causal and descriptive research.  

Causal research examines a research question’s variables and how they interact. It’s easier to pinpoint cause and effect since the experiment often happens in a controlled setting. 

Researchers can conduct causal research at any stage, but they typically use it once they know more about the topic.

In contrast, causal research tends to be more structured and can be combined with exploratory and descriptive research to help you attain your research goals. 

• How can you use causal research effectively?

Here are common ways that market researchers leverage causal research effectively:

Market and advertising research

Do you want to know if your new marketing campaign is affecting your organization positively? You can use causal research to determine the variables causing negative or positive impacts on your campaign. 

Improving customer experiences and loyalty levels

Consumers generally enjoy purchasing from brands aligned with their values. They’re more likely to purchase from such brands and positively represent them to others. 

You can use causal research to identify the variables contributing to increased or reduced customer acquisition and retention rates. 

Could the cause of increased customer retention rates be streamlined checkout? 

Perhaps you introduced a new solution geared towards directly solving their immediate problem. 

Whatever the reason, causal research can help you identify the cause-and-effect relationship. You can use this to enhance your customer experiences and loyalty levels.

Improving problematic employee turnover rates

Is your organization experiencing skyrocketing attrition rates? 

You can leverage the features and benefits of causal research to narrow down the possible explanations or variables with significant effects on employees quitting. 

This way, you can prioritize interventions, focusing on the highest priority causal influences, and begin to tackle high employee turnover rates. 

• Advantages of causal research

The main benefits of causal research include the following:

Effectively test new ideas

If causal research can pinpoint the precise outcome through combinations of different variables, researchers can test ideas in the same manner to form viable proof of concepts.

Achieve more objective results

Market researchers typically use random sampling techniques to choose experiment participants or subjects in causal research. This reduces the possibility of exterior, sample, or demography-based influences, generating more objective results. 

Improved business processes

Causal research helps businesses understand which variables positively impact target variables, such as customer loyalty or sales revenues. This helps them improve their processes, ROI, and customer and employee experiences.

Guarantee reliable and accurate results

Upon identifying the correct variables, researchers can replicate cause and effect effortlessly. This creates reliable data and results to draw insights from. 

Internal organization improvements

Businesses that conduct causal research can make informed decisions about improving their internal operations and enhancing employee experiences. 

• Disadvantages of causal research

Like any other research method, casual research has its set of drawbacks that include:

Extra research to ensure validity

Researchers can't simply rely on the outcomes of causal research since it isn't always accurate. There may be a need to conduct other research types alongside it to ensure accurate output.

Coincidence

Coincidence tends to be the most significant error in causal research. Researchers often misinterpret a coincidental link between a cause and effect as a direct causal link. 

Administration challenges

Causal research can be challenging to administer since it's impossible to control the impact of extraneous variables . 

Giving away your competitive advantage

If you intend to publish your research, it exposes your information to the competition. 

Competitors may use your research outcomes to identify your plans and strategies to enter the market before you. 

• Causal research examples

Multiple fields can use causal research, so it serves different purposes, such as. 

Customer loyalty research

Organizations and employees can use causal research to determine the best customer attraction and retention approaches. 

They monitor interactions between customers and employees to identify cause-and-effect patterns. That could be a product demonstration technique resulting in higher or lower sales from the same customers. 

Example: Business X introduces a new individual marketing strategy for a small customer group and notices a measurable increase in monthly subscriptions. 

Upon getting identical results from different groups, the business concludes that the individual marketing strategy resulted in the intended causal relationship.

Advertising research

Businesses can also use causal research to implement and assess advertising campaigns. 

Example: Business X notices a 7% increase in sales revenue a few months after a business introduces a new advertisement in a certain region. The business can run the same ad in random regions to compare sales data over the same period. 

This will help the company determine whether the ad caused the sales increase. If sales increase in these randomly selected regions, the business could conclude that advertising campaigns and sales share a cause-and-effect relationship. 

Educational research

Academics, teachers, and learners can use causal research to explore the impact of politics on learners and pinpoint learner behavior trends. 

Example: College X notices that more IT students drop out of their program in their second year, which is 8% higher than any other year. 

The college administration can interview a random group of IT students to identify factors leading to this situation, including personal factors and influences. 

With the help of in-depth statistical analysis, the institution's researchers can uncover the main factors causing dropout. They can create immediate solutions to address the problem.

Is a causal variable dependent or independent?

When two variables have a cause-and-effect relationship, the cause is often called the independent variable. As such, the effect variable is dependent, i.e., it depends on the independent causal variable. An independent variable is only causal under experimental conditions. 

What are the three criteria for causality?

The three conditions for causality are:

Temporality/temporal precedence: The cause must precede the effect.

Rationality: One event predicts the other with an explanation, and the effect must vary in proportion to changes in the cause.

Control for extraneous variables: The covariables must not result from other variables.  

Is causal research experimental?

Causal research is mostly explanatory. Causal studies focus on analyzing a situation to explore and explain the patterns of relationships between variables. 

Further, experiments are the primary data collection methods in studies with causal research design. However, as a research design, causal research isn't entirely experimental.

What is the difference between experimental and causal research design?

One of the main differences between causal and experimental research is that in causal research, the research subjects are already in groups since the event has already happened. 

On the other hand, researchers randomly choose subjects in experimental research before manipulating the variables.

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Causal Research: Definition, Design, Tips, Examples

Appinio Research · 21.02.2024 · 34min read

Ever wondered why certain events lead to specific outcomes? Understanding causality—the relationship between cause and effect—is crucial for unraveling the mysteries of the world around us. In this guide on causal research, we delve into the methods, techniques, and principles behind identifying and establishing cause-and-effect relationships between variables. Whether you're a seasoned researcher or new to the field, this guide will equip you with the knowledge and tools to conduct rigorous causal research and draw meaningful conclusions that can inform decision-making and drive positive change.

What is Causal Research?

Causal research is a methodological approach used in scientific inquiry to investigate cause-and-effect relationships between variables. Unlike correlational or descriptive research, which merely examine associations or describe phenomena, causal research aims to determine whether changes in one variable cause changes in another variable.

Importance of Causal Research

Understanding the importance of causal research is crucial for appreciating its role in advancing knowledge and informing decision-making across various fields. Here are key reasons why causal research is significant:

• Establishing Causality:  Causal research enables researchers to determine whether changes in one variable directly cause changes in another variable. This helps identify effective interventions, predict outcomes, and inform evidence-based practices.
• Guiding Policy and Practice:  By identifying causal relationships, causal research provides empirical evidence to support policy decisions, program interventions, and business strategies. Decision-makers can use causal findings to allocate resources effectively and address societal challenges.
• Informing Predictive Modeling :  Causal research contributes to the development of predictive models by elucidating causal mechanisms underlying observed phenomena. Predictive models based on causal relationships can accurately forecast future outcomes and trends.
• Advancing Scientific Knowledge:  Causal research contributes to the cumulative body of scientific knowledge by testing hypotheses, refining theories, and uncovering underlying mechanisms of phenomena. It fosters a deeper understanding of complex systems and phenomena.
• Mitigating Confounding Factors:  Understanding causal relationships allows researchers to control for confounding variables and reduce bias in their studies. By isolating the effects of specific variables, researchers can draw more valid and reliable conclusions.

Causal Research Distinction from Other Research

Understanding the distinctions between causal research and other types of research methodologies is essential for researchers to choose the most appropriate approach for their study objectives. Let's explore the differences and similarities between causal research and descriptive, exploratory, and correlational research methodologies .

Descriptive vs. Causal Research

Descriptive research  focuses on describing characteristics, behaviors, or phenomena without manipulating variables or establishing causal relationships. It provides a snapshot of the current state of affairs but does not attempt to explain why certain phenomena occur.

Causal research , on the other hand, seeks to identify cause-and-effect relationships between variables by systematically manipulating independent variables and observing their effects on dependent variables. Unlike descriptive research, causal research aims to determine whether changes in one variable directly cause changes in another variable.

Similarities:

• Both descriptive and causal research involve empirical observation and data collection.
• Both types of research contribute to the scientific understanding of phenomena, albeit through different approaches.

Differences:

• Descriptive research focuses on describing phenomena, while causal research aims to explain why phenomena occur by identifying causal relationships.
• Descriptive research typically uses observational methods, while causal research often involves experimental designs or causal inference techniques to establish causality.

Exploratory vs. Causal Research

Exploratory research  aims to explore new topics, generate hypotheses, or gain initial insights into phenomena. It is often conducted when little is known about a subject and seeks to generate ideas for further investigation.

Causal research , on the other hand, is concerned with testing hypotheses and establishing cause-and-effect relationships between variables. It builds on existing knowledge and seeks to confirm or refute causal hypotheses through systematic investigation.

• Both exploratory and causal research contribute to the generation of knowledge and theory development.
• Both types of research involve systematic inquiry and data analysis to answer research questions.
• Exploratory research focuses on generating hypotheses and exploring new areas of inquiry, while causal research aims to test hypotheses and establish causal relationships.
• Exploratory research is more flexible and open-ended, while causal research follows a more structured and hypothesis-driven approach.

Correlational vs. Causal Research

Correlational research  examines the relationship between variables without implying causation. It identifies patterns of association or co-occurrence between variables but does not establish the direction or causality of the relationship.

Causal research , on the other hand, seeks to establish cause-and-effect relationships between variables by systematically manipulating independent variables and observing their effects on dependent variables. It goes beyond mere association to determine whether changes in one variable directly cause changes in another variable.

• Both correlational and causal research involve analyzing relationships between variables.
• Both types of research contribute to understanding the nature of associations between variables.
• Correlational research focuses on identifying patterns of association, while causal research aims to establish causal relationships.
• Correlational research does not manipulate variables, while causal research involves systematically manipulating independent variables to observe their effects on dependent variables.

How to Formulate Causal Research Hypotheses?

Crafting research questions and hypotheses is the foundational step in any research endeavor. Defining your variables clearly and articulating the causal relationship you aim to investigate is essential. Let's explore this process further.

1. Identify Variables

Identifying variables involves recognizing the key factors you will manipulate or measure in your study. These variables can be classified into independent, dependent, and confounding variables.

• Independent Variable (IV):  This is the variable you manipulate or control in your study. It is the presumed cause that you want to test.
• Dependent Variable (DV):  The dependent variable is the outcome or response you measure. It is affected by changes in the independent variable.
• Confounding Variables:  These are extraneous factors that may influence the relationship between the independent and dependent variables, leading to spurious correlations or erroneous causal inferences. Identifying and controlling for confounding variables is crucial for establishing valid causal relationships.

2. Establish Causality

Establishing causality requires meeting specific criteria outlined by scientific methodology. While correlation between variables may suggest a relationship, it does not imply causation. To establish causality, researchers must demonstrate the following:

• Temporal Precedence:  The cause must precede the effect in time. In other words, changes in the independent variable must occur before changes in the dependent variable.
• Covariation of Cause and Effect:  Changes in the independent variable should be accompanied by corresponding changes in the dependent variable. This demonstrates a consistent pattern of association between the two variables.
• Elimination of Alternative Explanations:  Researchers must rule out other possible explanations for the observed relationship between variables. This involves controlling for confounding variables and conducting rigorous experimental designs to isolate the effects of the independent variable.

3. Write Clear and Testable Hypotheses

Hypotheses serve as tentative explanations for the relationship between variables and provide a framework for empirical testing. A well-formulated hypothesis should be:

• Specific:  Clearly state the expected relationship between the independent and dependent variables.
• Testable:  The hypothesis should be capable of being empirically tested through observation or experimentation.
• Falsifiable:  There should be a possibility of proving the hypothesis false through empirical evidence.

For example, a hypothesis in a study examining the effect of exercise on weight loss could be: "Increasing levels of physical activity (IV) will lead to greater weight loss (DV) among participants (compared to those with lower levels of physical activity)."

By formulating clear hypotheses and operationalizing variables, researchers can systematically investigate causal relationships and contribute to the advancement of scientific knowledge.

Causal Research Design

Designing your research study involves making critical decisions about how you will collect and analyze data to investigate causal relationships.

Experimental vs. Observational Designs

One of the first decisions you'll make when designing a study is whether to employ an experimental or observational design. Each approach has its strengths and limitations, and the choice depends on factors such as the research question, feasibility , and ethical considerations.

• Experimental Design: In experimental designs, researchers manipulate the independent variable and observe its effects on the dependent variable while controlling for confounding variables. Random assignment to experimental conditions allows for causal inferences to be drawn. Example: A study testing the effectiveness of a new teaching method on student performance by randomly assigning students to either the experimental group (receiving the new teaching method) or the control group (receiving the traditional method).
• Observational Design: Observational designs involve observing and measuring variables without intervention. Researchers may still examine relationships between variables but cannot establish causality as definitively as in experimental designs. Example: A study observing the association between socioeconomic status and health outcomes by collecting data on income, education level, and health indicators from a sample of participants.

Control and Randomization

Control and randomization are crucial aspects of experimental design that help ensure the validity of causal inferences.

• Control: Controlling for extraneous variables involves holding constant factors that could influence the dependent variable, except for the independent variable under investigation. This helps isolate the effects of the independent variable. Example: In a medication trial, controlling for factors such as age, gender, and pre-existing health conditions ensures that any observed differences in outcomes can be attributed to the medication rather than other variables.
• Randomization: Random assignment of participants to experimental conditions helps distribute potential confounders evenly across groups, reducing the likelihood of systematic biases and allowing for causal conclusions. Example: Randomly assigning patients to treatment and control groups in a clinical trial ensures that both groups are comparable in terms of baseline characteristics, minimizing the influence of extraneous variables on treatment outcomes.

Internal and External Validity

Two key concepts in research design are internal validity and external validity, which relate to the credibility and generalizability of study findings, respectively.

• Internal Validity: Internal validity refers to the extent to which the observed effects can be attributed to the manipulation of the independent variable rather than confounding factors. Experimental designs typically have higher internal validity due to their control over extraneous variables. Example: A study examining the impact of a training program on employee productivity would have high internal validity if it could confidently attribute changes in productivity to the training intervention.
• External Validity: External validity concerns the extent to which study findings can be generalized to other populations, settings, or contexts. While experimental designs prioritize internal validity, they may sacrifice external validity by using highly controlled conditions that do not reflect real-world scenarios. Example: Findings from a laboratory study on memory retention may have limited external validity if the experimental tasks and conditions differ significantly from real-life learning environments.

Types of Experimental Designs

Several types of experimental designs are commonly used in causal research, each with its own strengths and applications.

• Randomized Control Trials (RCTs): RCTs are considered the gold standard for assessing causality in research. Participants are randomly assigned to experimental and control groups, allowing researchers to make causal inferences. Example: A pharmaceutical company testing a new drug's efficacy would use an RCT to compare outcomes between participants receiving the drug and those receiving a placebo.
• Quasi-Experimental Designs: Quasi-experimental designs lack random assignment but still attempt to establish causality by controlling for confounding variables through design or statistical analysis . Example: A study evaluating the effectiveness of a smoking cessation program might compare outcomes between participants who voluntarily enroll in the program and a matched control group of non-enrollees.

By carefully selecting an appropriate research design and addressing considerations such as control, randomization, and validity, researchers can conduct studies that yield credible evidence of causal relationships and contribute valuable insights to their field of inquiry.

Causal Research Data Collection

Collecting data is a critical step in any research study, and the quality of the data directly impacts the validity and reliability of your findings.

Choosing Measurement Instruments

Selecting appropriate measurement instruments is essential for accurately capturing the variables of interest in your study. The choice of measurement instrument depends on factors such as the nature of the variables, the target population , and the research objectives.

• Surveys :  Surveys are commonly used to collect self-reported data on attitudes, opinions, behaviors, and demographics . They can be administered through various methods, including paper-and-pencil surveys, online surveys, and telephone interviews.
• Observations:  Observational methods involve systematically recording behaviors, events, or phenomena as they occur in natural settings. Observations can be structured (following a predetermined checklist) or unstructured (allowing for flexible data collection).
• Psychological Tests:  Psychological tests are standardized instruments designed to measure specific psychological constructs, such as intelligence, personality traits, or emotional functioning. These tests often have established reliability and validity.
• Physiological Measures:  Physiological measures, such as heart rate, blood pressure, or brain activity, provide objective data on bodily processes. They are commonly used in health-related research but require specialized equipment and expertise.
• Existing Databases:  Researchers may also utilize existing datasets, such as government surveys, public health records, or organizational databases, to answer research questions. Secondary data analysis can be cost-effective and time-saving but may be limited by the availability and quality of data.

Ensuring accurate data collection is the cornerstone of any successful research endeavor. With the right tools in place, you can unlock invaluable insights to drive your causal research forward. From surveys to tests, each instrument offers a unique lens through which to explore your variables of interest.

At Appinio , we understand the importance of robust data collection methods in informing impactful decisions. Let us empower your research journey with our intuitive platform, where you can effortlessly gather real-time consumer insights to fuel your next breakthrough.   Ready to take your research to the next level? Book a demo today and see how Appinio can revolutionize your approach to data collection!

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Sampling Techniques

Sampling involves selecting a subset of individuals or units from a larger population to participate in the study. The goal of sampling is to obtain a representative sample that accurately reflects the characteristics of the population of interest.

• Probability Sampling:  Probability sampling methods involve randomly selecting participants from the population, ensuring that each member of the population has an equal chance of being included in the sample. Common probability sampling techniques include simple random sampling , stratified sampling, and cluster sampling .
• Non-Probability Sampling:  Non-probability sampling methods do not involve random selection and may introduce biases into the sample. Examples of non-probability sampling techniques include convenience sampling, purposive sampling, and snowball sampling.

The choice of sampling technique depends on factors such as the research objectives, population characteristics, resources available, and practical constraints. Researchers should strive to minimize sampling bias and maximize the representativeness of the sample to enhance the generalizability of their findings.

Ethical Considerations

Ethical considerations are paramount in research and involve ensuring the rights, dignity, and well-being of research participants. Researchers must adhere to ethical principles and guidelines established by professional associations and institutional review boards (IRBs).

• Informed Consent:  Participants should be fully informed about the nature and purpose of the study, potential risks and benefits, their rights as participants, and any confidentiality measures in place. Informed consent should be obtained voluntarily and without coercion.
• Privacy and Confidentiality:  Researchers should take steps to protect the privacy and confidentiality of participants' personal information. This may involve anonymizing data, securing data storage, and limiting access to identifiable information.
• Minimizing Harm:  Researchers should mitigate any potential physical, psychological, or social harm to participants. This may involve conducting risk assessments, providing appropriate support services, and debriefing participants after the study.
• Respect for Participants:  Researchers should respect participants' autonomy, diversity, and cultural values. They should seek to foster a trusting and respectful relationship with participants throughout the research process.
• Publication and Dissemination:  Researchers have a responsibility to accurately report their findings and acknowledge contributions from participants and collaborators. They should adhere to principles of academic integrity and transparency in disseminating research results.

By addressing ethical considerations in research design and conduct, researchers can uphold the integrity of their work, maintain trust with participants and the broader community, and contribute to the responsible advancement of knowledge in their field.

Causal Research Data Analysis

Once data is collected, it must be analyzed to draw meaningful conclusions and assess causal relationships.

Causal Inference Methods

Causal inference methods are statistical techniques used to identify and quantify causal relationships between variables in observational data. While experimental designs provide the most robust evidence for causality, observational studies often require more sophisticated methods to account for confounding factors.

• Difference-in-Differences (DiD):  DiD compares changes in outcomes before and after an intervention between a treatment group and a control group, controlling for pre-existing trends. It estimates the average treatment effect by differencing the changes in outcomes between the two groups over time.
• Instrumental Variables (IV):  IV analysis relies on instrumental variables—variables that affect the treatment variable but not the outcome—to estimate causal effects in the presence of endogeneity. IVs should be correlated with the treatment but uncorrelated with the error term in the outcome equation.
• Regression Discontinuity (RD):  RD designs exploit naturally occurring thresholds or cutoff points to estimate causal effects near the threshold. Participants just above and below the threshold are compared, assuming that they are similar except for their proximity to the threshold.
• Propensity Score Matching (PSM):  PSM matches individuals or units based on their propensity scores—the likelihood of receiving the treatment—creating comparable groups with similar observed characteristics. Matching reduces selection bias and allows for causal inference in observational studies.

Assessing Causality Strength

Assessing the strength of causality involves determining the magnitude and direction of causal effects between variables. While statistical significance indicates whether an observed relationship is unlikely to occur by chance, it does not necessarily imply a strong or meaningful effect.

• Effect Size:  Effect size measures the magnitude of the relationship between variables, providing information about the practical significance of the results. Standard effect size measures include Cohen's d for mean differences and odds ratios for categorical outcomes.
• Confidence Intervals:  Confidence intervals provide a range of values within which the actual effect size is likely to lie with a certain degree of certainty. Narrow confidence intervals indicate greater precision in estimating the true effect size.
• Practical Significance:  Practical significance considers whether the observed effect is meaningful or relevant in real-world terms. Researchers should interpret results in the context of their field and the implications for stakeholders.

Handling Confounding Variables

Confounding variables are extraneous factors that may distort the observed relationship between the independent and dependent variables, leading to spurious or biased conclusions. Addressing confounding variables is essential for establishing valid causal inferences.

• Statistical Control:  Statistical control involves including confounding variables as covariates in regression models to partially out their effects on the outcome variable. Controlling for confounders reduces bias and strengthens the validity of causal inferences.
• Matching:  Matching participants or units based on observed characteristics helps create comparable groups with similar distributions of confounding variables. Matching reduces selection bias and mimics the randomization process in experimental designs.
• Sensitivity Analysis:  Sensitivity analysis assesses the robustness of study findings to changes in model specifications or assumptions. By varying analytical choices and examining their impact on results, researchers can identify potential sources of bias and evaluate the stability of causal estimates.
• Subgroup Analysis:  Subgroup analysis explores whether the relationship between variables differs across subgroups defined by specific characteristics. Identifying effect modifiers helps understand the conditions under which causal effects may vary.

By employing rigorous causal inference methods, assessing the strength of causality, and addressing confounding variables, researchers can confidently draw valid conclusions about causal relationships in their studies, advancing scientific knowledge and informing evidence-based decision-making.

Causal Research Examples

Examples play a crucial role in understanding the application of causal research methods and their impact across various domains. Let's explore some detailed examples to illustrate how causal research is conducted and its real-world implications:

Example 1: Software as a Service (SaaS) User Retention Analysis

Suppose a SaaS company wants to understand the factors influencing user retention and engagement with their platform. The company conducts a longitudinal observational study, collecting data on user interactions, feature usage, and demographic information over several months.

• Design:  The company employs an observational cohort study design, tracking cohorts of users over time to observe changes in retention and engagement metrics. They use analytics tools to collect data on user behavior , such as logins, feature usage, session duration, and customer support interactions.
• Data Collection:  Data is collected from the company's platform logs, customer relationship management (CRM) system, and user surveys. Key metrics include user churn rates, active user counts, feature adoption rates, and Net Promoter Scores ( NPS ).
• Analysis:  Using statistical techniques like survival analysis and regression modeling, the company identifies factors associated with user retention, such as feature usage patterns, onboarding experiences, customer support interactions, and subscription plan types.
• Findings: The analysis reveals that users who engage with specific features early in their lifecycle have higher retention rates, while those who encounter usability issues or lack personalized onboarding experiences are more likely to churn. The company uses these insights to optimize product features, improve onboarding processes, and enhance customer support strategies to increase user retention and satisfaction.

Example 2: Business Impact of Digital Marketing Campaign

Consider a technology startup launching a digital marketing campaign to promote its new product offering. The company conducts an experimental study to evaluate the effectiveness of different marketing channels in driving website traffic, lead generation, and sales conversions.

• Design:  The company implements an A/B testing design, randomly assigning website visitors to different marketing treatment conditions, such as Google Ads, social media ads, email campaigns, or content marketing efforts. They track user interactions and conversion events using web analytics tools and marketing automation platforms.
• Data Collection:  Data is collected on website traffic, click-through rates, conversion rates, lead generation, and sales revenue. The company also gathers demographic information and user feedback through surveys and customer interviews to understand the impact of marketing messages and campaign creatives .
• Analysis:  Utilizing statistical methods like hypothesis testing and multivariate analysis, the company compares key performance metrics across different marketing channels to assess their effectiveness in driving user engagement and conversion outcomes. They calculate return on investment (ROI) metrics to evaluate the cost-effectiveness of each marketing channel.
• Findings:  The analysis reveals that social media ads outperform other marketing channels in generating website traffic and lead conversions, while email campaigns are more effective in nurturing leads and driving sales conversions. Armed with these insights, the company allocates marketing budgets strategically, focusing on channels that yield the highest ROI and adjusting messaging and targeting strategies to optimize campaign performance.

These examples demonstrate the diverse applications of causal research methods in addressing important questions, informing policy decisions, and improving outcomes in various fields. By carefully designing studies, collecting relevant data, employing appropriate analysis techniques, and interpreting findings rigorously, researchers can generate valuable insights into causal relationships and contribute to positive social change.

How to Interpret Causal Research Results?

Interpreting and reporting research findings is a crucial step in the scientific process, ensuring that results are accurately communicated and understood by stakeholders.

Interpreting Statistical Significance

Statistical significance indicates whether the observed results are unlikely to occur by chance alone, but it does not necessarily imply practical or substantive importance. Interpreting statistical significance involves understanding the meaning of p-values and confidence intervals and considering their implications for the research findings.

• P-values:  A p-value represents the probability of obtaining the observed results (or more extreme results) if the null hypothesis is true. A p-value below a predetermined threshold (typically 0.05) suggests that the observed results are statistically significant, indicating that the null hypothesis can be rejected in favor of the alternative hypothesis.
• Confidence Intervals:  Confidence intervals provide a range of values within which the true population parameter is likely to lie with a certain degree of confidence (e.g., 95%). If the confidence interval does not include the null value, it suggests that the observed effect is statistically significant at the specified confidence level.

Interpreting statistical significance requires considering factors such as sample size, effect size, and the practical relevance of the results rather than relying solely on p-values to draw conclusions.

Discussing Practical Significance

While statistical significance indicates whether an effect exists, practical significance evaluates the magnitude and meaningfulness of the effect in real-world terms. Discussing practical significance involves considering the relevance of the results to stakeholders and assessing their impact on decision-making and practice.

• Effect Size:  Effect size measures the magnitude of the observed effect, providing information about its practical importance. Researchers should interpret effect sizes in the context of their field and the scale of measurement (e.g., small, medium, or large effect sizes).
• Contextual Relevance:  Consider the implications of the results for stakeholders, policymakers, and practitioners. Are the observed effects meaningful in the context of existing knowledge, theory, or practical applications? How do the findings contribute to addressing real-world problems or informing decision-making?

Discussing practical significance helps contextualize research findings and guide their interpretation and application in practice, beyond statistical significance alone.

Addressing Limitations and Assumptions

No study is without limitations, and researchers should transparently acknowledge and address potential biases, constraints, and uncertainties in their research design and findings.

• Methodological Limitations:  Identify any limitations in study design, data collection, or analysis that may affect the validity or generalizability of the results. For example, sampling biases , measurement errors, or confounding variables.
• Assumptions:  Discuss any assumptions made in the research process and their implications for the interpretation of results. Assumptions may relate to statistical models, causal inference methods, or theoretical frameworks underlying the study.
• Alternative Explanations:  Consider alternative explanations for the observed results and discuss their potential impact on the validity of causal inferences. How robust are the findings to different interpretations or competing hypotheses?

Addressing limitations and assumptions demonstrates transparency and rigor in the research process, allowing readers to critically evaluate the validity and reliability of the findings.

Communicating Findings Clearly

Effectively communicating research findings is essential for disseminating knowledge, informing decision-making, and fostering collaboration and dialogue within the scientific community.

• Clarity and Accessibility:  Present findings in a clear, concise, and accessible manner, using plain language and avoiding jargon or technical terminology. Organize information logically and use visual aids (e.g., tables, charts, graphs) to enhance understanding.
• Contextualization:  Provide context for the results by summarizing key findings, highlighting their significance, and relating them to existing literature or theoretical frameworks. Discuss the implications of the findings for theory, practice, and future research directions.
• Transparency:  Be transparent about the research process, including data collection procedures, analytical methods, and any limitations or uncertainties associated with the findings. Clearly state any conflicts of interest or funding sources that may influence interpretation.

By communicating findings clearly and transparently, researchers can facilitate knowledge exchange, foster trust and credibility, and contribute to evidence-based decision-making.

Causal Research Tips

When conducting causal research, it's essential to approach your study with careful planning, attention to detail, and methodological rigor. Here are some tips to help you navigate the complexities of causal research effectively:

• Define Clear Research Questions:  Start by clearly defining your research questions and hypotheses. Articulate the causal relationship you aim to investigate and identify the variables involved.
• Consider Alternative Explanations:  Be mindful of potential confounding variables and alternative explanations for the observed relationships. Take steps to control for confounders and address alternative hypotheses in your analysis.
• Prioritize Internal Validity:  While external validity is important for generalizability, prioritize internal validity in your study design to ensure that observed effects can be attributed to the manipulation of the independent variable.
• Use Randomization When Possible:  If feasible, employ randomization in experimental designs to distribute potential confounders evenly across experimental conditions and enhance the validity of causal inferences.
• Be Transparent About Methods:  Provide detailed descriptions of your research methods, including data collection procedures, analytical techniques, and any assumptions or limitations associated with your study.
• Utilize Multiple Methods:  Consider using a combination of experimental and observational methods to triangulate findings and strengthen the validity of causal inferences.
• Be Mindful of Sample Size:  Ensure that your sample size is adequate to detect meaningful effects and minimize the risk of Type I and Type II errors. Conduct power analyses to determine the sample size needed to achieve sufficient statistical power.
• Validate Measurement Instruments:  Validate your measurement instruments to ensure that they are reliable and valid for assessing the variables of interest in your study. Pilot test your instruments if necessary.
• Seek Feedback from Peers:  Collaborate with colleagues or seek feedback from peer reviewers to solicit constructive criticism and improve the quality of your research design and analysis.

Conclusion for Causal Research

Mastering causal research empowers researchers to unlock the secrets of cause and effect, shedding light on the intricate relationships between variables in diverse fields. By employing rigorous methods such as experimental designs, causal inference techniques, and careful data analysis, you can uncover causal mechanisms, predict outcomes, and inform evidence-based practices. Through the lens of causal research, complex phenomena become more understandable, and interventions become more effective in addressing societal challenges and driving progress. In a world where understanding the reasons behind events is paramount, causal research serves as a beacon of clarity and insight. Armed with the knowledge and techniques outlined in this guide, you can navigate the complexities of causality with confidence, advancing scientific knowledge, guiding policy decisions, and ultimately making meaningful contributions to our understanding of the world.

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What is Convenience Sampling? Definition, Method, Examples

Introduction to the foundations of causal discovery

• Regular Paper
• Published: 28 December 2016
• Volume 3 , pages 81–91, ( 2017 )

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• Frederick Eberhardt 1  

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This article presents an overview of several known approaches to causal discovery. It is organized by relating the different fundamental assumptions that the methods depend on. The goal is to indicate that for a large variety of different settings the assumptions necessary and sufficient for causal discovery are now well understood.

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a and c are two possible causal models that would explain an observed dependence between wine drinking and heart disease. But only in the case of ( a ) would that dependence persist if one were to intervene on wine drinking in an experiment ( b ). In the intervention would destroy the dependence and make wine drinking independent of heart disease ( d )

1 Introduction

Like many scientific concepts, causal relations are not features that can be directly read off from the data but have to be inferred. The field of causal discovery is concerned with this inference and the assumptions that support it. We might have measures of different quantities obtained from, say, a cross-sectional study, on the amount of wine consumption (for some unit of time) and the prevalence of cardiovascular disease, and be interested in whether wine consumption is a cause of cardiovascular disease (positivey or negatively), and not just whether it is correlated with it. That is, we would like to know whether the observed dependence between wine consumption and cardiovascular disease (suppose there is one) persists even if we change, say, in an experiment, the amount of wine that is consumed (see Fig.  1 ). The observed dependence between wine consumption and cardiovascular disease may, after all, be due to a common cause, such as socio-economic-status (SES), where those people with a higher SES consume more wine and are able to afford better health care, whereas those with a lower SES do not consume as much wine and have poorer healthcare Footnote 1 . The example illustrates the common mantra that “correlation does not imply causation” and suggests that causal relations can be identified in an experimental setting, such as a randomized controlled trial where each individual in the experiment is randomly assigned to either the treatment or control group (in this case, to different levels of wine consumption) and the effect on cardiovascular disease is measured. The randomized assignment makes the wine consumption independent of its normal causes (at least in the large sample limit) and thereby destroys the “confounding” effect of SES. Naturally, there are many concerns about such an analysis, starting from the ethical concerns of such a study, the compliance with treatment, the precise treatment levels, the representativeness of the experimental population with respect to the larger population, etc., but the general methodological reason, explicitly emphasized in Fisher’s [ 6 ] well-known work on experimental design, of why randomized controlled trials are useful for causal discovery becomes evident: randomization breaks confounding, whether due to an observed or unobserved common cause.

Causal relations are of interest because only an understanding of the underlying causal relations can support predictions about how a system will behave when it is subject to intervention. If moderate wine consumption, in fact, causes the reduction in the risk of cardiovascular disease (this article takes no stand on the truth of this claim), then a health policy that suggests moderate wine consumption can be expected to be effective in reducing cardiovascular disease (with due note to all the other concerns about implementation). But if the observed dependence is only due to some common cause, such as SES, then a policy that changes wine consumption independently of SES would have no effect on cardiovascular disease.

A purely probabilistic representation of these relations is ambiguous with respect to the underlying causal relations: That is, if we let wine consumption be X and cardiovascular disease be Y , then, without further specification, P ( Y | X ), the conditional probability of cardiovascular disease given a particular level of wine consumption, is ambiguous with regard to whether it describes the relation in an experimental setting in which the wine consumption was determined by randomization or whether it describes observational relations, such as in the initial example of a cross-sectional study. Pearl [ 31 ] introduced the do (.)-operator as a notation to distinguish the two cases. Thus, P ( Y | X ) is the observational conditional probability describing how the probability of Y would change if one observed X (e.g., in a cross-sectional study) while P ( Y | do ( X )) is the interventional conditional probability, describing the probability of Y when X has been set experimentally. Of course, not all data can be classified cleanly as observational vs. interventional, since there might well be experiments that do not fully determine the value of the intervened variable. But for the sake of this article, the distinction will suffice (see [ 28 ] and [ 5 ] for further discussion).

In light of the general underdetermination of causal relations given any probability distribution, it is useful to represent the causal structure explicitly in terms of a directed graph. Unlike other graphical models with directed or undirected edges, which merely represent an independence structure, causal graphical models support a very a strong interpretation: For a given set of variables \(\mathbf{{V}}= \{X_1,\ldots , X_n\}\) , a causal graph \(G = \{\mathbf{{V}}, \mathbf{E}\}\) represents the causal relations over the set of variables \(\mathbf{{V}}\) , in the sense that for any directed edge \(e= X_i \rightarrow X_j\) in \(\mathbf{E}\) , \(X_i\) is a direct cause of \(X_j\) relative to variables in \(\mathbf{{V}}\) . So the claim of an edge in G is that even if you randomize all other variables in \(\mathbf{{V}}\setminus \{X_i,X_j\}\) , thereby breaking any causal connection between \(X_i\) and \(X_j\) through these other variables, \(X_i\) still has a causal effect on \(X_j\) . Moreover, the causal graph characterizes the effect of an intervention on \(X_i\) on the remaining variables precisely in terms of the subgraph that results when all directed edges into \(X_i\) are removed from G . Thus, a causal graph not only makes claims about the causal pathways active in an observational setting, but also indicates which causal pathways are active in any experiment on a set of variables in \(\mathbf{{V}}\) . Naturally, a direct cause between \(X_i\) and \(X_j\) may no longer be direct once additional variables are introduced—hence the relativity to the set \(\mathbf{{V}}\) .

We use intuitive (and standard) terminology to refer to particular features of the graph: A path between two variables X and Y in G is defined as a non-repeating sequence of edges (oriented in either direction) in G where any two adjacent edges in the sequence share a common endpoint and the first edge “starts” with X and the last “ends” with Y . A directed path is a path whose edges all point in the same direction. A descendent of a vertex Z is a vertex \(W \in \mathbf{{V}}\) , such that there is a directed path \(Z \rightarrow \cdots \rightarrow W\) in the graph G . Correspondingly, Z is ancestor of X . The parents of a vertex X are the vertices in \(\mathbf{{V}}\) with a directed edge oriented into X , similarly for the children of a vertex. Footnote 2 A collider on a path p is a vertex on p whose adjacent edges both point into the vertex, i.e., \(\rightarrow Z\leftarrow \) . A non-collider on p is a vertex on p that is not a collider, i.e., it is a mediator ( \(\rightarrow Z \rightarrow \) ) or a common cause ( \(\leftarrow Z \rightarrow \) ). Note that a vertex can take on different roles with respect to different paths.

2 Basic assumptions of causal discovery

Given the representation of causal relations over a set of variables in terms of causal graphs, causal discovery can be characterized as the problem of identifying as much as possible about the causal relations of interest (ideally the whole graph G ) given a dataset of measurements over the variables \(\mathbf{{V}}\) . To separate the causal part from the statistical part of the inference it is—at least for an introduction—useful to think of causal discovery as the inference task from the joint distribution \(P(\mathbf{{V}})\) to the graph G , leaving the task of estimating \(P(\mathbf{{V}})\) from the finite data to the statistician. Footnote 3 In principle, there is no a priori reason for the joint distribution \(P(\mathbf{{V}})\) to constrain the possible true generating causal structures at all. We noted earlier that correlation does not imply causation (and similarly, the converse is not true either, though that may not be as obvious initially). Yet, we do take both dependencies and independencies as indicators of causal relations (or the lack thereof). For example, it seemed perfectly reasonable above to claim that if a dependence between X and Y was detected in a randomized controlled trial where X was subject to intervention, then X is a cause of Y (again modulo the many other assumptions about successful experiment implementation). Similarly, in the observational case, the dependence between X and Y , if it was not a result of a direct cause, was explained by a common cause. Consequently, there seem to be principles we use—more or less explicitly—that connect probabilistic relations to causal relations.

Two such principles that have received wide application in the methods of causal discovery are the causal Markov and the causal faithfulness conditions. The high-level idea is that the causal Markov and faithfulness conditions together imply a correspondence between the (conditional) independences in the probability distribution and the causal connectivity relations within the graph G . Causal connectivity in a graph is defined in terms of d-separation and d-connection [ 30 ]: A path p between X and Y d-connects X and Y given a conditioning set \(\mathbf{C}\subseteq \mathbf{{V}}\setminus \{X, Y\}\) if and only if (i) all colliders on p are in \(\mathbf{C}\) or have a descendent in \(\mathbf{C}\) and (ii) no non-colliders of p are in \(\mathbf{C}\) . X and Y are d-separated if and only if there are no d-connecting paths between them. D-separation is often denoted by the single turnstile ‘ \(\bot \) ’.

The causal Markov and the causal faithfulness assumptions (defined and discussed below) together ensure that (conditional) d-separation corresponds to (conditional) probabilistic independence, i.e.,

For causal discovery, this type of correspondence is enormously useful as it allows inferences from the (conditional) independence relations testable in data to the underlying causal structure. It can now be seen in what sense the claim that “correlation does not imply causation” still holds true, while a nonzero correlation can still provide an indication about existing causal relations: In particular, for two variables, a nonzero correlation would imply that the variables are d-connected given the empty set, i.e., that one causes the other or vice versa, or that there is a third variable that causes both. So while no specific causal relation can be determined, a subset of possible causal relations—an equivalence class of causal structures—can be identified. The correspondence also implies that two independent variables are causally disconnected (d-separated). So in the case of a linear Gaussian model, where no correlation implies independence, it follows that no correlation implies no causation.

Of course, (in)dependence features are only one set of features that a distribution \(P(\mathbf{{V}})\) may exhibit, and to the extent that one is able to characterize other principles that connect other features of the distribution to the underlying causal structure, they can also be exploited for causal discovery—as we shall see below. Causal Markov and causal faithfulness only provide one set of what one might call “bridge principles”, and they underlie many methods of so-called “constraint-based causal discovery”.

The Markov equivalence classes for all directed acyclic graphs over three variables without latent variables: Graphs in the same equivalence class share the same (conditional) independence structure

The situation is quite different with regard to causal faithfulness. It states the converse of the Markov condition, i.e., if a variable X is independent of Y given a conditioning set \(\mathbf{C}\) in the probability distribution \(P(\mathbf{{V}})\) , then X is d-separated from Y given \(\mathbf{C}\) in the graph G . Faithfulness can be thought of as a simplicity assumption and it is relatively easy to find violations of it—there only have to be causal connections that do not exhibit a dependence. For example, if two causal pathways cancel out each other’s effects exactly, then the causally connected variables will remain independent. A practical example is a back-up generator: Normally the machine is powered by electricity from the grid, but when the grid fails, a back-up generator kicks in to supply the energy, thereby making the operation of the machine independent of the grid, even though of course the grid normally causes the machine to work or when it fails it causes the generator to switch on, which causes the machine to work. Footnote 4 While such failures of faithfulness require an exact cancelation of the causal pathways, with finite data two variables may often appear independent despite the fact that they are (weakly) causally connected (see [ 47 ]).

To keep the present introduction to causal discovery simple initially, we can add additional assumptions about the underlying causal structure. Two commonly used assumptions are that the causal structure is assumed to be acyclic , i.e., that there is no directed path from a vertex back to itself in G , and causal sufficiency , i.e., that there are no unmeasured common causes of any pair of variables in \(\mathbf{{V}}\) . Both of these assumptions are obviously not true in many domains (e.g., biology, social sciences, etc.) and below we will see how methods have been developed that do not depend on them. For now, they help to keep the causal discovery task more tractable and easy to illustrate. Footnote 5

With these conditions in hand (Markov, faithfulness, acyclicity and causal sufficiency), we can now ask what one can learn about the underlying causal relations given the (estimated) joint distribution \(P(\mathbf{{V}})\) over a set of variables \(\mathbf{{V}}\) . Can we learn anything about the causal relation at all without performing experiments or having information about the time order of variables?

In fact, substantial information can be learned about the underlying causal structure from an observational probability distribution \(P(\mathbf{{V}})\) given these assumptions alone. In 1990, Verma and Pearl [ 32 ] and Frydenberg [ 7 ] independently showed that any two acyclic causal structures (without unmeasured variables) that are Markov and faithful to the same distribution \(P(\mathbf{{V}})\) share the same adjacencies (the same undirected graphical skeleton) and the same unshielded colliders. An unshielded collider is a collider whose two parents are not adjacent in G . Thus, Markov and faithfulness imply an equivalence structure over directed acyclic graphs, where graphs that are in the same equivalence class have the same (conditional) independence structure, the same adjacencies and the same unshielded colliders. For three variables, the Markov equivalence classes are shown in Fig.  2 . Note that the graph \(X\rightarrow Z\leftarrow Y\) is in its own equivalence class. That means that independence constraints alone are sufficient to uniquely determine the true causal structure G if it is of the form \(X\rightarrow Z\leftarrow Y\) (given the conditions stated). This is rather significant, since it implies that sometimes no time order information or experiment is necessary to uniquely determine the causal structure over a set of variables. More generally, knowing the Markov equivalence class of the true causal structure substantively reduces the underdetermination. In general, no closed form is known for how many equivalence classes there are or how many graphs there are per equivalence class, but large scale simulations have been run [ 9 , 11 ]. It is worth noting that for any number of variables N , there will always be several singleton equivalence classes (e.g., the empty graph, or those containing only unshielded colliders), but that there will also always be at least one equivalence class that contains N ! graphs, namely the class containing all the graphs for which each pair of variables is connected by an edge—the set of complete graphs.

Algorithms have been developed that use conditional independence tests to determine the Markov equivalence class of causal structures consistent with a given dataset. For example, the PC-algorithm [ 41 ] was developed on the basis of exactly the set of assumptions just discussed (Markov, faithfulness, acyclicity and causal sufficiency) and uses a sequence of carefully selected (conditional) independence tests to both identify as much as possible about the causal structure and to perform as few tests as possible. In a certain sense, the PC-algorithm is complete: it extracts all information about the underlying causal structure that is available in the statements of conditional (in)dependence. Or more formally, this bound can be characterized in terms of a limiting result due to Geiger and Pearl [ 8 ] and Meek [ 26 ]:

(Markov completeness) For linear Gaussian and for multinomial causal relations, an algorithm that identifies the Markov equivalence class is complete.

That is, if the causal relations between the causes and effects in G can be characterized either by a linear Gaussian relation of the form \(x_i = \sum _{j \ne i} a_jx_j+ \epsilon _i\) with \(\epsilon _i\sim N(\mu _i, \sigma _i^2)\) or by conditional distributions \(P(X_i { \; | \; }pa(X_i))\) that are multinomial, then the PC-algorithm, which in the large sample limit identifies the Markov equivalence class of the true causal model, identifies as much as there is to identify about the underlying causal model.

One can see such a result as a success in that there are methods that reach the limit of what can be discovered about the underlying causal relations, or one can be disappointed about the underdetermination one is left with given that at best this only allows the identification of the Markov equivalence class. Moreover, one might have reason to think that even some of the assumptions required to achieve this limit are unreasonably optimistic about real world causal discovery. Consequently, there are a variety of ways to proceed:

One could weaken the assumptions, thereby (in general) increasing the underdetermination of what one will be able to discover about the underlying causal structure. For example, the FCI-algorithm [ 41 ] drops the assumption of causal sufficiency and allows for unmeasured common causes of the observed variables; the CCD-algorithm [ 36 ] drops the assumption of acyclicity and allows for feedback, and the SAT-based causal discovery methods discussed below can drop both assumptions. Alternatively, Zhang and Spirtes [ 49 ] have worked on weakening the assumption of faithfulness, with corresponding algorithms presented in a paper in this issue. In all cases, the aim of these more general approaches is to develop causal discovery methods that identify as much as possible about the underlying causal relations.

The limits to causal discovery described in Theorem  1 apply to restricted cases—multinomials and linear Gaussian parameterizations. One can exclude these cases and ask what happens when the distributions are not linear Gaussian or not multinomial. We consider several such approaches below.

One could consider more general data collection set-ups to help reduce the underdetermination. For example, one could consider the inclusion of specific experimental data to reduce the underdetermination or use additional “overlapping” datasets that share some but perhaps not all the observed variables (see [ 44 ] for an overview).

We will start by pursuing the second option in Sects.  3 ,   4 and 5 , and return to consider the first and third option in Sect.  6 .

3 Linear non-Gaussian models

One way of avoiding the limitation of causal discovery to only identifying the Markov equivalence class of the true causal model is to exclude the restrictions of Theorem  1 . We will first consider the case of linear non- Gaussian models, that is, we will consider causal models where each variable is determined by a linear function of the values of its parents plus a noise term that has a distribution that is anything (non-degenerate) except Gaussian:

The remarkable result for causal discovery, shown by Shimizu et al. [ 39 ], is that this rather weak assumption about the error distribution is sufficient to uniquely identify the true causal model. Thus,

(Linear Non-Gaussian) Under the assumption of causal Markov, acyclicity and a linear non-Gaussian parameterization (Eq.  2 ), the causal structure can be uniquely determined.

Not even faithfulness is required here. Thus, merely the assumption that the causal relations are linear and that the added noise is anything but Gaussian guarantees in the large sample limit that the true causal model can be uniquely identified.

It helps to gain some intuition regarding this result from the two variable case: If we find that x and y are dependent and we assume acyclicity and causal sufficiency, then the Markov equivalence class contains two causal structures, \(x\rightarrow y\) and \(x \leftarrow y\) . Consider the “forwards” model in Fig.  3 , in which the (unobserved) noise terms are represented in terms of explicit variables:

We can rewrite the equation for the backwards model, and substituting the forwards model for y , we get

Note that Eqs.  3 and 5 are linear in terms of the random variables x and \(\epsilon _y\) , which are both non-Gaussian, but—if the forwards model is true— independent of one another. We can now apply the Darmois-Skitovich theorem that states:

(Darmois-Skitovich) Let \(X_1,\ldots , X_n\) be independent, non-degenerate random variables. If for two linear combinations

are independent, then each \(X_i\) is normally distributed.

These powerful identifiability results have been implemented in causal discovery algorithms that go by the acronym of LinGaM, for Linear non-Gaussian Models, and have been generalized (with slight weakenings of the identifiability) to settings where either causal sufficiency [ 15 ] or acyclicity [ 23 ] is dropped, or where the data generating process satisfies the LinGaM assumptions, but the actual data is the result of an invertible nonlinear transformation, resulting in the so-called post-nonlinear model [ 50 , 51 ].

4 Nonlinear additive noise models

Alternatively, in the continuous case the restrictions of Theorem  1 can be avoided by considering nonlinear causal relations, i.e., when each variable \(x_j\) is determined by a nonlinear function \(f_j\) of the values of its parents plus some additive noise

a Linear Gaussian model with \(x = \epsilon _x\) and \(y = x + \epsilon _y\) with \(\epsilon _x, \epsilon _y\) distributed according to independent Gaussians. Both a “forwards” model ( \(x \rightarrow y\) ) and a “backwards” model ( \(x \leftarrow y\) ) can be fit to the data ( b , c ). However, in the case of a nonlinear Gaussian model as in ( d ), where \(x = \epsilon _x\) , but \(y = x+ x^3 +\epsilon _y\) with \(\epsilon _x, \epsilon _y\) distributed according to independent Gaussians, we see that when fitting the “backwards” model ( f ), the distribution of the residuals on x are dependent on the value of y , while the residuals on y are independent of x when fitting the (correct) “forwards” model ( e ) (Graphics taken from [ 14 ])

We know (from the previous section) that when the \(f_j\) are linear, then identifiability requires that the error distributions are non-Gaussian. But one can ask what the conditions for unique identifiability of the causal structure are when the \(f_j\) are nonlinear (and there are no restrictions other than non-degeneracy on the error distributions). Identifiability results of this kind are developed in Hoyer et al. [ 14 ] and Mooij et al. [ 27 ]. The authors characterize a very intricate condition – I will here only refer to it as the Hoyer condition —on the relation between the function f , the noise distribution and the parent distribution Footnote 6 , and provide the following theorem:

(nonlinear additive noise) Under the assumption of Markov, acyclicity and causal sufficiency and a nonlinear additive noise parameterization (Eq.  6 ), unless the Hoyer condition is satisfied, the true causal structure can be uniquely identified.

In particular, this theorem has the following corrolaries:

If the (additive) error distributions are all Gaussian, then the only functional form that satisfies the Hoyer condition is linearity, otherwise the model is uniquely identifiable.

If the (additive) error distributions are non-Gaussian, then there exist (rather contrived) functions that satisfy the Hoyer condition, but in general the model is uniquely identifiable.

If the functions are linear, but the (additive) error distributions are non-Gaussian, then there does not exist a linear backwards model (this is the result of the LinGaM approach of the previous section), but there exist cases where one can fit a nonlinear backwards model [ 51 ].

The basic point of these identifiability results is that—although somewhat more complex than the linear non-Gaussian case—as soon as the functional relation between cause and effect becomes nonlinear, and as long as the noise is additive, then (except for the rather special cases that satisfy the Hoyer condition), the true model is uniquely identifiable.

Causal discovery algorithms have been developed for these settings (see the papers) and the identifiability results have been generalized [ 35 ], including to certain types of discrete distributions (see next section). There have—to my knowledge— not been extensions to the causally insufficient or cyclic case.

In light of the identifiability results of this section and the previous one it is ironic that so much of structural equation modeling has historically focused on the linear Gaussian case. The identifiability results mentioned here indicate that this focus on computationally simple models came at the expense of the identifiability of the underlying causal model. So in cases when the true causal model is known, then linear Gaussian parameterizations make the computation of causal effects very easy, but for the identifiability of the model in the first place, the linear Gaussian case is about as bad as it could be.

5 Restrictions on multinomial distributions

Naturally, one can also consider the possibilities of avoiding the limitations placed on causal discovery by Theorem  1 with respect to discrete distributions. This has been a much less explored direction of inquiry, possibly due to the difficulty of estimating specific features of discrete distributions, especially when the state space is finite. Alternatively, the domain of application of discrete distributions may provide only much weaker grounds for the justification of assumptions that pick out specific discrete distributions. The multinomial distribution therefore provides a useful unconstrained model, yet causal identifiability is limited to the Markov equivalence class.

However, in a couple of papers by Peters et al. [ 33 , 34 ], the authors extend the additive noise approach discussed in the previous section to the discrete case. While the variables take on discrete values, the causal relations follow the formal restrictions of the continuous case:

where the noise term N and the variable X are probabilistic and the addition now is in the space of integers \(\mathbb {Z}\) or some “cyclic” space of values \(\mathbb {Z}/m\mathbb {Z}\) for some integer m . The associated identifiability results under the assumption of causal sufficiency and acyclicity of the causal structure show that only for very specific choices of functions f and distributions over N is it possible to fit both a forwards model \(X\rightarrow Y\) and backwards model \(X \leftarrow Y\) to the data. In the generic case, the causal direction is identified.

Instead of considering additive noise models, Park & Raskutti [ 29 ] consider discrete variables with Poisson distributions. Again, the causal structure can be identified as long as the variables have nonzero variances in specific settings (see their Theorem 3.1 for the precise condition). The key idea that drives the identifiability result in this case is overdispersion . For a variable X that is marginally Poisson distributed, we have \(E(X) = Var(X)\) , but for a variable \(Y{ \; | \; }X\) that is conditionally Poisson distributed, we have \(Var(Y) > E(Y)\) . The argument is nicely illustrated with the simple bivariate example on p. 3 in [ 29 ].

To my knowledge, there is very little work (other than some subcases of the additive noise models referred to above) that has developed general restrictions to enable identifiability of the causal structure for discrete models with finite state spaces, even though it is known that the assumption of a so-called “noisy-OR” parameterization enables in some cases identifiability beyond that of Markov equivalence.

6 Experiments and background knowledge

The previous several sections have considered the challenge of causal discovery in terms of finding weak generic assumptions about the nature of the underlying causal system that will enable or at least aid the identifiability of the true causal model. But for any concrete problem of causal discovery in application, the search space of candidate causal models will often not include all possible causal structures over the set of variables in the first place, but be highly constrained by available background knowledge concerning, e.g., particular causal pathways, time ordering, tier orderings of variables (i.e., that some subsets of variables come before others) or even less specific prior knowledge about, say, the edge density or the connectivity of the true causal structure. This type of background knowledge can similarly aid the identifiability of the causal model, possibly even without making additional assumptions about the functional form of the causal relations.

Recent developments using general constraint satisfaction solvers have enabled the integration of extraordinarily general background information into the causal discovery procedure. The high-level idea of these approaches is to encode (to the extent possible) all the available information as constraints in propositional logic on the underlying causal graph structure. For example, if data were collected and a conditional independence test was performed, then the implications of that test for the d-separation relations in the graph should be encoded in propositional logic. Similarly, if background information concerning specific pathways is available, it should also be translated into a logical constraint. To do so, fundamental propositional variables have to be defined that, if true, state that a particular directed edge is present in the graph. Thus, we might have

If there are only two variables ( \(\mathbf{{V}}= \{x,y\}\) ) then an independence can be encoded as

When there are more than two variables, the implied logical constraints will become larger. A pathway could be formulated as a conjunction of edges or, if it is only known that there is a causal pathway from x to y , but it is not known which other variables it passes through, it could be formulated as a dependence between x and y in an experiment in which only x is subject to intervention. Such a dependence would in turn be spelled out in terms of a disjunction of possible d-connecting pathways. The key is to find a logical encoding that enables a concise representation of such statements so that one does not have to explicitly state all the possible disjunctions. Hyttinen et al. [ 16 , 18 ] have experimented with various encodings for a completely general search space that allows for causal models with latent variables and cycles. Triantafillou et al. [ 45 , 46 ] have developed encodings restricted to the acyclic case.

Once all the information has been encoded in constraints in propositional logic, one can use standard Boolean SAT(isfiability) solvers to determine solutions consistent with the joint set of constraints. The nice feature of using these solvers is that they are entirely domain general and highly optimized. Consequently, with a suitably general encoding one can integrate heterogeneous information from a variety of different sources into the discovery procedure.

A solver will return either one solution consistent with the constraints—that is, one assignment of truth values to the atomic propositional variables, which in turn specify one graph—or it can return only the truth value for those atomic variables that have the same truth value in all the solutions consistent with the constraints. A so-called “backbone” of the constraints specifies those features of the causal graph that are determined in light of the constraints.

However, constraints may conflict, in particular if they are the result of statistical tests. In that case a SAT-solver only returns that there is no solution for the set of constraints. For example, for the following set of independence constraints there is no graph (satisfying Markov and faithfulness) that is consistent with them:

Rejecting the first constraint would make the constraints consistent with the graph \(x \rightarrow y \rightarrow z\) (and its Markov equivalence class). Rejecting the fourth constraint makes the constraints consistent with the graph \(x\rightarrow z \leftarrow y\) . But together they are inconsistent (assuming Markov and faithfulness).

However, if each constraint were accompanied by a weight representing the degree of confidence in the truth of that constraint, then one might have a preference over which constraint should be rejected. In particular, the following optimization used by [ 16 ] may seem reasonable: Select a graph that minimizes the sum of the weights of the unsatisfied constraints:

In this formalization, the causal discovery problem has now been converted into a weighted constrained optimization problem for which off-the-shelf maxSAT solvers can be applied, which guarantee to find the globally optimal solution. We now only have to determine suitable weights for the constraints. Hyttinen et al. [ 16 ] have experimented with different weighting schemes, from ones that are motivated by a preference for the simplest model in light of any detected dependencies, to a pseudo-Bayesian weighting scheme. Other weighting schemes, e.g., based on p-values, can be found in [ 45 ] and [ 24 ]. The more general question of how one should weight background knowledge such that it is well calibrated with any other available information remains an open research challenge, for which even the standard of success remains to be formulated.

While these SAT-based approaches are incredibly versatile in terms of the information they can integrate into the search procedure, and while they can achieve remarkably accurate results, they do not yet scale as well as other causal discovery algorithms. But there are several comments worth making in this regard: (1) The runtime of a constraint optimization using standard SAT-based solvers has a very high variance; many instances can be resolved in seconds while some can take vastly longer. (2) The runtime is highly dependent on the set of constraints available and the search spaces they are applied to; for example [ 19 ] used a SAT-based method for causal discovery in the highly constrained domain of sub-sampled time series and were able to scale to around 70 variables. (3) We can expect significant improvements in the scalability with the development of more efficient encodings and the parallelization of the computation. (4) One can always explore the accuracy/speed trade-off and settle for a more scalable method with less accurate or less informative output. And finally, (5) if one is actually doing causal discovery on a specific application, one might be willing to wait for a week for the super-computer to return a good result.

There is another aspect in which the SAT-based approach to causal discovery opens new doors: Previous methods have focused on the identification of the causal structure or some general representation of the equivalence class of causal structures. SAT-based methods do not output the equivalence class of causal structures explicitly, but rather represent it implicitly in terms of the constraints in the solver. So instead of requesting as output a “best” causal structure or an equivalence class, one can also query specific aspects of the underlying causal system. This is particularly useful if one is only interested in a specific pathway or the relations among a subset of variables. In that case, one need not compute the entire equivalence class but can query the solver directly to establish what is determined about the question of interest. Magliacane et al. [ 24 ] have taken this approach to only investigate the ancestral relations in a causal system and Hyttinen et al. [ 17 ] used a query-based approach to check the conditions for the applications of the rules of the do -calculus [ 31 ] when the true graph is unknown.

This article has highlighted some of the approaches to causal discovery and attempted to fit them together in terms of their motivations and in light of the formal limits to causal discovery that are known. This article is by no means exhaustive and I encourage the reader to pursue other review articles such as Spirtes and Zhang [ 42 ] to gain a more complete overview. Moreover, there are many questions concerning comparative efficiency, finite sample performance, robustness, etc. that I have not even touched on. Nevertheless, I hope to have shown that there is a vast array of different methods grounded on a whole set of different assumptions such that the reader may reasonably have some hope to find a method suitable (or adaptable) to their area of application. One almost paradigmatic application of a causal discovery method is illustrated in the article by Stekhoven et al. [ 43 ]. It exemplifies how a causal discovery method was applied to observational gene expression data to select candidate causes of the onset of flowering of the plant Arabidopsis thaliana . Once candidate causes had been identified, the researchers actually planted specimen, in which the genes, which had been determined to be relevant by the causal discovery method, had been knocked out—the causal hypothesis was put to the experimental test. I think it is fair to say that the results were positive.

Finally, I will highlight a few areas of causal discovery that I think still require a significant development in understanding. Again, the list is not supposed to be exhaustive, and it is certainly colored by my own interests and of course there already exists some interesting work in each.

Dynamics and time series Many areas of scientific investigation describe systems in terms of sets of dynamical equations. How can these results be integrated with the methods for causal discovery in time series? (See e.g., [ 3 , 4 , 21 , 40 , 48 ].)

Variable construction Standard causal discovery methods (such as the ones discussed in this article) take as input a statistical data set of measurements of well-defined causal variables. The goal is to find the causal relations between them. But how are these causal variables identified or constructed in the first place? Often we have sensor level data but assume that the relevant causal interactions occur at a higher scale of aggregation. Sometimes we only have aggregate measurements of causal interactions at a finer scale. (See e.g., [ 1 , 2 , 38 ].)

Relational data In many cases there can be in addition to the causal relation, a dependence structure among the causal variables that is not due to the causal relations, but due to relational features among the causal variables, e.g., whether an actor is in a movie, or which friendship relations are present. In this case, we need methods that can disentangle the dependencies due to the relational structure from the dependencies due to causality, and there may be causal effects from the relations to the individuals and vice versa. (See e.g., [ 25 , 37 ]).

In each of these cases, the challenge is not simply to develop a new discovery method, but also to first characterize precisely the different concepts and what the goals of causal discovery in these domains are. So while there is a whole set of causal discovery algorithms ready to be applied to different domains, there also remain significant theoretical and conceptual hurdles that need to be addressed.

See a discussion of this example in Scientific American [ 22 ].

In a somewhat counter-intuitive usage of terms, a vertex is also its own ancestor and its own descendent, but not its own parent or child.

In order to separate out limitations and sources of error in the overall inference it can be helpful to make the following three-way distinction: Statistical inference concerns the inference from data to the generating distribution or properties of the generating distribution, such as parameter values or (in)dependence relations. Causal discovery concerns the inference of identifying as much as possible about the causal structure given the statistical quantities, such as a probability distribution or its features. Causal inference concerns the determination of quantitative causal effects given the causal structure and associated statistical quantities. Of course, these three inference steps are not always completely separable and there are plenty of interesting approaches that combine them.

This example is taken from [ 12 ].

Especially with regard to the assumption of acyclicity it is worth noting that very subtle issues arise both about what exactly we mean when we allow for causal cycles, and how one may infer something about a system in which there are such feedback loops. The interested reader is encouraged to purse the references on cyclic models mentioned below.

An explicit statement of the condition is omitted here as it requires a fair bit of notation and no further insight is gained by just stating it. The intrigued reader should refer to the original paper, which is a worthwhile read in any case.

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Acknowledgements

I am very grateful to the organizers of the 2016 KDD Causal Discovery Workshop for encouraging me to put together and write up this overview. I am also very grateful to two anonymous reviewers who made several suggestions to improve the presentation and who alerted me to additional important papers that I was not aware of before.

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Eberhardt, F. Introduction to the foundations of causal discovery. Int J Data Sci Anal 3 , 81–91 (2017). https://doi.org/10.1007/s41060-016-0038-6

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DOI : https://doi.org/10.1007/s41060-016-0038-6

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Research Hypothesis In Psychology: Types, & Examples

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

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A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

• A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
• It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
• A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
• Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
• For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
• Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

• Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

• Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
• However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

• Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
• Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
• Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
• Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
• Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

• The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
• The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

• Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
• Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
• Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
• Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
• Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
• Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
• Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
• Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

Causal Hypothesis

Ai generator.

In scientific research, understanding causality is key to unraveling the intricacies of various phenomena. A causal hypothesis is a statement that predicts a cause-and-effect relationship between variables in a study. It serves as a guide to study design, data collection, and interpretation of results. This thesis statement segment aims to provide you with clear examples of causal hypotheses across diverse fields, along with a step-by-step guide and useful tips for formulating your own. Let’s delve into the essential components of constructing a compelling causal hypothesis.

What is Causal Hypothesis?

A causal hypothesis is a predictive statement that suggests a potential cause-and-effect relationship between two or more variables. It posits that a change in one variable (the independent or cause variable) will result in a change in another variable (the dependent or effect variable). The primary goal of a causal hypothesis is to determine whether one event or factor directly influences another. This type of Simple hypothesis is commonly tested through experiments where one variable can be manipulated to observe the effect on another variable.

What is an example of a Causal Hypothesis Statement?

Example 1: If a person increases their physical activity (cause), then their overall health will improve (effect).

Explanation: Here, the independent variable is the “increase in physical activity,” while the dependent variable is the “improvement in overall health.” The hypothesis suggests that by manipulating the level of physical activity (e.g., by exercising more), there will be a direct effect on the individual’s health.

Other examples can range from the impact of a change in diet on weight loss, the influence of class size on student performance, or the effect of a new training method on employee productivity. The key element in all causal hypotheses is the proposed direct relationship between cause and effect.

100 Causal Hypothesis Statement Examples

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Causal hypotheses predict cause-and-effect relationships, aiming to understand the influence one variable has on another. Rooted in experimental setups, they’re essential for deriving actionable insights in many fields. Delve into these 100 illustrative examples to understand the essence of causal relationships.

• Dietary Sugar & Weight Gain: Increased sugar intake leads to weight gain.
• Exercise & Mental Health: Regular exercise improves mental well-being.
• Sleep & Productivity: Lack of adequate sleep reduces work productivity.
• Class Size & Learning: Smaller class sizes enhance student understanding.
• Smoking & Lung Disease: Regular smoking causes lung diseases.
• Pesticides & Bee Decline: Use of certain pesticides leads to bee population decline.
• Stress & Hair Loss: Chronic stress accelerates hair loss.
• Music & Plant Growth: Plants grow better when exposed to classical music.
• UV Rays & Skin Aging: Excessive exposure to UV rays speeds up skin aging.
• Reading & Vocabulary: Regular reading improves vocabulary breadth.
• Video Games & Reflexes: Playing video games frequently enhances reflex actions.
• Air Pollution & Respiratory Issues: High levels of air pollution increase respiratory diseases.
• Green Spaces & Happiness: Living near green spaces improves overall happiness.
• Yoga & Blood Pressure: Regular yoga practices lower blood pressure.
• Meditation & Stress Reduction: Daily meditation reduces stress levels.
• Social Media & Anxiety: Excessive social media use increases anxiety in teenagers.
• Alcohol & Liver Damage: Regular heavy drinking leads to liver damage.
• Training & Job Efficiency: Intensive training improves job performance.
• Seat Belts & Accident Survival: Using seat belts increases chances of surviving car accidents.
• Soft Drinks & Bone Density: High consumption of soft drinks decreases bone density.
• Homework & Academic Performance: Regular homework completion improves academic scores.
• Organic Food & Health Benefits: Consuming organic food improves overall health.
• Fiber Intake & Digestion: Increased dietary fiber enhances digestion.
• Therapy & Depression Recovery: Regular therapy sessions improve depression recovery rates.
• Financial Education & Savings: Financial literacy education increases personal saving rates.
• Brushing & Dental Health: Brushing teeth twice a day reduces dental issues.
• Carbon Emission & Global Warming: Higher carbon emissions accelerate global warming.
• Afforestation & Climate Stability: Planting trees stabilizes local climates.
• Ad Exposure & Sales: Increased product advertisement boosts sales.
• Parental Involvement & Academic Success: Higher parental involvement enhances student academic performance.
• Hydration & Skin Health: Regular water intake improves skin elasticity and health.
• Caffeine & Alertness: Consuming caffeine increases alertness levels.
• Antibiotics & Bacterial Resistance: Overuse of antibiotics leads to increased antibiotic-resistant bacteria.
• Pet Ownership & Loneliness: Having pets reduces feelings of loneliness.
• Fish Oil & Cognitive Function: Regular consumption of fish oil improves cognitive functions.
• Noise Pollution & Sleep Quality: High levels of noise pollution degrade sleep quality.
• Exercise & Bone Density: Weight-bearing exercises increase bone density.
• Vaccination & Disease Prevention: Proper vaccination reduces the incidence of related diseases.
• Laughter & Immune System: Regular laughter boosts the immune system.
• Gardening & Stress Reduction: Engaging in gardening activities reduces stress levels.
• Travel & Cultural Awareness: Frequent travel increases cultural awareness and tolerance.
• High Heels & Back Pain: Prolonged wearing of high heels leads to increased back pain.
• Junk Food & Heart Disease: Excessive junk food consumption increases the risk of heart diseases.
• Mindfulness & Anxiety Reduction: Practicing mindfulness lowers anxiety levels.
• Online Learning & Flexibility: Online education offers greater flexibility to learners.
• Urbanization & Wildlife Displacement: Rapid urbanization leads to displacement of local wildlife.
• Vitamin C & Cold Recovery: High doses of vitamin C speed up cold recovery.
• Team Building Activities & Work Cohesion: Regular team-building activities improve workplace cohesion.
• Multitasking & Productivity: Multitasking reduces individual task efficiency.
• Protein Intake & Muscle Growth: Increased protein consumption boosts muscle growth in individuals engaged in strength training.
• Mentoring & Career Progression: Having a mentor accelerates career progression.
• Fast Food & Obesity Rates: High consumption of fast food leads to increased obesity rates.
• Deforestation & Biodiversity Loss: Accelerated deforestation results in significant biodiversity loss.
• Language Learning & Cognitive Flexibility: Learning a second language enhances cognitive flexibility.
• Red Wine & Heart Health: Moderate red wine consumption may benefit heart health.
• Public Speaking Practice & Confidence: Regular public speaking practice boosts confidence.
• Fasting & Metabolism: Intermittent fasting can rev up metabolism.
• Plastic Usage & Ocean Pollution: Excessive use of plastics leads to increased ocean pollution.
• Peer Tutoring & Academic Retention: Peer tutoring improves academic retention rates.
• Mobile Usage & Sleep Patterns: Excessive mobile phone use before bed disrupts sleep patterns.
• Green Spaces & Mental Well-being: Living near green spaces enhances mental well-being.
• Organic Foods & Health Outcomes: Consuming organic foods leads to better health outcomes.
• Art Exposure & Creativity: Regular exposure to art boosts creativity.
• Gaming & Hand-Eye Coordination: Engaging in video games improves hand-eye coordination.
• Prenatal Music & Baby’s Development: Exposing babies to music in the womb enhances their auditory development.
• Dark Chocolate & Mood Enhancement: Consuming dark chocolate can elevate mood.
• Urban Farms & Community Engagement: Establishing urban farms promotes community engagement.
• Reading Fiction & Empathy Levels: Reading fiction regularly increases empathy.
• Aerobic Exercise & Memory: Engaging in aerobic exercises sharpens memory.
• Meditation & Blood Pressure: Regular meditation can reduce blood pressure.
• Classical Music & Plant Growth: Plants exposed to classical music show improved growth.
• Pollution & Respiratory Diseases: Higher pollution levels increase respiratory diseases’ incidence.
• Parental Involvement & Child’s Academic Success: Direct parental involvement in schooling enhances children’s academic success.
• Sugar Intake & Tooth Decay: High sugar intake is directly proportional to tooth decay.
• Physical Books & Reading Comprehension: Reading physical books improves comprehension better than digital mediums.
• Daily Journaling & Self-awareness: Maintaining a daily journal enhances self-awareness.
• Robotics Learning & Problem-solving Skills: Engaging in robotics learning fosters problem-solving skills in students.
• Forest Bathing & Stress Relief: Immersion in forest environments (forest bathing) reduces stress levels.
• Reusable Bags & Environmental Impact: Using reusable bags reduces environmental pollution.
• Affirmations & Self-esteem: Regularly reciting positive affirmations enhances self-esteem.
• Local Produce Consumption & Community Economy: Buying and consuming local produce boosts the local economy.
• Sunlight Exposure & Vitamin D Levels: Regular sunlight exposure enhances Vitamin D levels in the body.
• Group Study & Learning Enhancement: Group studies can enhance learning compared to individual studies.
• Active Commuting & Fitness Levels: Commuting by walking or cycling improves overall fitness.
• Foreign Film Watching & Cultural Understanding: Watching foreign films increases understanding and appreciation of different cultures.
• Craft Activities & Fine Motor Skills: Engaging in craft activities enhances fine motor skills.
• Listening to Podcasts & Knowledge Expansion: Regularly listening to educational podcasts broadens one’s knowledge base.
• Outdoor Play & Child’s Physical Development: Encouraging outdoor play accelerates physical development in children.
• Thrift Shopping & Sustainable Living: Choosing thrift shopping promotes sustainable consumption habits.
• Nature Retreats & Burnout Recovery: Taking nature retreats aids in burnout recovery.
• Virtual Reality Training & Skill Acquisition: Using virtual reality for training accelerates skill acquisition in medical students.
• Pet Ownership & Loneliness Reduction: Owning a pet significantly reduces feelings of loneliness among elderly individuals.
• Intermittent Fasting & Metabolism Boost: Practicing intermittent fasting can lead to an increase in metabolic rate.
• Bilingual Education & Cognitive Flexibility: Being educated in a bilingual environment improves cognitive flexibility in children.
• Urbanization & Loss of Biodiversity: Rapid urbanization contributes to a loss of biodiversity in the surrounding environment.
• Recycled Materials & Carbon Footprint Reduction: Utilizing recycled materials in production processes reduces a company’s overall carbon footprint.
• Artificial Sweeteners & Appetite Increase: Consuming artificial sweeteners might lead to an increase in appetite.
• Green Roofs & Urban Temperature Regulation: Implementing green roofs in urban buildings contributes to moderating city temperatures.
• Remote Work & Employee Productivity: Adopting a remote work model can boost employee productivity and job satisfaction.
• Sensory Play & Child Development: Incorporating sensory play in early childhood education supports holistic child development.

Causal Hypothesis Statement Examples in Research

Research hypothesis often delves into understanding the cause-and-effect relationships between different variables. These causal hypotheses attempt to predict a specific effect if a particular cause is present, making them vital for experimental designs.

• Artificial Intelligence & Job Market: Implementation of artificial intelligence in industries causes a decline in manual jobs.
• Online Learning Platforms & Traditional Classroom Efficiency: The introduction of online learning platforms reduces the efficacy of traditional classroom teaching methods.
• Nano-technology & Medical Treatment Efficacy: Using nano-technology in drug delivery enhances the effectiveness of medical treatments.
• Genetic Editing & Lifespan: Advancements in genetic editing techniques directly influence the lifespan of organisms.
• Quantum Computing & Data Security: The rise of quantum computing threatens the security of traditional encryption methods.
• Space Tourism & Aerospace Advancements: The demand for space tourism propels advancements in aerospace engineering.
• E-commerce & Retail Business Model: The surge in e-commerce platforms leads to a decline in the traditional retail business model.
• VR in Real Estate & Buyer Decisions: Using virtual reality in real estate presentations influences buyer decisions more than traditional methods.
• Biofuels & Greenhouse Gas Emissions: Increasing biofuel production directly reduces greenhouse gas emissions.
• Crowdfunding & Entrepreneurial Success: The availability of crowdfunding platforms boosts the success rate of start-up enterprises.

Causal Hypothesis Statement Examples in Epidemiology

Epidemiology is a study of how and why certain diseases occur in particular populations. Causal hypotheses in this field aim to uncover relationships between health interventions, behaviors, and health outcomes.

• Vaccine Introduction & Disease Eradication: The introduction of new vaccines directly leads to the reduction or eradication of specific diseases.
• Urbanization & Rise in Respiratory Diseases: Increased urbanization causes a surge in respiratory diseases due to pollution.
• Processed Foods & Obesity Epidemic: The consumption of processed foods is directly linked to the rising obesity epidemic.
• Sanitation Measures & Cholera Outbreaks: Implementing proper sanitation measures reduces the incidence of cholera outbreaks.
• Tobacco Consumption & Lung Cancer: Prolonged tobacco consumption is the primary cause of lung cancer among adults.
• Antibiotic Misuse & Antibiotic-Resistant Strains: Misuse of antibiotics leads to the evolution of antibiotic-resistant bacterial strains.
• Alcohol Consumption & Liver Diseases: Excessive and regular alcohol consumption is a leading cause of liver diseases.
• Vitamin D & Rickets in Children: A deficiency in vitamin D is the primary cause of rickets in children.
• Airborne Pollutants & Asthma Attacks: Exposure to airborne pollutants directly triggers asthma attacks in susceptible individuals.
• Sedentary Lifestyle & Cardiovascular Diseases: Leading a sedentary lifestyle is a significant risk factor for cardiovascular diseases.

Causal Hypothesis Statement Examples in Psychology

In psychology, causal hypotheses explore how certain behaviors, conditions, or interventions might influence mental and emotional outcomes. These hypotheses help in deciphering the intricate web of human behavior and cognition.

• Childhood Trauma & Personality Disorders: Experiencing trauma during childhood increases the risk of developing personality disorders in adulthood.
• Positive Reinforcement & Skill Acquisition: The use of positive reinforcement accelerates skill acquisition in children.
• Sleep Deprivation & Cognitive Performance: Lack of adequate sleep impairs cognitive performance in adults.
• Social Isolation & Depression: Prolonged social isolation is a significant cause of depression among teenagers.
• Mindfulness Meditation & Stress Reduction: Regular practice of mindfulness meditation reduces symptoms of stress and anxiety.
• Peer Pressure & Adolescent Risk Taking: Peer pressure significantly increases risk-taking behaviors among adolescents.
• Parenting Styles & Child’s Self-esteem: Authoritarian parenting styles negatively impact a child’s self-esteem.
• Multitasking & Attention Span: Engaging in multitasking frequently leads to a reduced attention span.
• Childhood Bullying & Adult PTSD: Individuals bullied during childhood have a higher likelihood of developing PTSD as adults.
• Digital Screen Time & Child Development: Excessive digital screen time impairs cognitive and social development in children.

Causal Inference Hypothesis Statement Examples

Causal inference is about deducing the cause-effect relationship between two variables after considering potential confounders. These hypotheses aim to find direct relationships even when other influencing factors are present.

• Dietary Habits & Chronic Illnesses: Even when considering genetic factors, unhealthy dietary habits increase the chances of chronic illnesses.
• Exercise & Mental Well-being: When accounting for daily stressors, regular exercise improves mental well-being.
• Job Satisfaction & Employee Turnover: Even when considering market conditions, job satisfaction inversely relates to employee turnover.
• Financial Literacy & Savings Behavior: When considering income levels, financial literacy is directly linked to better savings behavior.
• Online Reviews & Product Sales: Even accounting for advertising spends, positive online reviews boost product sales.
• Prenatal Care & Child Health Outcomes: When considering genetic factors, adequate prenatal care ensures better health outcomes for children.
• Teacher Qualifications & Student Performance: Accounting for socio-economic factors, teacher qualifications directly influence student performance.
• Community Engagement & Crime Rates: When considering economic conditions, higher community engagement leads to lower crime rates.
• Eco-friendly Practices & Brand Loyalty: Accounting for product quality, eco-friendly business practices boost brand loyalty.
• Mental Health Support & Workplace Productivity: Even when considering workload, providing mental health support enhances workplace productivity.

What are the Characteristics of Causal Hypothesis

Causal hypotheses are foundational in many research disciplines, as they predict a cause-and-effect relationship between variables. Their unique characteristics include:

• Cause-and-Effect Relationship: The core of a causal hypothesis is to establish a direct relationship, indicating that one variable (the cause) will bring about a change in another variable (the effect).
• Testability: They are formulated in a manner that allows them to be empirically tested using appropriate experimental or observational methods.
• Specificity: Causal hypotheses should be specific, delineating clear cause and effect variables.
• Directionality: They typically demonstrate a clear direction in which the cause leads to the effect.
• Operational Definitions: They often use operational definitions, which specify the procedures used to measure or manipulate variables.
• Temporal Precedence: The cause (independent variable) always precedes the effect (dependent variable) in time.

What is a causal hypothesis in research?

In research, a causal hypothesis is a statement about the expected relationship between variables, or explanation of an occurrence, that is clear, specific, testable, and falsifiable. It suggests a relationship in which a change in one variable is the direct cause of a change in another variable. For instance, “A higher intake of Vitamin C reduces the risk of common cold.” Here, Vitamin C intake is the independent variable, and the risk of common cold is the dependent variable.

What is the difference between causal and descriptive hypothesis?

• Causal Hypothesis: Predicts a cause-and-effect relationship between two or more variables.
• Descriptive Hypothesis: Describes an occurrence, detailing the characteristics or form of a particular phenomenon.
• Causal: Consuming too much sugar can lead to diabetes.
• Descriptive: 60% of adults in the city exercise at least thrice a week.
• Causal: To establish a causal connection between variables.
• Descriptive: To give an accurate portrayal of the situation or fact.
• Causal: Often involves experiments.
• Descriptive: Often involves surveys or observational studies.

How do you write a Causal Hypothesis? – A Step by Step Guide

• Identify Your Variables: Pinpoint the cause (independent variable) and the effect (dependent variable). For instance, in studying the relationship between smoking and lung health, smoking is the independent variable while lung health is the dependent variable.
• State the Relationship: Clearly define how one variable affects another. Does an increase in the independent variable lead to an increase or decrease in the dependent variable?
• Be Specific: Avoid vague terms. Instead of saying “improved health,” specify the type of improvement like “reduced risk of cardiovascular diseases.”
• Use Operational Definitions: Clearly define any terms or variables in your hypothesis. For instance, define what you mean by “regular exercise” or “high sugar intake.”
• Ensure It’s Testable: Your hypothesis should be structured so that it can be disproven or supported by data.
• Review Existing Literature: Check previous research to ensure that your hypothesis hasn’t already been tested, and to ensure it’s plausible based on existing knowledge.
• Draft Your Hypothesis: Combine all the above steps to write a clear, concise hypothesis. For instance: “Regular exercise (defined as 150 minutes of moderate exercise per week) decreases the risk of cardiovascular diseases.”

Tips for Writing Causal Hypothesis

• Simplicity is Key: The clearer and more concise your hypothesis, the easier it will be to test.
• Avoid Absolutes: Using words like “all” or “always” can be problematic. Few things are universally true.
• Seek Feedback: Before finalizing your hypothesis, get feedback from peers or mentors.
• Stay Objective: Base your hypothesis on existing literature and knowledge, not on personal beliefs or biases.
• Revise as Needed: As you delve deeper into your research, you may find the need to refine your hypothesis for clarity or specificity.
• Falsifiability: Always ensure your hypothesis can be proven wrong. If it can’t be disproven, it can’t be validated either.
• Avoid Circular Reasoning: Ensure that your hypothesis doesn’t assume what it’s trying to prove. For example, “People who are happy have a positive outlook on life” is a circular statement.
• Specify Direction: In causal hypotheses, indicating the direction of the relationship can be beneficial, such as “increases,” “decreases,” or “leads to.”

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Statistics By Jim

Making statistics intuitive

Causation in Statistics: Hill’s Criteria

By Jim Frost 11 Comments

Causation indicates that an event affects an outcome. Do fatty diets cause heart problems? If you study for a test, does it cause you to get a higher score?

In statistics , causation is a bit tricky. As you’ve no doubt heard, correlation doesn’t necessarily imply causation. An association or correlation between variables simply indicates that the values vary together. It does not necessarily suggest that changes in one variable cause changes in the other variable. Proving causality can be difficult.

If correlation does not prove causation, what statistical test do you use to assess causality? That’s a trick question because no statistical analysis can make that determination. In this post, learn about why you want to determine causation and how to do that.

Relationships and Correlation vs. Causation

The expression is, “correlation does not imply causation.” Consequently, you might think that it applies to things like Pearson’s correlation coefficient . And, it does apply to that statistic. However, we’re really talking about relationships between variables in a broader context. Pearson’s is for two continuous variables . However, a relationship can involve different types of variables such as categorical variables , counts, binary data, and so on.

For example, in a medical experiment, you might have a categorical variable that defines which treatment group subjects belong to—control group, placebo group, and several different treatment groups. If the health outcome is a continuous variable, you can assess the differences between group means. If the means differ by group, then you can say that mean health outcomes depend on the treatment group. There’s a correlation, or relationship, between the type of treatment and health outcome. Or, maybe we have the treatment groups and the outcome is binary, say infected and not infected. In that case, we’d compare group proportions of the infected/not infected between groups to determine whether treatment correlates with infection rates.

Through this post, I’ll refer to correlation and relationships in this broader sense—not just literal correlation coefficients . But relationships between variables, such as differences between group means and proportions, regression coefficients , associations between pairs of categorical variables , and so on.

Why Determining Causality Is Important

If you’re only predicting events, not trying to understand why they happen, and do not want to alter the outcomes, correlation can be perfectly fine. For example, ice cream sales correlate with shark attacks. If you just need to predict the number of shark attacks, ice creams sales might be a good thing to measure even though it’s not causing the shark attacks.

However, if you want to reduce the number of attacks, you’ll need to find something that genuinely causes a change in the attacks. As far as I know, sharks don’t like ice cream!

There are many occasions where you want to affect the outcome. For example, you might want to do the following:

• Improve health by using medicine, exercising, or flu vaccinations .
• Reducing the risk of adverse outcomes, such as procedures for reducing manufacturing defects.
• Improving outcomes, such as studying for a test.

For intentional changes in one variable to affect the outcome variable, there must be a causal relationship between the variables. After all, if studying does not cause an increase in test scores, there’s no point for studying. If the medicine doesn’t cause an improvement in your health or ward off disease, there’s no reason to take it.

Before you can state that some course of action will improve your outcomes, you must be sure that a causal relationship exists between your variables.

Confounding Variables and Their Role in Causation

How does it come to be that variables are correlated but do not have a causal relationship? A common reason is a confounding variable that creates a spurious correlation. A confounding variable correlates with both of your variables of interest. It’s possible that the confounding variable might be the real causal factor ! Let’s go through the ice cream and shark attack example.

In this example, the number of people at the beach is a confounding variable. A confounding variable correlates with both variables of interest—ice cream and shark attacks in our example.

In the diagram below, imagine that as the number of people increases, ice cream sales also tend to increase. In turn, more people at the beach cause shark attacks to increase. The correlation structure creates an apparent, or spurious, correlation between ice cream sales and shark attacks, but it isn’t causation.

Confounders are common reasons for associations between variables that are not causally connected.

Related post : Confounding Variables Can Bias Your Results

Causation and Hypothesis Tests

Before moving on to determining whether a relationship is causal, let’s take a moment to reflect on why statistically significant hypothesis test results do not signify causation.

Hypothesis tests are inferential procedures . They allow you to use relatively small samples to draw conclusions about entire populations. For the topic of causation, we need to understand what statistical significance means.

When you see a relationship in sample data, whether it is a correlation coefficient, a difference between group means, or a regression coefficient, hypothesis tests help you determine whether your sample provides sufficient evidence to conclude that the relationship exists in the population . You can see it in your sample, but you need to know whether it exists in the population. It’s possible that random sampling error (i.e., luck of the draw) produced the “relationship” in your sample.

Statistical significance indicates that you have sufficient evidence to conclude that the relationship you observe in the sample also exists in the population.

That’s it. It doesn’t address causality at all.

Related post : Understanding P-values and Statistical Significance

Hill’s Criteria of Causation

Determining whether a causal relationship exists requires far more in-depth subject area knowledge and contextual information than you can include in a hypothesis test. In 1965, Austin Hill, a medical statistician, tackled this question in a paper* that’s become the standard. While he introduced it in the context of epidemiological research, you can apply the ideas to other fields.

Hill describes nine criteria to help establish causal connections. The goal is to satisfy as many criteria possible. No single criterion is sufficient. However, it’s often impossible to meet all the criteria. These criteria are an exercise in critical thought. They show you how to think about determining causation and highlight essential qualities to consider.

Studies can take steps to increase the strength of their case for a causal relationship, which statisticians call internal validity . To learn more about this, read my post about internal and external validity .

A strong, statistically significant relationship is more likely to be causal. The idea is that causal relationships are likely to produce statistical significance. If you have significant results, at the very least you have reason to believe that the relationship in your sample also exists in the population—which is a good thing. After all, if the relationship only appears in your sample, you don’t have anything meaningful! Correlation still does not imply causation, but a statistically significant relationship is a good starting point.

However, there are many more criteria to satisfy! There’s a critical caveat for this criterion as well. Confounding variables can mask a correlation that actually exists. They can also create the appearance of correlation where causation doesn’t exist, as shown with the ice cream and shark attack example. A strong relationship is simply a hint.

Consistency and causation

When there is a real, causal connection, the result should be repeatable. Other experimenters in other locations should be able to produce the same results. It’s not one and done. Replication builds up confidence that the relationship is causal. Preferably, the replication efforts use other methods, researchers, and locations.

In my post with five tips for using p-values without being misled , I emphasize the need for replication.

Specificity

It’s easier to determine that a relationship is causal if you can rule out other explanations. I write about ruling out other explanations in my posts about randomized experiments and observational studies. In a more general sense, it’s essential to study the literature, consider other plausible hypotheses, and, hopefully, be able to rule them out or otherwise control for them. You need to be sure that what you’re studying is causing the observed change rather than something else of which you’re unaware.

It’s important to note that you don’t need to prove that your variable of interest is the only factor that affects the outcome. For example, smoking causes lung cancer, but it’s not the only thing that causes it. However, you do need to perform experiments that account for other relevant factors and be able to attribute some causation to your variable of interest specifically.

For example, in regression analysis , you control for other factors by including them in the model .

Temporality and causation

Causes should precede effects. Ensure that what you consider to be the cause occurs before the effect . Sometimes it can be challenging to determine which way causality runs. Hill uses the following example. It’s possible that a particular diet leads to an abdominal disease. However, it’s also possible that the disease leads to specific dietary habits.

The Granger Causality Test assesses potential causality by determining whether earlier values in one time series predicts later values in another time series. Analysts say that time series A Granger-causes time series B when significant statistical tests indicate that values in series A predict future values of series B.

Despite being called a “causality test,” it really is only a test of prediction. After all, the increase of Christmas card sales Granger-causes Christmas!

Temporality is just one aspect of causality!

Biological Gradient

Hill was a biologist, hence the focus on biological questions. He suggests that for a genuinely causal relationship, there should be a dose-response type of relationship. If a little bit of exposure causes a little bit of change, a larger exposure should cause more change. Hill uses cigarette smoking and lung cancer as an example—greater amounts of smoking are linked to a greater risk of lung cancer. You can apply the same type of thinking in other fields. Does more studying lead to even higher scores?

However, be aware that the relationship might not remain linear. As the dose increases beyond a threshold, the response can taper off. You can check for this by modeling curvature in regression analysis .

Plausibility

If you can find a plausible mechanism that explains the causal nature of the relationship, it supports the notion of a causal relationship. For example, biologists understand how antibiotics inhibit microbes on a biological level. However, Hill points out that you have to be careful because there are limits to scientific knowledge at any given moment. A causal mechanism might not be known at the time of the study even if one exists. Consequently, Hill says, “we should not demand” that a study meets this requirement.

Coherence and causation

The probability that a relationship is causal is higher when it is consistent with related causal relationships that are generally known and accepted as facts. If your results outright disagree with accepted facts, it’s more likely to be correlation. Assess causality in the broader context of related theory and knowledge.

Experiments and causation

Randomized experiments are the best way to identify causal relationships. Experimenters control the treatment (or factors involved), randomly assign the subjects, and help manage other sources of variation. Hill calls satisfying this criterion the strongest support for causation. However, randomized experiments are not always possible as I write about in my post about observational studies. Learn more about Experimental Design: Definition, Types and Examples .

Related posts : Randomized Experiments and Observational Studies

If there is an accepted, causal relationship that is similar to a relationship in your research, it supports causation for the current study. Hill writes, “With the effects of thalidomide and rubella before us we would surely be ready to accept slighter but similar evidence with another drug or another viral disease in pregnancy.”

Determining whether a correlation also represents causation requires much deliberation. Properly designing experiments and using statistical procedures can help you make that determination. But there are many other factors to consider.

Use your critical thinking and subject-area expertise to think about the big picture. If there is a causal relationship, you’d expect to see consistent results that have been replicated, other causes have been ruled out, the results fit with established theory and other findings, there is a plausible mechanism, and the cause precedes the effect.

Austin Bradford Hill, “The Environment and Disease: Association or Causation?,” Proceedings of the Royal Society of Medicine , 58 (1965), 295-300.

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Reader Interactions

December 2, 2020 at 9:06 pm

I believe there is a logical flaw in the movie “Good Will Hunting”. Specifically, in the scene where psychologist Dr. Sean Maguire (Robin Williams) tells Will (Matt Damon) about the first time he met his wife, there seems to be an implied assumption that if Sean had gone to “the game” (Game 6 of the World Series in 1975), instead of staying at the bar where he had just met his future wife, then the very famous home run hit by Carlton Fisk would still have occurred. I contend that if Sean had gone to the game, the game would have played out completely differently, and the famous home run which actually occurred would not have occurred – that’s not to say that some other famous home run could not have occurred. It seems to be clear that neither characters Sean nor Will understand this – and I contend these two supposedly brilliant people would have known better! It is certainly clear that neither Matt Damon nor Ben Affleck (the writers) understand this. What do you think?

August 24, 2019 at 8:00 pm

Hi Jim Thanks for the great site and content. Being new to statistics I am finding it daunting to understand all of these concepts. I have read most of the articles in the basics section and whilst I am gaining some insights I feel like I need to take a step back in order to move forward. Could you recommend some resources for a rank beginner such as my self? Maybe some books that you read when you where starting out that where useful. I am really keen to jump in and start doing some statistics but I am wondering if it is even possible for someone like me to do so. To clearly define my question where is the best place to start?? I realize this doesn’t really relate to the above article but hopefully this question might be useful to others as well. Thanks.

August 25, 2019 at 2:45 pm

I’m glad that my website has been helpful! I do understand your desire to get the pick picture specifically for starting out. In just about a week, September 3rd to be exact, I’m launching a new ebook that does just that. The book is titled Introduction to Statistics: An Intuitive Guide for Analyzing Data and Unlocking Discoveries . My goal is to provide the big picture about the field of statistics. It covers the basics of data analysis up to larger issues such as using experiments and data to make discoveries.

To be sure that you receive the latest about this book, please subscribe to my email list using the form in the right column of every page in my website.

August 16, 2019 at 12:55 am

Jim , I am new to stats and find ur blog very useful. Yet , I am facing an issue of very low R square values , as low as 1 percent, 3 percent… do we still hold these values valid? Any references on research while accepting such low values . request ur valuable inputs please.

August 17, 2019 at 4:11 pm

Low R-squared can be a problem. It depends on several other factors. Are any independent variables significant? Is the F-test of overall significance significant?

I have posts about this topic and answers those questions. Please read: Low R-squared values and F-test of overall significance .

If you have further questions, please post them in the comments section of the relevant post. It helps keep the questions and answers organized for other readers. Thanks!

June 27, 2019 at 11:23 am

Thank you so much for your website. It has helped me tremendously with my stats, particularly regression. I have a question concerning correlation testing. I have a continuous dependent variable, quality of life, and 3 independent variables, which are categorical (education = 4 levels, marital status = 3 levels, stress = 3 levels). How can I test for a relationship among the dependent and independent variables? Thank you Jim.

June 27, 2019 at 1:30 pm

You can use either ANOVA or OLS regression to assess the relationship between categorical IVs to a continuous DV.

I write about this in my ebook, Regression Analysis: An Intuitive Guide . I recommend you get that ebook to learn about how it works with categorical IVs. I discuss that in detail in the ebook. Unfortunately, I don’t have a blog post to point you towards.

Best of luck with your analysis!

June 25, 2019 at 3:24 pm

great post, Jim. Thanks!

June 25, 2019 at 11:32 am

Useful post

June 24, 2019 at 4:51 am

Very nice and interesting post. And very educational. Many thanks for your efforts!

June 24, 2019 at 10:13 am

Thank you very much! I appreciate the kind words!

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Causal Approaches to Scientific Explanation

This entry discusses some accounts of causal explanation developed after approximately 1990. For a discussion of earlier accounts of explanation including the deductive-nomological (DN) model, Wesley Salmon’s statistical relevance and causal mechanical models, and unificationist models, see the general entry on scientific explanation . Recent accounts of non-causal explanation will be discussed in a separate entry. In addition, a substantial amount of recent discussion of causation and causal explanation has been conducted within the framework of causal models. To avoid overlap with the entry on causal models we do not discuss this literature here.

Our focus in this entry is on the following three accounts – Section 1 those that focus on mechanisms and mechanistic explanations, Section 2 the kairetic account of explanation, and Section 3 interventionist accounts of causal explanation. All of these have as their target explanations of why or perhaps how some phenomenon occurs (in contrast to, say, explanations of what something is, which is generally taken to be non-causal) and they attempt to capture causal explanations that aim at such explananda. Section 4 then takes up some recent proposals having to do with how causal explanations may differ in explanatory depth or goodness. Section 5 discusses some issues having to do with what is distinctive about causal (as opposed to non-causal) explanations.

We also make the following preliminary observation. An account of causal explanation in science may leave open the possibility that there are other sorts of explanations of a non-causal variety (it is just that the account does not claim to capture these, at least without substantial modifications) or it may, more ambitiously, claim that all explanations of the why/how variety are, at least in some extended sense, causal. The kairetic model makes this latter claim, as do many advocates of mechanistic models. By contrast, interventionist models, need not deny that there are non-causal explanations, although the version described below does not attempt to cover such explanations. Finally, we are very conscious that, for reasons of space, we omitted many recent discussions of causal explanation from this entry. We provide brief references to a number of these at the end of this article (Section 6).

1. Mechanisms and Mechanistic Explanations

2. the kairetic account of explanation, 3. interventionist theories, 4. explanatory depth, 5. non-causal and mathematical explanation, 6. additional issues, other internet resources, related entries.

Many accounts of causation and explanation assign a central importance to the notion of mechanism. While discussions of mechanism are present in the early modern period, with the work of Descartes and others, a distinct and very influential research program emerged with the “new mechanist” approaches of the late twentieth and early twenty-first century. This section focuses on work in this tradition.

Wesley Salmon’s causal mechanical (CM) model of explanation (Salmon 1984) was an influential late twentieth century precursor to the work on mechanisms that followed. The CM model is described in the SEP entry on scientific explanation and readers are referred to this for details. For present purposes we just note the following. First, Salmon’s model is proposed as an alternative to the deductive-nomological (DN) model and the “new mechanist” work that follows also rejects the DN model, although in some cases for reasons somewhat different from Salmon’s. Like the CM model and in contrast to the DN model, the new mechanist tradition downplays the role of laws in explanation, in part because (it is thought) there are relatively few laws in the life sciences, which are the primary domain of application of recent work on mechanisms. Second, although Salmon provides an account of causal relationships that are in an obvious sense “mechanical”, he focuses virtually entirely on physical examples (like billiard ball collisions) rather than examples from the life sciences. Third Salmon presents his model as an “ontic” account of explanation, according to which explanations are things or structures in the world and contrasts this with what he regarded as “epistemic” accounts of explanation (including in his view, the DN model) which instead conceive of explanations as representations of what is in the world (Salmon 1984). This “ontic” orientation has been important in the work of some of the new mechanists, such as Craver (2007a), but less so for others. Finally, Salmon’s model introduces a distinction between the “etiological” aspects of explanation which have to do with tracing the causal history of some event E and the “constitutive” aspects which have to do with “the internal causal mechanisms that account for E ’s nature” (Salmon 1984: 275). This focus on the role of “constitution” is retained by a number of the new mechanists.

We may think of the “new mechanism” research program properly speaking as initiated by writers like Bechtel and Richardson (1993 [2010]), Glennan (1996, 1997), and Machamer, Darden, and Craver (2000). Although these writers provide accounts that differ in detail, [ 1 ] they share common elements: mechanisms are understood as causal systems, exhibiting a characteristic organization, with multiple causal factors that work together in a coordinated manner to produce some effect of interest. Providing a mechanistic explanation involves explaining an outcome by appealing to the causal mechanism that produces it. The components of a mechanism stand in causal relationships but most accounts conceptualize the relationship between these components and the mechanism itself as a part-whole or “constitutive relationship” – e.g., a human cell is constituted by various molecules, compounds and organelles, the human visual system is constituted by various visual processing areas (including V1–V5) and an automobile engine may be constituted by pistons, cylinders, camshaft and carburetor, among other components. Such part/whole relations are generally conceptualized as non-causal – that is, constitution is seen as a non-causal relationship. Thus, on these accounts, mechanisms are composed of or constituted by lower-level causal parts that interact together to produce the higher-level behavior of the (whole) mechanism understood as some effect of interest. This part-whole picture gives mechanistic explanation a partially reductive character, in the sense that higher-level outcomes characterizing the whole mechanism are explained by the lower-level causes that produce them. In many accounts this is depicted in nested, hierarchical diagrams describing these relations between levels of mechanisms (Craver 2007a).

Although philosophical discussion has often focused on the role of constitutive relations in mechanisms and how best to understand these, it is, as noted above, also common to think of mechanism as consisting of factors or components that stand in causal (“etiological”) relations to one another with accompanying characteristic spatial, temporal or geometrical organization. This feature of mechanism and mechanistic explanation is emphasized by Illari and Williamson (2010, 2012) and Woodward (2002, 2013). In particular, elucidating a mechanism is often understood as involving the identification of “mediating” factors that are “between” the input to the mechanism and its eventual output – “between” both in the sense of causally between and in the sense that the operation of these mediating factors often can be thought of as spatially and temporally between the input to the mechanism and its output. (The causal structure and the spatiotemporal structure thus “mirror” or run parallel to each other.) Often this information about intermediates can be thought of as describing the “steps” by which the mechanism operates over time. For example, mechanistic explanations of the action potential will cite the (anatomical) structure of the neural cell membrane, the relative location and structure of ion channels (in this membrane), ion types on either side of this membrane, and the various temporal steps in the opening and closing of ion channels that generate the action potential. A step-by-step description of this mechanism cites all of these parts and their interactions from the beginning of the causal process to the end. In this respect a description of a mechanism will provide more detail than, say, directed acyclic graphs which describe causal relations among variables but do not provide spatio-temporal or geometrical information.

A hotly debated issue in the literature on mechanisms concerns the amount of detail descriptions of mechanisms or mechanistic explanations need to contain. While some mechanists suggest that mechanisms (or their descriptions) can be abstract or lacking in detail (Levy & Bechtel 2012), it is more commonly claimed that mechanistic explanations must contain significant detail – perhaps as much “relevant” detail as possible or at least that this should be so for an “ideally complete description” of a mechanism (see Craver 2006 and the discussion in Section 4 ). Thus, a mere description of an input-output causal relation, even if correct, lacks sufficient detail to count as a description of a mechanism. For example, a randomized control trial can support the claim that drug X causes recovery Y , but this alone doesn’t elucidate the “mechanism of action” of the drug. Craver (2007a: 113–4) goes further, suggesting that even models that provide substantial information about anatomical structures and causal intermediaries are deficient qua mechanistic explanations if they omit detail thought to be relevant. For example, the original Hodgkin-Huxley (HH) model of the action potential identified a role for the opening and closing of membrane channels but did not specify the molecular mechanisms involved in the opening and closing of those channels. Craver (2006, 2007a, 2008) takes this to show that the HH model is explanatorily deficient – it is a “mechanism sketch” rather than a fully satisfactory mechanistic explanation. (This is echoed by Glennan who states that the monocausal model of disease – a one cause-one effect relationship – is “the sketchiest of mechanism sketches” [Glennan 2017: 226].) This “the more relevant detail the better” view has in turn been criticized by those who think that one can sometimes improve the quality of an explanation or at least make it no worse by omitting detail. For such criticism see, e.g., Batterman and Rice (2014), Levy (2014), Chirimuuta (2014), Ross (2015, 2020), etc. and for a response see by Craver and Kaplan (2020). [ 2 ]

The new mechanists differ among themselves in their views of causation and their attitudes toward general theories of causation found in the philosophical literature. Since a mechanism involves components standing in causal relations, one might think that a satisfactory treatment of mechanisms should include an account of what is meant by “causal relations”. Some mechanists have attempted to provide such an account. For example, Craver (2007a) appeals to elements of Woodward’s interventionist account of causation in this connection and for other purposes – e.g., to provide an account of constitutive relevance (Craver 2007b). By contrast, Glennan (1996, 2017) argues that the notion of mechanism is more fundamental than that of causation and that the former can be used to elucidate the latter – roughly, X causes Y when there is a mechanism connecting X to Y . Of course, for Glennan’s project this requires that mechanism is elucidated in a way that doesn’t appeal to the notion causation. Yet another view, inspired by Anscombe (1971) and advocated by Machamer, Darden, and Craver (MDC) (2000), Machamer (2004) and others, eschews any appeal to general theories of causation and instead describes the causal features of mechanism in terms of specific causal verbs. For example, according to MDC, mechanisms involve entities that engage in “activities”, with examples of the latter including “attraction”, “repulsion”, “pushing” and so on (MDC 2000: 5). It is contended that no more general account according to which these are instances of some common genus (causation) is likely to be illuminating. A detailed evaluation of this claim is beyond the scope of this entry, but we do wish to note that relatively general theories of causation that go beyond the cataloging of particular causal activities now flourish not just in philosophy but in disciplines like computer science and statistics (Pearl 2000 [2009]; Morgan & Winship, 2014) where they are often thought to provide scientific and mathematical illumination.

Another issue raised by mechanistic accounts concerns their scope. As we have seen these accounts were originally devised to capture a form of explanation thought to be widespread in the life sciences. This aspiration raises several questions. First, are all explanations in the life sciences “mechanistic” in the sense captured by some model of mechanistic explanation? Many new mechanists have answered this question in the affirmative but there has been considerable pushback to this claim, with other philosophers claiming that there are explanations in the life sciences that appeal to topological or network features (Lange 2013; Huneman 2010; Rathkopf 2018; Kostić 2020; Ross 2021b), to dynamical systems models (Ross 2015) and to other features deemed “non-mechanical” as with computational models in neuroscience (Chirimuuta 2014, 2018). This debate raises the question of how broadly it is appropriate to extend the notion of “mechanism” (Silberstein & Chemero 2013).

While the examples above are generally claimed to be non-causal and non-mechanistic, a further question is whether there are also types of causal explanation that are non-mechanistic. Answering this question depends, in part, on how “mechanism” is defined and what types of causal structures count as “mechanisms”. If mechanisms have the particular features mentioned above – part-whole relationships, some significant detail, and mechanical interactions – it would seem clear that some causal explanations are non-mechanistic in the sense that they cite causal systems and information with different features. For example, causal systems including pathways, networks, and cascades have been advanced as important types of causal structures that do not meet standard mechanism characteristics (Ross 2018, 2021a, forthcoming). Other examples include complex causal processes that lack machine-like and fixed causal parts (Dupré 2013). This work often questions whether “mechanism” fruitfully captures the diversity of causal structures and causal explanations that are present in scientific contexts.

There is an understandable tendency among mechanists to attempt to extend the scope of their accounts as far as possible but presumably the point of the original project was that mechanistic explanations have some distinctive features. Extending the models too far may lead to loss of sight of these. The problem is compounded by the fact that “mechanism” is used in many areas of science as general term of valorization or approval, as is arguably the case for talk of the “mechanism” of natural selection or of “externalizing tendencies” as a “mechanism” leading to substance abuse. The question is whether these candidates for mechanisms have enough in common with, say, the mechanism by which the action potential is produced to warrant the treatment of both by some common model. Of course, this problem also arises when one considers the extent to which talk of mechanisms is appropriate outside of the life sciences. Chemists talk of mechanisms of reaction, physicists of the Higgs mechanism, and economists of mechanism design, but again this raises the question of whether an account of mechanistic explanation should aspire to cover all of these.

This account is developed by Michael Strevens in his Depth (2008) and in a number of papers (2004, 2013, 2018). Strevens describes his theory as a “two factor” account (Strevens 2008: 4). The first factor – Strevens’ starting point – is the notion of causation or dependence (Strevens calls it “causal influence”) that figures in fundamental physics. Strevens is ecumenical about what this involves. He holds that a number of different philosophical treatments of causal influence – conserved quantity, counterfactual or interventionist – will fit his purposes. This notion of causal influence is then used as input to an account of causal explanation – Strevens’ second factor. A causal explanation of an individual event e (Strevens’ starting point) assembles all and only those causal influences that make a difference to (are explanatorily relevant to) e. A key idea here is the notion of causal entailment (Strevens 2008: 74). [ 3 ] A set of premises that causally entail that e occurs deductively entail this claim and do this in a way that “mirrors” the causal influences (ascertained from the first stage) leading to e . This notion of mirroring is largely left at an intuitive level but as an illustration a derivation of an effect from premises describing the cause mirrors the causal influences leading to the effect while the reverse derivation from effect to cause does not. However, more than mirroring is required for causal explanation: The premises in a causal entailment of the sort just described are subjected to a process (a kind of “abstraction”) in which premises that are not necessary for the entailment of e are removed or replaced with weaker alternatives that are still sufficient to entail e – the result of this being to identify factors which are genuinely difference-makers or explanatorily relevant to e . The result is what Strevens calls a “stand-alone” explanation for e (Strevens 2008: 70). (Explanatory relevance or difference-making is thus understood in terms of what, so to speak, is minimally required for causal entailment, constrained by a cohesiveness requirement described below, rather than, as in some other models of explanation, in terms of counterfactuals or statistical relevance.) As an illustration, if the event e is the shattering of a window the causal influences on e , identified from fundamental physics, will be extremely detailed and will consist of influences that affect fine grained features of e ’s occurrence, having to do, e.g., with exactly how the window shatters. But to the extent that the explanandum is just whether e occurs most of those details will be irrelevant in the sense that they will affect only the details of how the shattering occurs and not whether it occurs at all. Dropping these details will result in a derivation that still causally entails e. The causal explanation of e is what remains after all such details have been dropped and only what is necessary for the causal entailment of e is retained.

As Strevens is fully aware, this account faces the following apparent difficulty. There are a number of different causal scenarios that realize causes of bottle shatterings – the impact of rocks but also, say, sonic booms (cf. Hall 2012). In Strevens’ view, we should not countenance causal explanations that disjoin causal models that describe such highly different realizers, even though weakening derivations via the inclusion of such disjunctions may preserve causal entailment. Strevens’ solution appeals to the notion of cohesion ; when different processes serve as “realizers” for the causes of e , these must be “cohesive” in the sense that they are “causally contiguous” from the point of view of the underlying physics. Roughly, contiguous causal processes are those that are nearby or neighbors to one another in a space provided by fundamental physics. [ 4 ] Sonic booms and rock impacts do not satisfy this cohesiveness requirement and hence models involving them as disjunctive premises are excluded. Fundamental physics is thus the arbitrator of whether upper-level properties with different realizers are sufficiently similar to satisfy the cohesion requirement. Or at least this is so for deep “stand alone” explanations in contrast to those explanations that are “framework” dependent (see below).

As Strevens sees it, a virtue of his account is that it separates difficult (“metaphysical”) questions about the nature of the causal relationships (at least as these are found in physics which is Strevens’ starting point) from issues about causal explanation, which are the main focus of the kairetic account. It also follows that most of the causal claims that we consider in common sense and in science (outside of fundamental physics) are in fact claims about causal explanation and explanatory relevance as determined by the kairetic abstraction procedure rather than claims about causation per se. In effect when one claims that “aspirin causes headache relief” one is making a rather complicated causal explanatory claim about the upshot of the application of the abstraction procedure to the causal claims that, properly speaking, are provided by physics. This contrasts with an account in which causal claims outside of physics are largely univocal with causal claims (assuming that there are such) within physics.

We noted above that Strevens imposes a cohesiveness requirement on his abstraction procedure. This seems to have the consequence that upper-level causal generalizations that have realizers that are rather disparate from the point of view of the underlying physics are defective qua explainers, even though there are many examples of such generalizations that (rightly or wrongly) are regarded as explanatory. Strevens addresses this difficulty by introducing the notion of a framework – roughly a set of presuppositions for an explanation. When scientists “framework” some aspect of a causal story, they put that aspect aside (it is presupposed rather an explicit part of the explanation) and focus on getting the story right for the part that remains. A common example is to framework details of implementation, in effect black-boxing the low-level causal explanation of why certain parts of a system behave in the way they do. The resulting explanation simply presupposes that these parts do what they do, without attempting to explain why. Consequently, the black boxes in such explanations are not subject to the cohesion requirement, because they are not the locus of explanatory attention . Thus although explanations appealing to premises with disparate realizers are defective when considered by themselves as stand-alone explanations, we may regard such explanations as dependent on a framework with the framework incorporating information about a presupposed mechanism that satisfies the coherence constraint. [ 5 ] When this is the case, the explanation will be acceptable qua frameworked explanation. Nonetheless in such cases the explanation should in principle be deepened by making explicit the information presupposed in the framework.

Strevens describes his account as “descriptive” rather than “normative” in aspiration. Presumably, however, it is not intended as a description of the bases on which lay people or scientists come to accept causal explanations outside of fundamental physics – people don’t actually go through the abstraction from fundamental physics process that Strevens describes when they arrive at or reason about upper-level causal explanations. Instead, as we understand his account, it is intended to characterize something like what must be the case from the point of view of fundamental physics for upper-level causal judgments to be explanatory – the explanatory upper-level claims must fit with physics in the right way as specified in Strevens’ abstraction procedure and the accompanying cohesiveness constraint. [ 6 ] Perhaps then the account is intended to be descriptive in the sense that the upper-level causal explanations people regard as satisfactory do in fact satisfy the constraints he describes. In addition, the account is intended to be descriptive in the sense that it contends that as a matter of empirical fact people regard their explanations as committed to various claims about the underlying physics even if these claims are presently unknown – e.g., to claims about the cohesiveness of these realizers. [ 7 ] At the same time the kairetic account is also normative in the sense that it judges that explanations that fail to satisfy the constraints of the abstraction procedure are in some way unsatisfactory – thus people are correct to have the commitments described above.

Depth also contains an interesting treatment of the role of idealizations in explanation. It is often thought that idealizations involve the presence of “falsehoods”, or “distortions”. Strevens claims that these “false” features involve claims that do not have to do with difference-makers, in the sense captured by the abstraction procedure. Thus, according to the kairetic model, it does not matter if idealizations involve falsehoods or if they omit certain information since the falsehoods or omitted information do not concern difference-makers – their presence thus does not detract from the resulting explanation. Moreover, we can think of idealizations as conveying useful information about which factors are not difference-makers.

The kairetic account covers a great deal more that we lack the space to discuss including treatments of what Strevens calls “entanglement”, equilibrium explanations, statistical explanation and much else.

As is always the case with ambitious theories in philosophy, there have been a number of criticisms of the kairetic model. Here we mention just two. First, the kairetic model assumes that all legitimate explanation is causal or at least that all explanation must in some way reference or connect with causal information. (A good deal of the discussion in Depth is concerned to show that explanations that might seem to be non-causal can nonetheless be regarded as working by conveying causal information.) This claim that all explanation is causal is by no means an implausible idea – until recently it was widely assumed in the literature on explanation (Skow 2014). Nonetheless this idea has recently been challenged by a number of philosophers (Baker 2005; Batterman 2000, 2002, 2010a; Lange 2013, 2016; Lyon 2012; Pincock 2007). Relatedly, the kairetic account assumes that fundamental physics is “causal” – physics describes causal relations, and indeed lots of causal relations, enough to generate a large range of upper-level causal explanations when the abstraction procedure is applied. Some hold instead that the dependence relations described in physics are either not causal at all (causation being a notion that applies only to upper-level or macroscopic relationships) or else that these dependence relations lack certain important features (such as asymmetry) that are apparently present in causal explanatory claims outside of physics (Ney 2009, 2016). These claims about the absence of causation in physics are controversial but if correct, it follows that physics does not provide the input that Strevens’ account needs. [ 8 ]

A second set of issues concern the kairetic abstraction process. Here there are several worries. First, the constraints on this process have struck some as vague since they involve judgments of cohesiveness of realizers from the point of view of underlying physics. Does physics or any other science really provide a principled, objective basis for such judgments? Second, it seems, as suggested above, that upper-level causal explanations often generalize over realizers that are very disparate from the point of view of the underlying physics. Potochnik (2011, 2017) focuses on the example, also discussed by Strevens, of the Lotka-Volterra (LV) equations which are applied to a large variety of different organisms that stand in predator/prey relations. Strevens uses his ideas about frameworks to argue that use of the LV equations is in some sense justifiable, but it also appears to be a consequence of his account (and Strevens seems to agree) that explanations appealing to the LV equations are not very deep, considered as standalone explanations. But, at least as a descriptive matter, Potochnik claims, this does not seem to correspond to the judgments or practices of the scientists using these equations, who seem happy to use the LV equations despite the fact that they fail to satisfy the causal contiguity requirement. Potochnik thus challenges this portion of the descriptive adequacy of Strevens’ account. Of course, one might respond that these scientists ought to judge in accord with Strevens’ account, but as noted above, this involves taking the account to have normative implications and not as merely descriptive.

A more general form of this issue arises in connection with “universal” behavior (Batterman 2002). There are a number of cases in which physical and biological systems that are very different from one another in terms of their low-level realizers exhibit similar or identical upper-level behavior (Batterman 2002; Batterman & Rice 2014; Ross 2015). As a well-known example, substances as diverse as ferromagnets and various liquid/gas systems exhibit similar behavior around their critical points (Batterman 2000, 2002). Renormalization techniques are often thought to explain this commonality in behavior, but they do so precisely by showing that the physical details of these systems do not matter for (are irrelevant to) the aspects of their upper-level behavior of interest. The features of these systems that are relevant to their behavior have to do with their dimensionality and symmetry properties among others and this is revealed by the renormalization group analysis (RGA) (Batterman 2010b). One interesting question is whether we can think of that analysis as an instance of Strevens’ kairetic procedure. On the one hand the RGA can certainly be viewed as an abstraction procedure that discards non-difference-making factors. On the other hand, it is perhaps not so clear the RGA respects the cohesiveness requirements that Strevens proposes since the upshot is that systems that are very different at the level of fundamental physics are given a common explanation. That is, the RGA does not seem to work by showing (at least in any obvious way) that the systems to which it applies are contiguous with respect to the underlying physics. [ 9 ]

Another related issue is this: a number of philosophers claim that the RGA provides a non-causal explanation (Batterman 2002, 2010a; Reutlinger 2014). As we have seen, Strevens denies that there are non-causal explanations in his extended sense of “causal” but, in addition, if it is thought the RGA implements Strevens’ abstraction procedure, this raises the question of whether (contrary to Strevens’ expectations) this procedure can take causal information as input and yield a non-causal explanation as output. A contrary view, which may be Strevens’, is that as long as the explanation is the result of applying the kairetic procedure to causal input, that result must be causal.

The issue that we have been addressing so far has to do with whether causal contiguity is a defensible requirement to impose on upper-level explanations. There is also a related question – assuming that the requirement is defensible, how can we tell whether it is satisfied? The contiguity requirement as well as the whole abstraction procedure with which it is associated is characterized with reference to fundamental physics but, as we have noted, users of upper-level explanations usually have little or no knowledge of how to connect these with the underlying physics. If Strevens’ model is to be applicable to the assessment of upper-level explanations it must be possible to tell, from the vantage point of those explanations and the available information that surrounds their use, whether they satisfy the contiguity and other requirements but without knowing in detail how they connect to the underlying physics. Strevens clearly thinks this is possible (as he should, given his views) and in some cases this seems plausible. For example, it seems fairly plausible, as we take Strevens to assume, that predator/prey pairs consisting of lions and zebras are disparate from pairs consisting of spiders and house flies from the point of view of the underlying physics and thus constitute heterogeneous realizers of the LV equations. [ 10 ] On the other hand, in a case of pre-emption in which Billy’s rock shatters a bottle very shortly before Suzy’s rock arrives at the same space, Strevens seems committed to the claim that these two causal processes are non-contiguous – indeed he needs this result to avoid counting Suzy’s throw as a cause of the shattering [ 11 ] (Non-contiguity must hold even if the throws involve rocks with the same mass and velocity following very similar trajectories, differing only slightly in their timing.) In other examples, Strevens claims that airfoils of different flexibility and different materials satisfy the contiguity constraint, as do different molecular scattering processes in gases – apparently this is so even if the latter are governed by rather different potential functions (as they sometimes are) (Strevens 2008: 165–6). The issue here is not that these judgments are obviously wrong but rather that one would like to have a more systematic and principled story about the basis on which they are to be made.

That said, we think that Strevens has put his finger on an important issue that deserves more philosophical attention. This is that there is something explanatorily puzzling or incomplete about a stable upper-level generalization that appears to have very disparate realizers: one naturally wants a further explanation of how this comes about – one that does not leave it as a kind of unexplained coincidence that this uniformity of behavior occurs. [ 12 ] The RGA purports to do this for certain aspects of behavior around critical points and it does not seem unreasonable to hope for accounts (perhaps involving some apparatus very different from the RGA) for other cases. What is less clear is whether such an explanation will always appeal to causal contiguity at the level of fundamental physics – for example in the case of the RGA the relevant factors (and where causal contiguity appears to obtain) are relatively abstract and high-level, although certainly “physical”.

Interventionist theories are intended both as theories of causation and of causal explanation. Here we provide only a very quick overview of the former, referring readers to the entry causation and manipulability for more detailed discussion of the former and instead focus on causal explanation. Consider a causal claim (generalization) of the form

where “ C ” and “ E ” are variables – that is, they refer to properties or quantities that can take at least two values. Examples are “forces cause accelerations” and “Smoking causes lung cancer”. According to interventionist accounts (G) is true if and only if there is a possible intervention I such that if I were to change the value of C , the value of E or the probability distribution of E would change (Woodward 2003). The notion of an intervention is described in more detail in the causation and manipulability entry, but the basic idea is that this is an unconfounded experimental manipulation of C that changes E , if at all, via a route that goes through C and not in any other way. Counterfactuals that describe would happen if an intervention were to be performed are called interventionist counterfactuals . A randomized experiment provides one paradigm of an intervention.

Causal explanations can take several different forms within an interventionist framework [ 13 ] – for instance, a causal explanation of some explanandum \(E =e\) requires:

and also meeting the condition

By meeting these conditions (and especially in virtue of satisfying (3.3)) an explanation answers what Woodward (2003) calls “what-if-things-had-been-different questions” (w-questions) about E – it tells us how E would have been different under changes in the values of the C variable from the value specified in (3.2).

As an example, consider an explanation of why the strength (E) of the electrical field created by a long straight wire along which the charge is uniformly distributed is described by \(E= \lambda/2 \pi r \epsilon_{o}\) where \(\lambda\) is the charge density and \(r\) is the distance from the wire. An explanation of this can be constructed by appealing to Coulomb’s law (playing the role of (3.1) above) in conjunction with information about the shape of the wire and the charge distribution along it ( (3.2) above). This information allows for the derivation of \(E= \lambda/2 \pi r \epsilon_{o}\) but it also can be used to provide answers to a number of other w-questions. For example, Coulomb’s law and a similar modeling strategy can be used to answer questions about what the field would be if the wire had a different shape (e.g., if twisted to form a loop) or if it was somehow flattened into a plane or deformed into a sphere.

The condition that the explanans answer a range of w-questions is intended to capture the requirement that the explanans must be explanatorily relevant to the explanandum. That is, factors having to do with the charge density and the shape of the conductor are explanatorily relevant to the field intensity because changes in these factors would lead to changes in the field intensity. Other factors such as the color of the conductor are irrelevant and should be omitted from the explanation because changes in them will not lead to changes in the field intensity. As an additional illustration, consider Salmon’s (1971a: 34) example of a purported explanation of ( F ) a male’s failure to get pregnant that appeals to his taking birth control pills ( B ). Intuitively ( B ) is explanatorily irrelevant to ( F ). The interventionist model captures this by observing that B fails to satisfy the what-if-things-had-been-different requirement with respect to F : F would not change if B were to change. (Note the contrast with the rather different way in which the kairetic model captures explanatory relevance.)

Another key idea of the interventionist model is the notion of invariance of a causal generalization (Woodward & Hitchcock 2003). Consider again a generalization (G) relating \(C\) to \(E\), \(E= f(C)\). As we have seen, for (G) to describe a causal relationship at all it must at least be the case that (G) correctly tells how E would change under at least some interventions on C . However, causal generalizations can vary according to the range of interventions over which this is true. It might be that (G) correctly describes how E would change under some substantial range R of interventions that set C to different values or this might instead be true only for some restricted range of interventions on C . The interventions on C over which (G) continues to hold are the interventions over which (G) is invariant. As an illustration consider a type of spring for which the restoring force F under extensions X is correctly described by Hooke’s law:

for some range R of interventions on X . Extending the spring too much will cause it to break so that its behavior will no longer be described by Hooke’s law. (3.4) is invariant under interventions in R but not so for interventions outside of R . (3.4) is, intuitively, invariant only under a somewhat narrow range of interventions. Contrast (3.4) with the gravitational inverse square law:

(3.5) is invariant under a rather wide range of interventions that set \(m_1,\) \(m_2,\) and \(r\) to different values but there are also values for these variables for which (3.5) fails to hold – e.g., values at which general relativistic effects become important. Moreover, invariance under interventions is just one variety of invariance. One may also talk about the invariance of a generalization under many other sorts of changes – for example, changes in background conditions, understood as conditions that are not explicitly included in the generalization itself. As an illustration, the causal connection between smoking and lung cancer holds for subjects with different diets, in different environmental conditions, with different demographic characteristics and so on. [ 14 ] However, as explained below, it is invariance under interventions that is most crucial to evaluating whether an explanation is good or deep within the interventionist framework.

Given the account of causal explanation above it follows that for a generalization to figure in a causal explanation it must be invariant under at least some interventions. As a general rule a generalization that is invariant under a wider range of interventions and other changes will be such that it can be used to answer a wider range of w-questions. (See section 4 below.) In this respect such a generalization might be regarded as having superior explanatory credentials – it at least explains more than generalizations with a narrower range of invariance. Generalizations that are invariant under a very wide range of interventions and that have the sort of mathematical formulation that allows for precise predictions are those that we tend to regard as laws of nature. Generalizations that have a narrower range of invariance like Hooke’s “law” capture causal information but are not plausible candidates for laws of nature. An interventionist model of form (3.1–3.3) above thus requires generalizations with some degree of invariance or relationships that support interventionist counterfactuals, but it does not require laws. In this respect, like the other models considered in this entry, it departs from the DN model which does require laws for successful explanation (see the entry on scientific explanation ).

Turning now to criticisms of the interventionist model, some of these are also criticisms of interventionist accounts of causation. Several of these (and particularly the delicate question of what it means for an intervention to be “possible”) are addressed if not resolved in the causation and manipulability entry.

Another criticism, not addressed in the above entry, concerns the “truth makers” or “grounds” for the interventionist counterfactuals that figure in causal explanation. Many philosophers hold that it is necessary to provide a metaphysical account of some kind for these. There are a variety of different proposals – perhaps interventionist counterfactuals or causal claims more generally are made true by “powers” or “dispositions”. Perhaps instead such counterfactuals are grounded in laws of nature, with the latter being understood in terms of some metaphysical framework, as in the Best Systems Analysis. For the most part interventionists, have declined to provide truth conditions of this sort and this has struck some metaphysically minded philosophers as a serious omission. One response is that while it certainly makes sense to ask for deeper explanations of why various interventionist counterfactuals hold, the only explanation that is needed is an ordinary scientific explanation in terms of some deeper theory, rather than any kind of distinctively “metaphysical” explanation (Woodward 2017b). For example, one might explain why the interventionist counterfactual “if I were to drop this bottle it will fall to the ground” is true by appealing to Newtonian gravitational theory and “grounding” it in this way. (There is also the task of providing a semantics for interventionist counterfactuals and here there have been a variety of proposals – see, e.g., Briggs 2012. But again, this needn’t take the form of providing metaphysical grounding.) This response raises the question of whether in addition to ordinary scientific explanations there are metaphysical explanations (of counterfactuals, laws and so on) that it is the task of philosophy to provide – a very large topic that is beyond the scope of this entry.

Yet another criticism (pressed by Franklin-Hall 2016 and Weslake 2010) is that the w-condition implies that explanations at the lowest level of detail are always superior to explanations employing upper-level variables – the argument being that lower-level explanations will always answer more w-questions than upper-level explanations. (But see Woodward (2021) for further discussion.)

Presumably all models of causal explanation (and certainly all of the models considered above) agree that a causal explanation involves the assembly of causal information that is relevant to the explanandum of interest, although different models may disagree about how to understand causation, causal relevance, and exactly what causal information is needed for explanation. There is also widespread agreement (at least among the models considered above) that causal explanations can differ in how deep or good they are. Capturing what is involved in variations in depth is thus an important task for a theory of causal explanation (or for that matter, for any theory of explanation, causal or non-causal). Unsurprisingly different treatments of causal explanation provide different accounts of what explanatory depth consists in. One common idea is that explanations that drill down (provide information) about lower-level realizing detail are (to that extent) better – this is taken to be one dimension of depth even if not the only one.

This idea is discussed by Sober (1999) in the context of reduction, multiple realizability, and causal explanations in biology. Sober suggests that lower-level details provide objectively superior explanations compared to higher-level ones and he supports this in three main ways. First, he suggests that for any explanatory target, lower-level details can always be included without detracting from an explanation. The worst offense committed by this extra detail is that it “explains too much,” while the same cannot be said for higher-level detail (Sober 1999: 547). Second, Sober claims that lower-level details do the “work” in producing higher-level phenomena and that this justifies their privilege or priority in explanations. A similar view is expressed by Waters, who claims that higher-level detail, while more general, provides “shallow explanations” compared to the “deeper accounts” provided by lower-level detail (1990: 131). A third reason is that physics has a kind of “causal completeness” that other sciences do not have. It is argued that this causal completeness provides an objective measure of explanatory strength, in contrast to the more “subjective” measures sometimes invoked in defenses of the explanatory credentials of upper level-sciences. As Sober (1999: 561) puts it,

illumination is to some degree in the eye of the beholder; however, the sense in which physics can provide complete explanations is supposed to be perfectly objective.

Furthermore,

if singular occurrences can be explained by citing their causes, then the causal completeness of physics [ensures] that physics has a variety of explanatory completeness that other sciences do not possess. (1999: 562)

Cases where some type-level effect (e.g., a disease) has a shared causal etiology at higher-levels, but where this etiology is multiply-realized at lower ones present challenges for such views (Ross 2020). In Sober’s example, “smoking causes lung cancer” is a higher-level (macro) causal relationship. He suggests that lower-level realizers of smoking (distinct carcinogens) provide deeper explanations of this outcome. One problem with this claim is that any single lower-level carcinogen only “makes a difference to” and explains a narrow subset of all cases of the disease. By contrast, the higher-level causal factor “smoking” makes a difference to all (or most) cases of this disease. This is reflected in the fact that biomedical researchers and nonexperts appeal to smoking as the cause of lung cancer and explicitly target smoking cessation in efforts to control and prevent this disease. This suggests that there can be drawbacks to including too much lower-level detail.

The kairetic theory also incorporates, in some respects, the idea that explanatory depth is connected to tracking lower-level detail. This is reflected in the requirement that deeper explanations are those that are cohesive with respect to fundamental physics – at the very least we will be in a better position to see that this requirement is satisfied when there is supporting information about low-level realizers. [ 15 ] On the other hand, as we have seen, the kairetic abstraction procedure taken in itself pushes away from the inclusion of specific lower-level detail in the direction of greater generality which, in some form or other, is also regarded by most as a desirable feature in explanations, the result being a trade-off between these two desiderata. The role of lower-level detail is somewhat different in mechanistic models since in typical formulations generality per se is not given independent weight, and depth is associated with the provision of more rather than less relevant detail. Of course a great deal depends on what is meant by “relevant detail”. As noted above, this issue is taken up by Craver in several papers, including most recently, Craver and Kaplan (2020) who discuss what they call “norms of completeness” for mechanistic explanations, the idea being that there needs to be some “stopping point” at which a mechanistic explanation is complete in the sense that no further detail needs to be provided. Clearly, whatever “relevant detail” in this connection means it cannot mean all factors any variation in which would make a difference to some feature of the phenomenon P which is the explanatory target. After all, in a molecular level explanation of some P , variations at the quantum mechanical level – say in the potential functions governing the behavior of individual atoms will often make some difference to P , thus requiring (on this understanding of relevance) the addition of this information. Typically, however, such an explanation is taken by mechanists to be complete just at the molecular level – no need to drill down further. Similarly, from a mechanistic point of view an explanation T of the behavior of a gas in terms of thermodynamic variables like pressure and temperature is presumably less than fully adequate since the gas laws are regarded by some if not most mechanists as merely “phenomenological” and not as describing a mechanism. A statistical mechanical explanation (SM) of the behavior of the gas is better qua mechanistic explanation but ordinarily such explanations don’t advert to, say, the details of the potentials (DP) governing molecular interactions, even though variations in these would make some difference to some aspects of the behavior of the gas. The problem is thus to describe a norm of completeness that allows one to say that SM is superior to T without requiring DP rather than SM. Craver and Kaplan’s discussion (2020) is complex and we will not try to summarize it further here except to say that it does try to find this happy medium of capturing how a norm of completeness can be met, despite its being legitimate to omit some detail.

A closely related issue is this: fine-grained details can be relevant to an explanandum in the sense that variations in those details may make a difference to the explanandum but it can also be the case that those details sometimes can be “screened off” from or rendered conditionally irrelevant to this explanandum (or approximately so) by other, more coarse grained variables that provide less detail, as described in Woodward 2021. For example, thermodynamic variables can approximately screen off statistical mechanical variables from one another. In such a case is it legitimate to omit (do norms about completeness permit omitting) the more fine-grained details as long as the more coarse-grained but screening off detail is included?

Interventionist accounts, at least in the form described by Woodward (2003), Hitchcock and Woodward (2003) offer a somewhat different treatment of explanatory depth. Some candidate explanations will answer no w-questions and thus fail to be explanatory at all. Above this threshold explanations may differ in degree of goodness or depth, depending on the extent to which they provide more rather than less information relevant to answering w-questions about the explanandum – and thus more information about what the explanandum depends on. For example, an explanation of the behavior of a body falling near the earth’s surface in terms of Galileo’s law \(v=gt\) is less deep than an explanation in terms of the Newtonian law of gravitation since the latter makes explicit how the rate of fall depends on the mass of the earth and the distance of the body above the earth’s surface. That is, the Newtonian explanation provides answers to questions about how the velocity of the fall would have been different if the mass of the earth had been different, if the body was falling some substantial distance away from the earth’s surface and so on, thus answering more w-questions than the explanation appealing to Galileo’s law.

This account associates generality with explanatory depth but this connection holds only for a particular kind of generality. Consider the conjunction of Galileo’s law and Boyle’s law. In one obvious sense, this conjunction is more general than either Galileo’s law or Boyle’s law taken alone – more systems will satisfy either the antecedent of Galileo’s law or the antecedent of Boyle’s law than one of these generalizations alone. On the other hand, given an explanandum having to do with the pressure P exerted by a particular gas, the conjunctive law will tell us no more about what P depends on than Boyle’s law by itself does. In other words, the addition of Galileo’s law does not allow us to answer any additional w-questions about the pressure than are answered by Boyle’s law alone. For this reason, this version of interventionism judges that the conjunctive law does not provide a deeper explanation of P than Boyle’s law despite the conjunctive law being in one sense more general (Hitchcock & Woodward 2003).

To develop this idea in a bit more detail, let us say that the scope of a generalization has to do with the number of different systems or kinds of systems to which the generalization applies (in the sense that the systems satisfy the antecedent and consequents of the generalization). Then the interventionist analysis claims that greater scope per se does not contribute to explanatory depth. The conjunction of Galileo’s and Boyle’s law has greater scope than either law alone, but it does not provide deeper explanations.

As another, perhaps more controversial, illustration consider a set of generalizations N1 that successfully explain (by interventionist criteria) the behavior of a kind of neural circuit found only in a certain kind K of animal. Would the explanatory credentials of N1 or the depth of the explanations it provides be improved if this kind of neural circuit was instead found in many different kinds of animals or if N1 had many more instances? According to the interventionist treatment of depth under consideration, the answer to this question is “no” (Woodward 2003: 367). Such an extension of the application of N1 is a mere increase in scope. Learning that N1 applies to other kinds of animals does not tell us anything more about what the behavior of the original circuit depends on than if N1 applied just to a single kind of animal.

It is interesting that philosophical discussions of the explanatory credentials of various generalizations often assume (perhaps tacitly) that greater scope (or even greater potential scope in the sense that there are possible – perhaps merely metaphysically possible – but not actual systems to which the generalization would apply) per se contributes to explanatory goodness. For example, Fodor and many others argue for the explanatory value of folk psychology on the grounds that its generalizations apply not just to humans but would apply to other systems with the appropriate structure were these to exist (perhaps certain AI systems, Martians if appropriately similar to humans etc.) (Fodor 1981: 8–9). The interventionist treatment of depth denies there is any reason to think the explanatory value of folk psychology would be better in the circumstances imagined above than if it applied only to humans. As another illustration, Weslake (2010) argues that upper-level generalizations can provide better or deeper explanations of the same explananda than lower-level generalizations if there are physically impossible [but metaphysically possible] systems to which the upper-level explanation applies but to which the lower-level explanation does not (2010: 287), the reason being that in such cases the upper- level explanation is more general in the sense of applying to a wider variety of systems. Suppose for example, that for some systems governed by the laws of thermodynamics, the underlying micro theory is Newtonian mechanics and for other “possible” or actual systems governed by the same thermodynamic laws, the correct underlying micro-theory is quite different. Then, according to Weslake, thermodynamics provides a deeper explanation than the either of the two micro-theories. This is also an argument that identifies greater depth with greater scope. The underlying intuition about depth here is, so to speak, the opposite of Strevens’ since he would presumably draw the conclusion that in this scenario the generalizations of thermodynamics would lack causal cohesion if the different realizing microsystems were actual.

This section has focused on recent discussion of the roles played by the provision of more underlying detail, and generality (in several interpretations of that notion) in assessments of the depth of causal explanation. It is arguable that there are a number of other dimensions of depth that we do not discuss – readers are referred to Glymour (1980), Wigner (1967), Woodward (2010), Deutsch (2011) among many others.

We noted above that there has been considerable recent interest in the question of whether there are non-causal explanations (of the “why” variety) or whether instead all explanations are causal. Although this entry does not discuss non-causal explanations in detail, this issue raises the question of whether there is anything general that might be said about what makes an explanation “causal” as opposed to “non-causal”. In what follows we review some proposals about the causal/non-causal contrast, including ideas that abstract somewhat from the details of the theories described in previous sections.

We will follow the philosophical literature on this topic by focusing on candidate explanations that target empirical explananda within empirical science but (it is claimed) explain these non-causally. These contrast with explanations within mathematics, as when some mathematical proofs are regarded as explanatory (of mathematical facts). Accounts of non-causal explanation in empirical science typically focus on explanatory factors that seem “mathematical”, that abstract from lower-level causal details, and/or that are related to the explanatory target via dependency relations that are (in some sense) non-empirical, even though the explanatory target appears to be an empirical claim. A common suggestion is that explanations exhibiting one or more of these features, qualify as non-causal. Purported examples include appeals to mathematical facts to explain various traits in biological systems, such as the prime-number life cycles of cicadas, the hexagonal-shape of the bee’s honeycomb, and the fact that seeds on a sunflower head are described by the golden angle (Baker 2005; Lyon & Colyvan 2008; Lyon 2012). An additional illustration is Lange’s claim (e.g., 2013: 488) that one can explain why 23 strawberries cannot be evenly divided among three children by appealing to the mathematical fact that 23 is not evenly divisible by three. It is claimed that in these cases, explaining the outcome of interest requires appealing to mathematical relationships, which are distinct from causal relationships, in the sense that the former are non-contingent and part of some mathematical theory (e.g., arithmetic, geometry, graph theory, calculus) or a consequence of some mathematical axiom system.

A closely related idea is that in addition to appealing to mathematical relationships, non-causal explanations abstract from lower-level detail, with the implication that although these details may be causal, they are unnecessary for the explanation which is consequently taken to be non-causal. The question of whether it is possible to traverse each bridge in the city of Königsberg exactly once (hereafter just “traverse”) is a much-discussed example. Euler provided a mathematical proof that whether such traversability is possible depends on higher-level topological or graph-theoretical properties concerning the connectivity of the bridges, as opposed to any lower-level causal details of the system (Euler 1736 [1956]; Pincock 2012). This explanatory pattern is similar to other topological or network explanations in the literature, which explain despite abstracting from lower-level causal detail (Huneman 2012; Kostic 2020; Ross 2021b). Other candidates for non-causal explanations are minimal model explanations, in which the removal of at least some or perhaps all causal detail is used to explain why systems which differ microphysically all exhibit the same behavior in some respects (Batterman 2002; Chirimuuta 2014; Ross 2015; and the entry on models in science ).

Still other accounts (not necessarily inconsistent with those described above) attempt to characterize some non-causal explanations in terms of the absence of other features (besides those described above). Woodward (2018) discusses two types of cases.

An example of (5.1) is a purported explanation relating the possibility of stable planetary orbits to the dimensionality of space – given natural assumptions, stable orbits are possible in a three-dimensional space but not possible in a space of dimensionality greater than three, so that the possibility of stable orbits in this sense seems to depend on the dimensionality of space. (For discussion see Ehrenfest 1917; Büchel 1963 [1969]; Callendar 2005). Assuming it is not possible to intervene to change the dimensionality of space, this explanation (if that is what it is) is treated as non-causal within an interventionist framework because of this impossibility. In other words, the distinction between explanations that appeal to factors that are targets of possible interventions and those that appeal to factors that are not targets of possible interventions is taken to mark one dividing line between causal and non-causal explanations.

In the second set of cases (5.2) , there are factors cited in the explanans that can be changed under interventions but the relationship between this property and the explanandum is non-contingent and “mathematical”. For example, it is certainly possible to intervene to change the configuration of bridges in Königsberg and in this way to change their traversability but the relation between the bridge configuration and their traversability is, as we have seen, non-contingent. Many of the examples mentioned earlier – the cicada, honeybee, and sunflower cases – are similar. In these cases, the non-contingent character of the dependency relation between explanans and explanandum is claimed to mark off these explanations as non-causal.

A feature of many of the candidates for non-causal explanation discussed above (and arguably another consideration that distinguishes causal from non-causal explanations) is that the non-causal explanations often seem to explain why some outcome is possible or impossible (e.g., why stable orbits are possible or impossible in spaces of different dimensions, why it is possible or not to traverse various configurations of bridges). By contrast it seems characteristic of causal explanations that they are concerned with a range of outcomes all of which are taken to be possible and instead explain why one such outcome in contrast to an alternative is realized (why an electric field has a certain strength rather than some alternative strength.)

While many have taken the above examples to represent clear cases of non-causal, mathematical explanation, others have argued that these explanations remain causal through-and-through. One example of this expansive position about causal explanation is Strevens (2018). According to Strevens, the Königsberg and other examples are cases in which mathematics plays a merely representational role, for example the role of representing difference-makers that dictate the movement of causal processes in the world. Strevens refers to these as “non-tracking” explanations, which identify limitations on causal processes that can explain their final outcome, but not the exact path taken to them (Strevens 2018: 112). For Strevens the topological structure represented in the Königsberg’s case captures information about causal structure or the web of causal influence – in this way the information relevant to the explanation, although abstract, is claimed to be causal. While this argument is suggestive, one open question is how the kairetic account can capture the fact that some of these cases involve explanations of impossibilities, where the source of the impossibility is not obviously “structural” (Lange 2013, 2016). For example, the impossibility of evenly dividing 23 by 3 does not appear to be a consequence of the way in which a structure influences some causal process. [ 16 ]

In addition to the examples and considerations just described, the philosophical literature contains many other proposed contrasts between causal and non-causal explanations, with accompanying claims about how to classify particular cases. For example, Sober (1983) claims that “equilibrium explanations” are non-causal. These are explanations in which an outcome is explained by showing that, because it is an equilibrium (or better, a unique equilibrium) , any one of a large number of different more specific processes would have led to that outcome. As an illustration, for sexually reproducing populations meeting certain additional conditions (see below), natural selection will produce an equilibrium in which there are equal numbers of males and females, although the detailed paths by which this outcome is produced (which conception events lead to males or females) will vary on different occasions. The underlying intuition here is that causal explanations are those that track specific trajectories or concrete processes, while equilibrium explanations do not do this. By contrast the kairetic theory treats at least some equilibrium explanations as causal in an extended sense (Strevens 2008: 267). Interventionist accounts at least in form described in Woodward (2003) also take equilibrium explanations to be causal to the extent that information is provided about what the equilibrium itself depends on. (That is, the interventionist framework takes the explanandum to be why this equilibrium rather than some alternative equilibrium obtains.) For example, the sex ratio equilibrium depends on such factors as the amount of parental investment required to produce each sex. Differences in required investment can lead to equilibria in which there are unequal numbers of males and females. On interventionist accounts, parental investment is thus among the causes of the sex ratio because it makes a difference for which equilibrium is realized. Interventionist accounts are able to reach this conclusion because they treat relatively “abstract” factors like parental investment as causes as long as interventions on these are systematically associated with associated with changes in outcomes. Thus, in contrast to some of the accounts described above, interventionism does not regard the abstractness per se of an explanatory factor as a bar to interpreting it as causal.

There has also been considerable discussion of whether computational explanations of the sort found in cognitive psychology and cognitive neuroscience that relate inputs to outputs via computations are causal or mechanistic. Many advocates (Piccinini 2006; Piccinini & Craver 2011) of mechanistic models of explanation have regarded such explanations as at best mechanism sketches, since they say little or nothing about realizing (e.g., neurobiological) detail. Since these writers tend to treat “mechanistic explanation”, “causal explanation” and even “explanation” as co-extensional, at least in the biomedical sciences, they seem to leave no room for a notion of non-causal explanation. By contrast computational explanations count as causal by interventionist lights as long as they correctly describe how outputs vary under interventions on inputs (Rescorla 2014). But other analyses of computational models suggest that they are similar to non-causal forms of explanation (Chirimuuta 2014, 2018).

Besides the authors discussed above, there is a great deal of additional recent work related to causal explanation that we lack the space to discuss. For additional work on the role of abstraction and idealization in causal explanation (and whether the presence of various sorts of abstraction and idealization in an explanation implies that it is non-causal) see Janssen and Saatsi (2019), Reutlinger and Andersen (2016), Blanchard (2020), Rice (2021), and Pincock (2022). Another set of issues that has received a great deal of recent attention concerns causal explanation in contexts in which different “levels” are present (Craver & Bechtel 2007; Baumgartner 2010; Woodward 2020) This literature addresses questions of the following sort. Can there be “upper-level” causation at all or does all causal action occur at some lower, microphysical level, with upper-level variables being casually inert? Can there be “cross-level” causation – e.g., “downward” causation from upper to lower levels? Finally, in addition to the work on explanatory depth discussed in Section 4 , there has been a substantial amount of recent work on distinctions among different sorts of causal claims (Woodward 2010; Ross 2021a; Ross & Woodward 2022) and on what makes some causes more explanatorily significant than others (e.g., Potochnik 2015).

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• Ney, Alyssa, 2009, “Physical Causation and Difference-Making”, The British Journal for the Philosophy of Science , 60(4): 737–764. doi:10.1093/bjps/axp037
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• –––, 2022, “Concrete Scale Models, Essential Idealization, and Causal Explanation ”, The British Journal for the Philosophy of Science , 73(2): 299–323. doi:10.1093/bjps/axz019
• Rathkopf, Charles, 2018, “Network Representation and Complex Systems”, Synthese , 195(1): 55–78. doi:10.1007/s11229-015-0726-0
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• Rice, Collin, 2021, Leveraging Distortions: Explanation, Idealization, and Universality in Science , Cambridge, MA: The MIT Press.
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• –––, forthcoming, “Cascade versus Mechanism: The Diversity of Causal Structure in Science”, The British Journal for the Philosophy of Science , first online: 5 December 2022. doi:10.1086/723623
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causal models | causation: and manipulability | causation: regularity and inferential theories of | mathematical: explanation | models in science | scientific explanation

Acknowledgments

Thanks to Carl Craver, Michael Strevens and an anonymous referee for helpful comments on a draft of this entry.

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A Practical Guide to Writing Quantitative and Qualitative Research Questions and Hypotheses in Scholarly Articles

Edward barroga.

1 Department of General Education, Graduate School of Nursing Science, St. Luke’s International University, Tokyo, Japan.

Glafera Janet Matanguihan

2 Department of Biological Sciences, Messiah University, Mechanicsburg, PA, USA.

The development of research questions and the subsequent hypotheses are prerequisites to defining the main research purpose and specific objectives of a study. Consequently, these objectives determine the study design and research outcome. The development of research questions is a process based on knowledge of current trends, cutting-edge studies, and technological advances in the research field. Excellent research questions are focused and require a comprehensive literature search and in-depth understanding of the problem being investigated. Initially, research questions may be written as descriptive questions which could be developed into inferential questions. These questions must be specific and concise to provide a clear foundation for developing hypotheses. Hypotheses are more formal predictions about the research outcomes. These specify the possible results that may or may not be expected regarding the relationship between groups. Thus, research questions and hypotheses clarify the main purpose and specific objectives of the study, which in turn dictate the design of the study, its direction, and outcome. Studies developed from good research questions and hypotheses will have trustworthy outcomes with wide-ranging social and health implications.

INTRODUCTION

Scientific research is usually initiated by posing evidenced-based research questions which are then explicitly restated as hypotheses. 1 , 2 The hypotheses provide directions to guide the study, solutions, explanations, and expected results. 3 , 4 Both research questions and hypotheses are essentially formulated based on conventional theories and real-world processes, which allow the inception of novel studies and the ethical testing of ideas. 5 , 6

It is crucial to have knowledge of both quantitative and qualitative research 2 as both types of research involve writing research questions and hypotheses. 7 However, these crucial elements of research are sometimes overlooked; if not overlooked, then framed without the forethought and meticulous attention it needs. Planning and careful consideration are needed when developing quantitative or qualitative research, particularly when conceptualizing research questions and hypotheses. 4

There is a continuing need to support researchers in the creation of innovative research questions and hypotheses, as well as for journal articles that carefully review these elements. 1 When research questions and hypotheses are not carefully thought of, unethical studies and poor outcomes usually ensue. Carefully formulated research questions and hypotheses define well-founded objectives, which in turn determine the appropriate design, course, and outcome of the study. This article then aims to discuss in detail the various aspects of crafting research questions and hypotheses, with the goal of guiding researchers as they develop their own. Examples from the authors and peer-reviewed scientific articles in the healthcare field are provided to illustrate key points.

DEFINITIONS AND RELATIONSHIP OF RESEARCH QUESTIONS AND HYPOTHESES

A research question is what a study aims to answer after data analysis and interpretation. The answer is written in length in the discussion section of the paper. Thus, the research question gives a preview of the different parts and variables of the study meant to address the problem posed in the research question. 1 An excellent research question clarifies the research writing while facilitating understanding of the research topic, objective, scope, and limitations of the study. 5

On the other hand, a research hypothesis is an educated statement of an expected outcome. This statement is based on background research and current knowledge. 8 , 9 The research hypothesis makes a specific prediction about a new phenomenon 10 or a formal statement on the expected relationship between an independent variable and a dependent variable. 3 , 11 It provides a tentative answer to the research question to be tested or explored. 4

Hypotheses employ reasoning to predict a theory-based outcome. 10 These can also be developed from theories by focusing on components of theories that have not yet been observed. 10 The validity of hypotheses is often based on the testability of the prediction made in a reproducible experiment. 8

Conversely, hypotheses can also be rephrased as research questions. Several hypotheses based on existing theories and knowledge may be needed to answer a research question. Developing ethical research questions and hypotheses creates a research design that has logical relationships among variables. These relationships serve as a solid foundation for the conduct of the study. 4 , 11 Haphazardly constructed research questions can result in poorly formulated hypotheses and improper study designs, leading to unreliable results. Thus, the formulations of relevant research questions and verifiable hypotheses are crucial when beginning research. 12

CHARACTERISTICS OF GOOD RESEARCH QUESTIONS AND HYPOTHESES

Excellent research questions are specific and focused. These integrate collective data and observations to confirm or refute the subsequent hypotheses. Well-constructed hypotheses are based on previous reports and verify the research context. These are realistic, in-depth, sufficiently complex, and reproducible. More importantly, these hypotheses can be addressed and tested. 13

There are several characteristics of well-developed hypotheses. Good hypotheses are 1) empirically testable 7 , 10 , 11 , 13 ; 2) backed by preliminary evidence 9 ; 3) testable by ethical research 7 , 9 ; 4) based on original ideas 9 ; 5) have evidenced-based logical reasoning 10 ; and 6) can be predicted. 11 Good hypotheses can infer ethical and positive implications, indicating the presence of a relationship or effect relevant to the research theme. 7 , 11 These are initially developed from a general theory and branch into specific hypotheses by deductive reasoning. In the absence of a theory to base the hypotheses, inductive reasoning based on specific observations or findings form more general hypotheses. 10

TYPES OF RESEARCH QUESTIONS AND HYPOTHESES

Research questions and hypotheses are developed according to the type of research, which can be broadly classified into quantitative and qualitative research. We provide a summary of the types of research questions and hypotheses under quantitative and qualitative research categories in Table 1 .

Research questions in quantitative research

In quantitative research, research questions inquire about the relationships among variables being investigated and are usually framed at the start of the study. These are precise and typically linked to the subject population, dependent and independent variables, and research design. 1 Research questions may also attempt to describe the behavior of a population in relation to one or more variables, or describe the characteristics of variables to be measured ( descriptive research questions ). 1 , 5 , 14 These questions may also aim to discover differences between groups within the context of an outcome variable ( comparative research questions ), 1 , 5 , 14 or elucidate trends and interactions among variables ( relationship research questions ). 1 , 5 We provide examples of descriptive, comparative, and relationship research questions in quantitative research in Table 2 .

Hypotheses in quantitative research

In quantitative research, hypotheses predict the expected relationships among variables. 15 Relationships among variables that can be predicted include 1) between a single dependent variable and a single independent variable ( simple hypothesis ) or 2) between two or more independent and dependent variables ( complex hypothesis ). 4 , 11 Hypotheses may also specify the expected direction to be followed and imply an intellectual commitment to a particular outcome ( directional hypothesis ) 4 . On the other hand, hypotheses may not predict the exact direction and are used in the absence of a theory, or when findings contradict previous studies ( non-directional hypothesis ). 4 In addition, hypotheses can 1) define interdependency between variables ( associative hypothesis ), 4 2) propose an effect on the dependent variable from manipulation of the independent variable ( causal hypothesis ), 4 3) state a negative relationship between two variables ( null hypothesis ), 4 , 11 , 15 4) replace the working hypothesis if rejected ( alternative hypothesis ), 15 explain the relationship of phenomena to possibly generate a theory ( working hypothesis ), 11 5) involve quantifiable variables that can be tested statistically ( statistical hypothesis ), 11 6) or express a relationship whose interlinks can be verified logically ( logical hypothesis ). 11 We provide examples of simple, complex, directional, non-directional, associative, causal, null, alternative, working, statistical, and logical hypotheses in quantitative research, as well as the definition of quantitative hypothesis-testing research in Table 3 .

Research questions in qualitative research

Unlike research questions in quantitative research, research questions in qualitative research are usually continuously reviewed and reformulated. The central question and associated subquestions are stated more than the hypotheses. 15 The central question broadly explores a complex set of factors surrounding the central phenomenon, aiming to present the varied perspectives of participants. 15

There are varied goals for which qualitative research questions are developed. These questions can function in several ways, such as to 1) identify and describe existing conditions ( contextual research question s); 2) describe a phenomenon ( descriptive research questions ); 3) assess the effectiveness of existing methods, protocols, theories, or procedures ( evaluation research questions ); 4) examine a phenomenon or analyze the reasons or relationships between subjects or phenomena ( explanatory research questions ); or 5) focus on unknown aspects of a particular topic ( exploratory research questions ). 5 In addition, some qualitative research questions provide new ideas for the development of theories and actions ( generative research questions ) or advance specific ideologies of a position ( ideological research questions ). 1 Other qualitative research questions may build on a body of existing literature and become working guidelines ( ethnographic research questions ). Research questions may also be broadly stated without specific reference to the existing literature or a typology of questions ( phenomenological research questions ), may be directed towards generating a theory of some process ( grounded theory questions ), or may address a description of the case and the emerging themes ( qualitative case study questions ). 15 We provide examples of contextual, descriptive, evaluation, explanatory, exploratory, generative, ideological, ethnographic, phenomenological, grounded theory, and qualitative case study research questions in qualitative research in Table 4 , and the definition of qualitative hypothesis-generating research in Table 5 .

Qualitative studies usually pose at least one central research question and several subquestions starting with How or What . These research questions use exploratory verbs such as explore or describe . These also focus on one central phenomenon of interest, and may mention the participants and research site. 15

Hypotheses in qualitative research

Hypotheses in qualitative research are stated in the form of a clear statement concerning the problem to be investigated. Unlike in quantitative research where hypotheses are usually developed to be tested, qualitative research can lead to both hypothesis-testing and hypothesis-generating outcomes. 2 When studies require both quantitative and qualitative research questions, this suggests an integrative process between both research methods wherein a single mixed-methods research question can be developed. 1

FRAMEWORKS FOR DEVELOPING RESEARCH QUESTIONS AND HYPOTHESES

Research questions followed by hypotheses should be developed before the start of the study. 1 , 12 , 14 It is crucial to develop feasible research questions on a topic that is interesting to both the researcher and the scientific community. This can be achieved by a meticulous review of previous and current studies to establish a novel topic. Specific areas are subsequently focused on to generate ethical research questions. The relevance of the research questions is evaluated in terms of clarity of the resulting data, specificity of the methodology, objectivity of the outcome, depth of the research, and impact of the study. 1 , 5 These aspects constitute the FINER criteria (i.e., Feasible, Interesting, Novel, Ethical, and Relevant). 1 Clarity and effectiveness are achieved if research questions meet the FINER criteria. In addition to the FINER criteria, Ratan et al. described focus, complexity, novelty, feasibility, and measurability for evaluating the effectiveness of research questions. 14

The PICOT and PEO frameworks are also used when developing research questions. 1 The following elements are addressed in these frameworks, PICOT: P-population/patients/problem, I-intervention or indicator being studied, C-comparison group, O-outcome of interest, and T-timeframe of the study; PEO: P-population being studied, E-exposure to preexisting conditions, and O-outcome of interest. 1 Research questions are also considered good if these meet the “FINERMAPS” framework: Feasible, Interesting, Novel, Ethical, Relevant, Manageable, Appropriate, Potential value/publishable, and Systematic. 14

As we indicated earlier, research questions and hypotheses that are not carefully formulated result in unethical studies or poor outcomes. To illustrate this, we provide some examples of ambiguous research question and hypotheses that result in unclear and weak research objectives in quantitative research ( Table 6 ) 16 and qualitative research ( Table 7 ) 17 , and how to transform these ambiguous research question(s) and hypothesis(es) into clear and good statements.

a These statements were composed for comparison and illustrative purposes only.

b These statements are direct quotes from Higashihara and Horiuchi. 16

a This statement is a direct quote from Shimoda et al. 17

The other statements were composed for comparison and illustrative purposes only.

CONSTRUCTING RESEARCH QUESTIONS AND HYPOTHESES

To construct effective research questions and hypotheses, it is very important to 1) clarify the background and 2) identify the research problem at the outset of the research, within a specific timeframe. 9 Then, 3) review or conduct preliminary research to collect all available knowledge about the possible research questions by studying theories and previous studies. 18 Afterwards, 4) construct research questions to investigate the research problem. Identify variables to be accessed from the research questions 4 and make operational definitions of constructs from the research problem and questions. Thereafter, 5) construct specific deductive or inductive predictions in the form of hypotheses. 4 Finally, 6) state the study aims . This general flow for constructing effective research questions and hypotheses prior to conducting research is shown in Fig. 1 .

Research questions are used more frequently in qualitative research than objectives or hypotheses. 3 These questions seek to discover, understand, explore or describe experiences by asking “What” or “How.” The questions are open-ended to elicit a description rather than to relate variables or compare groups. The questions are continually reviewed, reformulated, and changed during the qualitative study. 3 Research questions are also used more frequently in survey projects than hypotheses in experiments in quantitative research to compare variables and their relationships.

Hypotheses are constructed based on the variables identified and as an if-then statement, following the template, ‘If a specific action is taken, then a certain outcome is expected.’ At this stage, some ideas regarding expectations from the research to be conducted must be drawn. 18 Then, the variables to be manipulated (independent) and influenced (dependent) are defined. 4 Thereafter, the hypothesis is stated and refined, and reproducible data tailored to the hypothesis are identified, collected, and analyzed. 4 The hypotheses must be testable and specific, 18 and should describe the variables and their relationships, the specific group being studied, and the predicted research outcome. 18 Hypotheses construction involves a testable proposition to be deduced from theory, and independent and dependent variables to be separated and measured separately. 3 Therefore, good hypotheses must be based on good research questions constructed at the start of a study or trial. 12

In summary, research questions are constructed after establishing the background of the study. Hypotheses are then developed based on the research questions. Thus, it is crucial to have excellent research questions to generate superior hypotheses. In turn, these would determine the research objectives and the design of the study, and ultimately, the outcome of the research. 12 Algorithms for building research questions and hypotheses are shown in Fig. 2 for quantitative research and in Fig. 3 for qualitative research.

EXAMPLES OF RESEARCH QUESTIONS FROM PUBLISHED ARTICLES

• EXAMPLE 1. Descriptive research question (quantitative research)
• - Presents research variables to be assessed (distinct phenotypes and subphenotypes)
• “BACKGROUND: Since COVID-19 was identified, its clinical and biological heterogeneity has been recognized. Identifying COVID-19 phenotypes might help guide basic, clinical, and translational research efforts.
• RESEARCH QUESTION: Does the clinical spectrum of patients with COVID-19 contain distinct phenotypes and subphenotypes? ” 19
• EXAMPLE 2. Relationship research question (quantitative research)
• - Shows interactions between dependent variable (static postural control) and independent variable (peripheral visual field loss)
• “Background: Integration of visual, vestibular, and proprioceptive sensations contributes to postural control. People with peripheral visual field loss have serious postural instability. However, the directional specificity of postural stability and sensory reweighting caused by gradual peripheral visual field loss remain unclear.
• Research question: What are the effects of peripheral visual field loss on static postural control ?” 20
• EXAMPLE 3. Comparative research question (quantitative research)
• - Clarifies the difference among groups with an outcome variable (patients enrolled in COMPERA with moderate PH or severe PH in COPD) and another group without the outcome variable (patients with idiopathic pulmonary arterial hypertension (IPAH))
• “BACKGROUND: Pulmonary hypertension (PH) in COPD is a poorly investigated clinical condition.
• RESEARCH QUESTION: Which factors determine the outcome of PH in COPD?
• STUDY DESIGN AND METHODS: We analyzed the characteristics and outcome of patients enrolled in the Comparative, Prospective Registry of Newly Initiated Therapies for Pulmonary Hypertension (COMPERA) with moderate or severe PH in COPD as defined during the 6th PH World Symposium who received medical therapy for PH and compared them with patients with idiopathic pulmonary arterial hypertension (IPAH) .” 21
• EXAMPLE 4. Exploratory research question (qualitative research)
• - Explores areas that have not been fully investigated (perspectives of families and children who receive care in clinic-based child obesity treatment) to have a deeper understanding of the research problem
• “Problem: Interventions for children with obesity lead to only modest improvements in BMI and long-term outcomes, and data are limited on the perspectives of families of children with obesity in clinic-based treatment. This scoping review seeks to answer the question: What is known about the perspectives of families and children who receive care in clinic-based child obesity treatment? This review aims to explore the scope of perspectives reported by families of children with obesity who have received individualized outpatient clinic-based obesity treatment.” 22
• EXAMPLE 5. Relationship research question (quantitative research)
• - Defines interactions between dependent variable (use of ankle strategies) and independent variable (changes in muscle tone)
• “Background: To maintain an upright standing posture against external disturbances, the human body mainly employs two types of postural control strategies: “ankle strategy” and “hip strategy.” While it has been reported that the magnitude of the disturbance alters the use of postural control strategies, it has not been elucidated how the level of muscle tone, one of the crucial parameters of bodily function, determines the use of each strategy. We have previously confirmed using forward dynamics simulations of human musculoskeletal models that an increased muscle tone promotes the use of ankle strategies. The objective of the present study was to experimentally evaluate a hypothesis: an increased muscle tone promotes the use of ankle strategies. Research question: Do changes in the muscle tone affect the use of ankle strategies ?” 23

EXAMPLES OF HYPOTHESES IN PUBLISHED ARTICLES

• EXAMPLE 1. Working hypothesis (quantitative research)
• - A hypothesis that is initially accepted for further research to produce a feasible theory
• “As fever may have benefit in shortening the duration of viral illness, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response when taken during the early stages of COVID-19 illness .” 24
• “In conclusion, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response . The difference in perceived safety of these agents in COVID-19 illness could be related to the more potent efficacy to reduce fever with ibuprofen compared to acetaminophen. Compelling data on the benefit of fever warrant further research and review to determine when to treat or withhold ibuprofen for early stage fever for COVID-19 and other related viral illnesses .” 24
• EXAMPLE 2. Exploratory hypothesis (qualitative research)
• - Explores particular areas deeper to clarify subjective experience and develop a formal hypothesis potentially testable in a future quantitative approach
• “We hypothesized that when thinking about a past experience of help-seeking, a self distancing prompt would cause increased help-seeking intentions and more favorable help-seeking outcome expectations .” 25
• “Conclusion
• Although a priori hypotheses were not supported, further research is warranted as results indicate the potential for using self-distancing approaches to increasing help-seeking among some people with depressive symptomatology.” 25
• EXAMPLE 3. Hypothesis-generating research to establish a framework for hypothesis testing (qualitative research)
• “We hypothesize that compassionate care is beneficial for patients (better outcomes), healthcare systems and payers (lower costs), and healthcare providers (lower burnout). ” 26
• Compassionomics is the branch of knowledge and scientific study of the effects of compassionate healthcare. Our main hypotheses are that compassionate healthcare is beneficial for (1) patients, by improving clinical outcomes, (2) healthcare systems and payers, by supporting financial sustainability, and (3) HCPs, by lowering burnout and promoting resilience and well-being. The purpose of this paper is to establish a scientific framework for testing the hypotheses above . If these hypotheses are confirmed through rigorous research, compassionomics will belong in the science of evidence-based medicine, with major implications for all healthcare domains.” 26
• EXAMPLE 4. Statistical hypothesis (quantitative research)
• - An assumption is made about the relationship among several population characteristics ( gender differences in sociodemographic and clinical characteristics of adults with ADHD ). Validity is tested by statistical experiment or analysis ( chi-square test, Students t-test, and logistic regression analysis)
• “Our research investigated gender differences in sociodemographic and clinical characteristics of adults with ADHD in a Japanese clinical sample. Due to unique Japanese cultural ideals and expectations of women's behavior that are in opposition to ADHD symptoms, we hypothesized that women with ADHD experience more difficulties and present more dysfunctions than men . We tested the following hypotheses: first, women with ADHD have more comorbidities than men with ADHD; second, women with ADHD experience more social hardships than men, such as having less full-time employment and being more likely to be divorced.” 27
• “Statistical Analysis
• ( text omitted ) Between-gender comparisons were made using the chi-squared test for categorical variables and Students t-test for continuous variables…( text omitted ). A logistic regression analysis was performed for employment status, marital status, and comorbidity to evaluate the independent effects of gender on these dependent variables.” 27

EXAMPLES OF HYPOTHESIS AS WRITTEN IN PUBLISHED ARTICLES IN RELATION TO OTHER PARTS

• EXAMPLE 1. Background, hypotheses, and aims are provided
• “Pregnant women need skilled care during pregnancy and childbirth, but that skilled care is often delayed in some countries …( text omitted ). The focused antenatal care (FANC) model of WHO recommends that nurses provide information or counseling to all pregnant women …( text omitted ). Job aids are visual support materials that provide the right kind of information using graphics and words in a simple and yet effective manner. When nurses are not highly trained or have many work details to attend to, these job aids can serve as a content reminder for the nurses and can be used for educating their patients (Jennings, Yebadokpo, Affo, & Agbogbe, 2010) ( text omitted ). Importantly, additional evidence is needed to confirm how job aids can further improve the quality of ANC counseling by health workers in maternal care …( text omitted )” 28
• “ This has led us to hypothesize that the quality of ANC counseling would be better if supported by job aids. Consequently, a better quality of ANC counseling is expected to produce higher levels of awareness concerning the danger signs of pregnancy and a more favorable impression of the caring behavior of nurses .” 28
• “This study aimed to examine the differences in the responses of pregnant women to a job aid-supported intervention during ANC visit in terms of 1) their understanding of the danger signs of pregnancy and 2) their impression of the caring behaviors of nurses to pregnant women in rural Tanzania.” 28
• EXAMPLE 2. Background, hypotheses, and aims are provided
• “We conducted a two-arm randomized controlled trial (RCT) to evaluate and compare changes in salivary cortisol and oxytocin levels of first-time pregnant women between experimental and control groups. The women in the experimental group touched and held an infant for 30 min (experimental intervention protocol), whereas those in the control group watched a DVD movie of an infant (control intervention protocol). The primary outcome was salivary cortisol level and the secondary outcome was salivary oxytocin level.” 29
• “ We hypothesize that at 30 min after touching and holding an infant, the salivary cortisol level will significantly decrease and the salivary oxytocin level will increase in the experimental group compared with the control group .” 29
• EXAMPLE 3. Background, aim, and hypothesis are provided
• “In countries where the maternal mortality ratio remains high, antenatal education to increase Birth Preparedness and Complication Readiness (BPCR) is considered one of the top priorities [1]. BPCR includes birth plans during the antenatal period, such as the birthplace, birth attendant, transportation, health facility for complications, expenses, and birth materials, as well as family coordination to achieve such birth plans. In Tanzania, although increasing, only about half of all pregnant women attend an antenatal clinic more than four times [4]. Moreover, the information provided during antenatal care (ANC) is insufficient. In the resource-poor settings, antenatal group education is a potential approach because of the limited time for individual counseling at antenatal clinics.” 30
• “This study aimed to evaluate an antenatal group education program among pregnant women and their families with respect to birth-preparedness and maternal and infant outcomes in rural villages of Tanzania.” 30
• “ The study hypothesis was if Tanzanian pregnant women and their families received a family-oriented antenatal group education, they would (1) have a higher level of BPCR, (2) attend antenatal clinic four or more times, (3) give birth in a health facility, (4) have less complications of women at birth, and (5) have less complications and deaths of infants than those who did not receive the education .” 30

Research questions and hypotheses are crucial components to any type of research, whether quantitative or qualitative. These questions should be developed at the very beginning of the study. Excellent research questions lead to superior hypotheses, which, like a compass, set the direction of research, and can often determine the successful conduct of the study. Many research studies have floundered because the development of research questions and subsequent hypotheses was not given the thought and meticulous attention needed. The development of research questions and hypotheses is an iterative process based on extensive knowledge of the literature and insightful grasp of the knowledge gap. Focused, concise, and specific research questions provide a strong foundation for constructing hypotheses which serve as formal predictions about the research outcomes. Research questions and hypotheses are crucial elements of research that should not be overlooked. They should be carefully thought of and constructed when planning research. This avoids unethical studies and poor outcomes by defining well-founded objectives that determine the design, course, and outcome of the study.

Disclosure: The authors have no potential conflicts of interest to disclose.

Author Contributions:

• Conceptualization: Barroga E, Matanguihan GJ.
• Methodology: Barroga E, Matanguihan GJ.
• Writing - original draft: Barroga E, Matanguihan GJ.
• Writing - review & editing: Barroga E, Matanguihan GJ.

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• Knowledge Base

Methodology

• Correlation vs. Causation | Difference, Designs & Examples

Correlation vs. Causation | Difference, Designs & Examples

Published on July 12, 2021 by Pritha Bhandari . Revised on June 22, 2023.

Correlation means there is a statistical association between variables. Causation means that a change in one variable causes a change in another variable.

In research, you might have come across the phrase “correlation doesn’t imply causation.” Correlation and causation are two related ideas, but understanding their differences will help you critically evaluate sources and interpret scientific research.

Table of contents

What’s the difference, why doesn’t correlation mean causation, correlational research, third variable problem, regression to the mean, spurious correlations, directionality problem, causal research, other interesting articles, frequently asked questions about correlation and causation.

Correlation describes an association between types of variables : when one variable changes, so does the other. A correlation is a statistical indicator of the relationship between variables. These variables change together: they covary. But this covariation isn’t necessarily due to a direct or indirect causal link.

Causation means that changes in one variable brings about changes in the other; there is a cause-and-effect relationship between variables. The two variables are correlated with each other and there is also a causal link between them.

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There are two main reasons why correlation isn’t causation. These problems are important to identify for drawing sound scientific conclusions from research.

The third variable problem means that a confounding variable affects both variables to make them seem causally related when they are not. For example, ice cream sales and violent crime rates are closely correlated, but they are not causally linked with each other. Instead, hot temperatures, a third variable, affects both variables separately. Failing to account for third variables can lead research biases to creep into your work.

The directionality problem occurs when two variables correlate and might actually have a causal relationship, but it’s impossible to conclude which variable causes changes in the other. For example, vitamin D levels are correlated with depression, but it’s not clear whether low vitamin D causes depression, or whether depression causes reduced vitamin D intake.

You’ll need to use an appropriate research design to distinguish between correlational and causal relationships:

• Correlational research designs can only demonstrate correlational links between variables.
• Experimental designs can test causation.

In a correlational research design, you collect data on your variables without manipulating them.

Correlational research is usually high in external validity , so you can generalize your findings to real life settings. But these studies are low in internal validity , which makes it difficult to causally connect changes in one variable to changes in the other.

These research designs are commonly used when it’s unethical, too costly, or too difficult to perform controlled experiments. They are also used to study relationships that aren’t expected to be causal.

Without controlled experiments, it’s hard to say whether it was the variable you’re interested in that caused changes in another variable. Extraneous variables are any third variable or omitted variable other than your variables of interest that could affect your results.

Limited control in correlational research means that extraneous or confounding variables serve as alternative explanations for the results. Confounding variables can make it seem as though a correlational relationship is causal when it isn’t.

When two variables are correlated, all you can say is that changes in one variable occur alongside changes in the other.

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Regression to the mean is observed when variables that are extremely higher or extremely lower than average on the first measurement move closer to the average on the second measurement. Particularly in research that intentionally focuses on the most extreme cases or events, RTM should always be considered as a possible cause of an observed change.

Players or teams featured on the cover of SI have earned their place by performing exceptionally well. But athletic success is a mix of skill and luck, and even the best players don’t always win.

Chances are that good luck will not continue indefinitely, and neither can exceptional success.

A spurious correlation is when two variables appear to be related through hidden third variables or simply by coincidence.

The Theory of the Stork draws a simple causal link between the variables to argue that storks physically deliver babies. This satirical study shows why you can’t conclude causation from correlational research alone.

When you analyze correlations in a large dataset with many variables, the chances of finding at least one statistically significant result are high. In this case, you’re more likely to make a type I error . This means erroneously concluding there is a true correlation between variables in the population based on skewed sample data.

To demonstrate causation, you need to show a directional relationship with no alternative explanations. This relationship can be unidirectional, with one variable impacting the other, or bidirectional, where both variables impact each other.

A correlational design won’t be able to distinguish between any of these possibilities, but an experimental design can test each possible direction, one at a time.

• Physical activity may affect self esteem
• Self esteem may affect physical activity
• Physical activity and self esteem may both affect each other

In correlational research, the directionality of a relationship is unclear because there is limited researcher control. You might risk concluding reverse causality, the wrong direction of the relationship.

Causal links between variables can only be truly demonstrated with controlled experiments . Experiments test formal predictions, called hypotheses , to establish causality in one direction at a time.

Experiments are high in internal validity , so cause-and-effect relationships can be demonstrated with reasonable confidence.

You can establish directionality in one direction because you manipulate an independent variable before measuring the change in a dependent variable.

In a controlled experiment, you can also eliminate the influence of third variables by using random assignment and control groups.

Random assignment helps distribute participant characteristics evenly between groups so that they’re similar and comparable. A control group lets you compare the experimental manipulation to a similar treatment or no treatment (or a placebo, to control for the placebo effect ).

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Chi square test of independence
• Statistical power
• Descriptive statistics
• Degrees of freedom
• Pearson correlation
• Null hypothesis
• Double-blind study
• Case-control study
• Research ethics
• Data collection
• Hypothesis testing
• Structured interviews

Research bias

• Hawthorne effect
• Unconscious bias
• Recall bias
• Halo effect
• Self-serving bias
• Information bias

A correlation reflects the strength and/or direction of the association between two or more variables.

• A positive correlation means that both variables change in the same direction.
• A negative correlation means that the variables change in opposite directions.
• A zero correlation means there’s no relationship between the variables.

Correlation describes an association between variables : when one variable changes, so does the other. A correlation is a statistical indicator of the relationship between variables.

Causation means that changes in one variable brings about changes in the other (i.e., there is a cause-and-effect relationship between variables). The two variables are correlated with each other, and there’s also a causal link between them.

While causation and correlation can exist simultaneously, correlation does not imply causation. In other words, correlation is simply a relationship where A relates to B—but A doesn’t necessarily cause B to happen (or vice versa). Mistaking correlation for causation is a common error and can lead to false cause fallacy .

The third variable and directionality problems are two main reasons why correlation isn’t causation .

The third variable problem means that a confounding variable affects both variables to make them seem causally related when they are not.

The directionality problem is when two variables correlate and might actually have a causal relationship, but it’s impossible to conclude which variable causes changes in the other.

Controlled experiments establish causality, whereas correlational studies only show associations between variables.

• In an experimental design , you manipulate an independent variable and measure its effect on a dependent variable. Other variables are controlled so they can’t impact the results.
• In a correlational design , you measure variables without manipulating any of them. You can test whether your variables change together, but you can’t be sure that one variable caused a change in another.

In general, correlational research is high in external validity while experimental research is high in internal validity .

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• Scientific Methods

What is Hypothesis?

We have heard of many hypotheses which have led to great inventions in science. Assumptions that are made on the basis of some evidence are known as hypotheses. In this article, let us learn in detail about the hypothesis and the type of hypothesis with examples.

A hypothesis is an assumption that is made based on some evidence. This is the initial point of any investigation that translates the research questions into predictions. It includes components like variables, population and the relation between the variables. A research hypothesis is a hypothesis that is used to test the relationship between two or more variables.

Characteristics of Hypothesis

Following are the characteristics of the hypothesis:

• The hypothesis should be clear and precise to consider it to be reliable.
• If the hypothesis is a relational hypothesis, then it should be stating the relationship between variables.
• The hypothesis must be specific and should have scope for conducting more tests.
• The way of explanation of the hypothesis must be very simple and it should also be understood that the simplicity of the hypothesis is not related to its significance.

Sources of Hypothesis

Following are the sources of hypothesis:

• The resemblance between the phenomenon.
• Observations from past studies, present-day experiences and from the competitors.
• Scientific theories.
• General patterns that influence the thinking process of people.

Types of Hypothesis

There are six forms of hypothesis and they are:

• Simple hypothesis
• Complex hypothesis
• Directional hypothesis
• Non-directional hypothesis
• Null hypothesis
• Associative and casual hypothesis

Simple Hypothesis

It shows a relationship between one dependent variable and a single independent variable. For example – If you eat more vegetables, you will lose weight faster. Here, eating more vegetables is an independent variable, while losing weight is the dependent variable.

Complex Hypothesis

It shows the relationship between two or more dependent variables and two or more independent variables. Eating more vegetables and fruits leads to weight loss, glowing skin, and reduces the risk of many diseases such as heart disease.

Directional Hypothesis

It shows how a researcher is intellectual and committed to a particular outcome. The relationship between the variables can also predict its nature. For example- children aged four years eating proper food over a five-year period are having higher IQ levels than children not having a proper meal. This shows the effect and direction of the effect.

Non-directional Hypothesis

It is used when there is no theory involved. It is a statement that a relationship exists between two variables, without predicting the exact nature (direction) of the relationship.

Null Hypothesis

It provides a statement which is contrary to the hypothesis. It’s a negative statement, and there is no relationship between independent and dependent variables. The symbol is denoted by “H O ”.

Associative and Causal Hypothesis

Associative hypothesis occurs when there is a change in one variable resulting in a change in the other variable. Whereas, the causal hypothesis proposes a cause and effect interaction between two or more variables.

Examples of Hypothesis

Following are the examples of hypotheses based on their types:

• Consumption of sugary drinks every day leads to obesity is an example of a simple hypothesis.
• All lilies have the same number of petals is an example of a null hypothesis.
• If a person gets 7 hours of sleep, then he will feel less fatigue than if he sleeps less. It is an example of a directional hypothesis.

Functions of Hypothesis

Following are the functions performed by the hypothesis:

• Hypothesis helps in making an observation and experiments possible.
• It becomes the start point for the investigation.
• Hypothesis helps in verifying the observations.
• It helps in directing the inquiries in the right direction.

How will Hypothesis help in the Scientific Method?

Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:

• Formation of question
• Doing background research
• Creation of hypothesis
• Designing an experiment
• Collection of data
• Result analysis
• Summarizing the experiment
• Communicating the results

Frequently Asked Questions – FAQs

What is hypothesis.

A hypothesis is an assumption made based on some evidence.

Give an example of simple hypothesis?

What are the types of hypothesis.

Types of hypothesis are:

• Associative and Casual hypothesis

State true or false: Hypothesis is the initial point of any investigation that translates the research questions into a prediction.

Define complex hypothesis..

A complex hypothesis shows the relationship between two or more dependent variables and two or more independent variables.

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Metabolic characteristics of gut microbiota and insomnia: evidence from a mendelian randomization analysis.

1. Introduction

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Xie, F.; Feng, Z.; Xu, B. Metabolic Characteristics of Gut Microbiota and Insomnia: Evidence from a Mendelian Randomization Analysis. Nutrients 2024 , 16 , 2943. https://doi.org/10.3390/nu16172943

Xie F, Feng Z, Xu B. Metabolic Characteristics of Gut Microbiota and Insomnia: Evidence from a Mendelian Randomization Analysis. Nutrients . 2024; 16(17):2943. https://doi.org/10.3390/nu16172943

Xie, Fuquan, Zhijun Feng, and Beibei Xu. 2024. "Metabolic Characteristics of Gut Microbiota and Insomnia: Evidence from a Mendelian Randomization Analysis" Nutrients 16, no. 17: 2943. https://doi.org/10.3390/nu16172943

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