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Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a or H 1 ).
Collect data in a way designed to test the hypothesis.
Perform an appropriate statistical test .
Decide whether to reject or fail to reject your null hypothesis.
Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

an estimate of the difference in average height between the two groups.
a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

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.

Normal distribution
Descriptive statistics
Measures of central tendency
Correlation coefficient

Methodology

Cluster sampling
Stratified sampling
Types of interviews
Cohort study
Thematic analysis

Research bias

Implicit bias
Cognitive bias
Survivorship bias
Availability heuristic
Nonresponse bias
Regression to the mean

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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Statistics By Jim

Making statistics intuitive

Hypothesis Testing: Uses, Steps & Example

By Jim Frost 4 Comments

What is Hypothesis Testing?

Hypothesis testing in statistics uses sample data to infer the properties of a whole population . These tests determine whether a random sample provides sufficient evidence to conclude an effect or relationship exists in the population. Researchers use them to help separate genuine population-level effects from false effects that random chance can create in samples. These methods are also known as significance testing.

For example, researchers are testing a new medication to see if it lowers blood pressure. They compare a group taking the drug to a control group taking a placebo. If their hypothesis test results are statistically significant, the medication’s effect of lowering blood pressure likely exists in the broader population, not just the sample studied.

Using Hypothesis Tests

A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement the sample data best supports. These two statements are called the null hypothesis and the alternative hypothesis . The following are typical examples:

Null Hypothesis : The effect does not exist in the population.
Alternative Hypothesis : The effect does exist in the population.

Hypothesis testing accounts for the inherent uncertainty of using a sample to draw conclusions about a population, which reduces the chances of false discoveries. These procedures determine whether the sample data are sufficiently inconsistent with the null hypothesis that you can reject it. If you can reject the null, your data favor the alternative statement that an effect exists in the population.

Statistical significance in hypothesis testing indicates that an effect you see in sample data also likely exists in the population after accounting for random sampling error , variability, and sample size. Your results are statistically significant when the p-value is less than your significance level or, equivalently, when your confidence interval excludes the null hypothesis value.

Conversely, non-significant results indicate that despite an apparent sample effect, you can’t be sure it exists in the population. It could be chance variation in the sample and not a genuine effect.

Learn more about Failing to Reject the Null .

5 Steps of Significance Testing

Hypothesis testing involves five key steps, each critical to validating a research hypothesis using statistical methods:

Formulate the Hypotheses : Write your research hypotheses as a null hypothesis (H 0 ) and an alternative hypothesis (H A ).
Data Collection : Gather data specifically aimed at testing the hypothesis.
Conduct A Test : Use a suitable statistical test to analyze your data.
Make a Decision : Based on the statistical test results, decide whether to reject the null hypothesis or fail to reject it.
Report the Results : Summarize and present the outcomes in your report’s results and discussion sections.

While the specifics of these steps can vary depending on the research context and the data type, the fundamental process of hypothesis testing remains consistent across different studies.

Let’s work through these steps in an example!

Hypothesis Testing Example

Researchers want to determine if a new educational program improves student performance on standardized tests. They randomly assign 30 students to a control group , which follows the standard curriculum, and another 30 students to a treatment group, which participates in the new educational program. After a semester, they compare the test scores of both groups.

Download the CSV data file to perform the hypothesis testing yourself: Hypothesis_Testing .

The researchers write their hypotheses. These statements apply to the population, so they use the mu (μ) symbol for the population mean parameter .

Null Hypothesis (H 0 ) : The population means of the test scores for the two groups are equal (μ 1 = μ 2 ).
Alternative Hypothesis (H A ) : The population means of the test scores for the two groups are unequal (μ 1 ≠ μ 2 ).

Choosing the correct hypothesis test depends on attributes such as data type and number of groups. Because they’re using continuous data and comparing two means, the researchers use a 2-sample t-test .

Here are the results.

Hypothesis testing results for the example.

The treatment group’s mean is 58.70, compared to the control group’s mean of 48.12. The mean difference is 10.67 points. Use the test’s p-value and significance level to determine whether this difference is likely a product of random fluctuation in the sample or a genuine population effect.

Because the p-value (0.000) is less than the standard significance level of 0.05, the results are statistically significant, and we can reject the null hypothesis. The sample data provides sufficient evidence to conclude that the new program’s effect exists in the population.

Limitations

Hypothesis testing improves your effectiveness in making data-driven decisions. However, it is not 100% accurate because random samples occasionally produce fluky results. Hypothesis tests have two types of errors, both relating to drawing incorrect conclusions.

Type I error: The test rejects a true null hypothesis—a false positive.
Type II error: The test fails to reject a false null hypothesis—a false negative.

Learn more about Type I and Type II Errors .

Our exploration of hypothesis testing using a practical example of an educational program reveals its powerful ability to guide decisions based on statistical evidence. Whether you’re a student, researcher, or professional, understanding and applying these procedures can open new doors to discovering insights and making informed decisions. Let this tool empower your analytical endeavors as you navigate through the vast seas of data.

Learn more about the Hypothesis Tests for Various Data Types .

Reader Interactions

June 10, 2024 at 10:51 am

Thank you, Jim, for another helpful article; timely too since I have started reading your new book on hypothesis testing and, now that we are at the end of the school year, my district is asking me to perform a number of evaluations on instructional programs. This is where my question/concern comes in. You mention that hypothesis testing is all about testing samples. However, I use all the students in my district when I make these comparisons. Since I am using the entire “population” in my evaluations (I don’t select a sample of third grade students, for example, but I use all 700 third graders), am I somehow misusing the tests? Or can I rest assured that my district’s student population is only a sample of the universal population of students?

June 10, 2024 at 1:50 pm

I hope you are finding the book helpful!

Yes, the purpose of hypothesis testing is to infer the properties of a population while accounting for random sampling error.

In your case, it comes down to how you want to use the results. Who do you want the results to apply to?

If you’re summarizing the sample, looking for trends and patterns, or evaluating those students and don’t plan to apply those results to other students, you don’t need hypothesis testing because there is no sampling error. They are the population and you can just use descriptive statistics. In this case, you’d only need to focus on the practical significance of the effect sizes.

On the other hand, if you want to apply the results from this group to other students, you’ll need hypothesis testing. However, there is the complicating issue of what population your sample of students represent. I’m sure your district has its own unique characteristics, demographics, etc. Your district’s students probably don’t adequately represent a universal population. At the very least, you’d need to recognize any special attributes of your district and how they could bias the results when trying to apply them outside the district. Or they might apply to similar districts in your region.

However, I’d imagine your 3rd graders probably adequately represent future classes of 3rd graders in your district. You need to be alert to changing demographics. At least in the short run I’d imagine they’d be representative of future classes.

Think about how these results will be used. Do they just apply to the students you measured? Then you don’t need hypothesis tests. However, if the results are being used to infer things about other students outside of the sample, you’ll need hypothesis testing along with considering how well your students represent the other students and how they differ.

I hope that helps!

June 10, 2024 at 3:21 pm

Thank you so much, Jim, for the suggestions in terms of what I need to think about and consider! You are always so clear in your explanations!!!!

June 10, 2024 at 3:22 pm

You’re very welcome! Best of luck with your evaluations!

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Hypothesis Testing – A Deep Dive into Hypothesis Testing, The Backbone of Statistical Inference

September 21, 2023

Explore the intricacies of hypothesis testing, a cornerstone of statistical analysis. Dive into methods, interpretations, and applications for making data-driven decisions.

In this Blog post we will learn:

What is Hypothesis Testing?
Steps in Hypothesis Testing 2.1. Set up Hypotheses: Null and Alternative 2.2. Choose a Significance Level (α) 2.3. Calculate a test statistic and P-Value 2.4. Make a Decision
Example : Testing a new drug.
Example in python

1. What is Hypothesis Testing?

In simple terms, hypothesis testing is a method used to make decisions or inferences about population parameters based on sample data. Imagine being handed a dice and asked if it’s biased. By rolling it a few times and analyzing the outcomes, you’d be engaging in the essence of hypothesis testing.

Think of hypothesis testing as the scientific method of the statistics world. Suppose you hear claims like “This new drug works wonders!” or “Our new website design boosts sales.” How do you know if these statements hold water? Enter hypothesis testing.

2. Steps in Hypothesis Testing

Set up Hypotheses : Begin with a null hypothesis (H0) and an alternative hypothesis (Ha).
Choose a Significance Level (α) : Typically 0.05, this is the probability of rejecting the null hypothesis when it’s actually true. Think of it as the chance of accusing an innocent person.
Calculate Test statistic and P-Value : Gather evidence (data) and calculate a test statistic.
p-value : This is the probability of observing the data, given that the null hypothesis is true. A small p-value (typically ≤ 0.05) suggests the data is inconsistent with the null hypothesis.
Decision Rule : If the p-value is less than or equal to α, you reject the null hypothesis in favor of the alternative.

2.1. Set up Hypotheses: Null and Alternative

Before diving into testing, we must formulate hypotheses. The null hypothesis (H0) represents the default assumption, while the alternative hypothesis (H1) challenges it.

For instance, in drug testing, H0 : “The new drug is no better than the existing one,” H1 : “The new drug is superior .”

2.2. Choose a Significance Level (α)

When You collect and analyze data to test H0 and H1 hypotheses. Based on your analysis, you decide whether to reject the null hypothesis in favor of the alternative, or fail to reject / Accept the null hypothesis.

The significance level, often denoted by $α$, represents the probability of rejecting the null hypothesis when it is actually true.

In other words, it’s the risk you’re willing to take of making a Type I error (false positive).

Type I Error (False Positive) :

Symbolized by the Greek letter alpha (α).
Occurs when you incorrectly reject a true null hypothesis . In other words, you conclude that there is an effect or difference when, in reality, there isn’t.
The probability of making a Type I error is denoted by the significance level of a test. Commonly, tests are conducted at the 0.05 significance level , which means there’s a 5% chance of making a Type I error .
Commonly used significance levels are 0.01, 0.05, and 0.10, but the choice depends on the context of the study and the level of risk one is willing to accept.

Example : If a drug is not effective (truth), but a clinical trial incorrectly concludes that it is effective (based on the sample data), then a Type I error has occurred.

Type II Error (False Negative) :

Symbolized by the Greek letter beta (β).
Occurs when you accept a false null hypothesis . This means you conclude there is no effect or difference when, in reality, there is.
The probability of making a Type II error is denoted by β. The power of a test (1 – β) represents the probability of correctly rejecting a false null hypothesis.

Example : If a drug is effective (truth), but a clinical trial incorrectly concludes that it is not effective (based on the sample data), then a Type II error has occurred.

Balancing the Errors :

In practice, there’s a trade-off between Type I and Type II errors. Reducing the risk of one typically increases the risk of the other. For example, if you want to decrease the probability of a Type I error (by setting a lower significance level), you might increase the probability of a Type II error unless you compensate by collecting more data or making other adjustments.

It’s essential to understand the consequences of both types of errors in any given context. In some situations, a Type I error might be more severe, while in others, a Type II error might be of greater concern. This understanding guides researchers in designing their experiments and choosing appropriate significance levels.

2.3. Calculate a test statistic and P-Value

Test statistic : A test statistic is a single number that helps us understand how far our sample data is from what we’d expect under a null hypothesis (a basic assumption we’re trying to test against). Generally, the larger the test statistic, the more evidence we have against our null hypothesis. It helps us decide whether the differences we observe in our data are due to random chance or if there’s an actual effect.

P-value : The P-value tells us how likely we would get our observed results (or something more extreme) if the null hypothesis were true. It’s a value between 0 and 1. – A smaller P-value (typically below 0.05) means that the observation is rare under the null hypothesis, so we might reject the null hypothesis. – A larger P-value suggests that what we observed could easily happen by random chance, so we might not reject the null hypothesis.

2.4. Make a Decision

Relationship between $α$ and P-Value

When conducting a hypothesis test:

We then calculate the p-value from our sample data and the test statistic.

Finally, we compare the p-value to our chosen $α$:

If $p−value≤α$: We reject the null hypothesis in favor of the alternative hypothesis. The result is said to be statistically significant.
If $p−value>α$: We fail to reject the null hypothesis. There isn’t enough statistical evidence to support the alternative hypothesis.

3. Example : Testing a new drug.

Imagine we are investigating whether a new drug is effective at treating headaches faster than drug B.

Setting Up the Experiment : You gather 100 people who suffer from headaches. Half of them (50 people) are given the new drug (let’s call this the ‘Drug Group’), and the other half are given a sugar pill, which doesn’t contain any medication.

Set up Hypotheses : Before starting, you make a prediction:
Null Hypothesis (H0): The new drug has no effect. Any difference in healing time between the two groups is just due to random chance.
Alternative Hypothesis (H1): The new drug does have an effect. The difference in healing time between the two groups is significant and not just by chance.

Calculate Test statistic and P-Value : After the experiment, you analyze the data. The “test statistic” is a number that helps you understand the difference between the two groups in terms of standard units.

For instance, let’s say:

The average healing time in the Drug Group is 2 hours.
The average healing time in the Placebo Group is 3 hours.

The test statistic helps you understand how significant this 1-hour difference is. If the groups are large and the spread of healing times in each group is small, then this difference might be significant. But if there’s a huge variation in healing times, the 1-hour difference might not be so special.

Imagine the P-value as answering this question: “If the new drug had NO real effect, what’s the probability that I’d see a difference as extreme (or more extreme) as the one I found, just by random chance?”

For instance:

P-value of 0.01 means there’s a 1% chance that the observed difference (or a more extreme difference) would occur if the drug had no effect. That’s pretty rare, so we might consider the drug effective.
P-value of 0.5 means there’s a 50% chance you’d see this difference just by chance. That’s pretty high, so we might not be convinced the drug is doing much.
If the P-value is less than ($α$) 0.05: the results are “statistically significant,” and they might reject the null hypothesis , believing the new drug has an effect.
If the P-value is greater than ($α$) 0.05: the results are not statistically significant, and they don’t reject the null hypothesis , remaining unsure if the drug has a genuine effect.

4. Example in python

For simplicity, let’s say we’re using a t-test (common for comparing means). Let’s dive into Python:

Making a Decision : “The results are statistically significant! p-value < 0.05 , The drug seems to have an effect!” If not, we’d say, “Looks like the drug isn’t as miraculous as we thought.”

5. Conclusion

Hypothesis testing is an indispensable tool in data science, allowing us to make data-driven decisions with confidence. By understanding its principles, conducting tests properly, and considering real-world applications, you can harness the power of hypothesis testing to unlock valuable insights from your data.

F statistic formula – explained, correlation – connecting the dots, the role of correlation in data analysis, sampling and sampling distributions – a comprehensive guide on sampling and sampling distributions, law of large numbers – a deep dive into the world of statistics, central limit theorem – a deep dive into central limit theorem and its significance in statistics, similar articles, complete introduction to linear regression in r, how to implement common statistical significance tests and find the p value, logistic regression – a complete tutorial with examples in r.

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Understanding Science

How science REALLY works...

Understanding Science 101
Misconceptions
Testing ideas with evidence is at the heart of the process of science.
Scientific testing involves figuring out what we would expect to observe if an idea were correct and comparing that expectation to what we actually observe.

Misconception: Science proves ideas.

Misconception: Science can only disprove ideas.

Correction: Science neither proves nor disproves. It accepts or rejects ideas based on supporting and refuting evidence, but may revise those conclusions if warranted by new evidence or perspectives. Read more about it.

Testing scientific ideas

Testing ideas about childbed fever.

As a simple example of how scientific testing works, consider the case of Ignaz Semmelweis, who worked as a doctor on a maternity ward in the 1800s. In his ward, an unusually high percentage of new mothers died of what was then called childbed fever. Semmelweis considered many possible explanations for this high death rate. Two of the many ideas that he considered were (1) that the fever was caused by mothers giving birth lying on their backs (as opposed to on their sides) and (2) that the fever was caused by doctors’ unclean hands (the doctors often performed autopsies immediately before examining women in labor). He tested these ideas by considering what expectations each idea generated. If it were true that childbed fever were caused by giving birth on one’s back, then changing procedures so that women labored on their sides should lead to lower rates of childbed fever. Semmelweis tried changing the position of labor, but the incidence of fever did not decrease; the actual observations did not match the expected results. If, however, childbed fever were caused by doctors’ unclean hands, having doctors wash their hands thoroughly with a strong disinfecting agent before attending to women in labor should lead to lower rates of childbed fever. When Semmelweis tried this, rates of fever plummeted; the actual observations matched the expected results, supporting the second explanation.

Testing in the tropics

Let’s take a look at another, very different, example of scientific testing: investigating the origins of coral atolls in the tropics. Consider the atoll Eniwetok (Anewetak) in the Marshall Islands — an oceanic ring of exposed coral surrounding a central lagoon. From the 1800s up until today, scientists have been trying to learn what supports atoll structures beneath the water’s surface and exactly how atolls form. Coral only grows near the surface of the ocean where light penetrates, so Eniwetok could have formed in several ways:

Hypothesis 2: The coral that makes up Eniwetok might have grown in a ring atop an underwater mountain already near the surface. The key to this hypothesis is the idea that underwater mountains don’t sink; instead the remains of dead sea animals (shells, etc.) accumulate on underwater mountains, potentially assisted by tectonic uplifting. Eventually, the top of the mountain/debris pile would reach the depth at which coral grow, and the atoll would form.

Which is a better explanation for Eniwetok? Did the atoll grow atop a sinking volcano, forming an underwater coral tower, or was the mountain instead built up until it neared the surface where coral were eventually able to grow? Which of these explanations is best supported by the evidence? We can’t perform an experiment to find out. Instead, we must figure out what expectations each hypothesis generates, and then collect data from the world to see whether our observations are a better match with one of the two ideas.

If Eniwetok grew atop an underwater mountain, then we would expect the atoll to be made up of a relatively thin layer of coral on top of limestone or basalt. But if it grew upwards around a subsiding island, then we would expect the atoll to be made up of many hundreds of feet of coral on top of volcanic rock. When geologists drilled into Eniwetok in 1951 as part of a survey preparing for nuclear weapons tests, the drill bored through more than 4000 feet (1219 meters) of coral before hitting volcanic basalt! The actual observation contradicted the underwater mountain explanation and matched the subsiding island explanation, supporting that idea. Of course, many other lines of evidence also shed light on the origins of coral atolls, but the surprising depth of coral on Eniwetok was particularly convincing to many geologists.

Take a sidetrip

Visit the NOAA website to see an animation of coral atoll formation according to Hypothesis 1.

Teaching resources

Scientists test hypotheses and theories. They are both scientific explanations for what we observe in the natural world, but theories deal with a much wider range of phenomena than do hypotheses. To learn more about the differences between hypotheses and theories, jump ahead to Science at multiple levels .

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Why hypothesis testing is important in research ?

Hypothesis Testing allows researchers to evaluate the validity of their assumptions and draw conclusions based on evidence. It provides a framework for making predictions and determining whether observed results are statistically significant or just occurred by chance. By applying various statistical tests, researchers can measure the strength of the evidence and quantify the uncertainty associated with their findings.

Table of Content

Importance of Hypothesis Testing in Research

Types of hypothesis tests, common errors in hypothesis testing, interpreting the results of hypothesis tests, examples of hypothesis testing in different fields, tools and software for conducting hypothesis tests.

Understanding the importance of hypothesis testing is essential for conducting rigorous and reliable research. It enables researchers to make well-informed decisions, support or challenge existing theories, and contribute to the advancement of knowledge in their respective fields. So, whether you are a scientist, a market analyst, or a student working on a research project, grasp the power of hypothesis testing and elevate the impact of your data analysis.

Hypothesis testing is the cornerstone of the scientific method and plays a vital role in the research process. It allows researchers to make informed decisions and draw reliable conclusions from their data. By formulating a hypothesis and then testing it against the observed data, researchers can determine whether their initial assumptions are supported or refuted. This systematic approach is crucial for advancing knowledge and understanding in various fields, from medicine and psychology to economics and engineering. Hypothesis testing enables researchers to move beyond mere observations and anecdotal evidence, and instead rely on statistical analysis to quantify the strength of their findings. It helps them differentiate between genuine effects and random fluctuations, ensuring that the conclusions drawn are based on rigorous and objective analysis.

Moreover, hypothesis testing is not limited to academic research; it is equally important in the business world, where data-driven decision-making is essential for success. Marketers, for instance, can use hypothesis testing to evaluate the effectiveness of their advertising campaigns, while financial analysts can use it to assess the performance of investment strategies. By incorporating hypothesis testing into their decision-making processes, organizations can make more informed choices and optimize their operations.

Understanding the Null and Alternative Hypotheses

At the heart of hypothesis testing lies the distinction between the null hypothesis (H0) and the alternative hypothesis (H1). The null hypothesis represents the status quo or the assumption that there is no significant difference or relationship between the variables being studied. Conversely, the alternative hypothesis suggests that there is a meaningful difference or relationship that is worth investigating.

Researchers begin by formulating their null and alternative hypotheses based on their research question and existing knowledge. For example, in a study examining the effect of a new drug on blood pressure, the null hypothesis might be that the drug has no effect on blood pressure, while the alternative hypothesis would be that the drug does have an effect on blood pressure.

Steps Involved in Hypothesis Testing

Hypothesis testing is a structured process that involves several key steps:

Clearly define the research question and formulate the null and alternative hypotheses.
Select an appropriate statistical test based on the nature of the data and research question.
Collect and organize data, ensuring it meets the assumptions required for the chosen test.
Calculate the test statistic and compare it to the critical value or p-value to determine significance.
Interpret the results and draw conclusions about the research question.
One-Sample Tests : These tests compare the mean or proportion of a single sample to a known or hypothesized value. Examples include the one-sample t-test and the one-sample z-test.
Two-Sample Tests: These tests compare the means or proportions of two independent samples. Examples include the two-sample t-test, the Mann-Whitney U test, and the chi-square test of independence.
Paired Tests: These tests compare the means or proportions of two related or paired samples, such as before-and-after measurements or matched pairs. Examples include the paired t-test and the Wilcoxon signed-rank test.
ANOVA Tests : These tests compare the means of three or more independent samples. Examples include one-way ANOVA, two-way ANOVA, and repeated-measures ANOVA.
Correlation and Regression Tests: These tests examine the relationship between two or more variables. Examples include Pearson’s correlation, Spearman’s rank correlation, and linear regression analysis.

While hypothesis testing is a powerful tool for data analysis, it is not immune to errors. Two common types of errors in hypothesis testing are Type I errors and Type II errors.

Type I Error

A Type I error occurs when the null hypothesis is true, but it is incorrectly rejected. The probability of making a Type I error is typically denoted by the significance level (α), which is the threshold used to determine statistical significance.

Type II Error

Conversely, a Type II error occurs when the null hypothesis is false, but it is not rejected. In this case, the researcher fails to detect a significant effect that is actually present. The probability of making a Type II error is denoted by β.

When a hypothesis test is conducted, the researcher is provided with a p-value, which represents the probability of obtaining the observed results if the null hypothesis is true. If the p-value is less than the chosen significance level (typically 0.05), the null hypothesis is rejected, and the alternative hypothesis is supported.

Medicine and Pharmacology: Researchers use hypothesis testing to evaluate the effectiveness of new drugs, treatments, or interventions. For example, a clinical trial might test the null hypothesis that a new drug has no effect on a health outcome.
Psychology and Behavioral Sciences: Psychologists use hypothesis testing to investigate human behavior, cognition, and social phenomena. For instance, a researcher might hypothesize that a new therapy has no effect on depression symptoms.
Economics and Finance: Economists use hypothesis testing to evaluate market performance, economic policies, and investment strategies. For example, testing the hypothesis that interest rates have no effect on the stock market.
Engineering and Technology: Engineers use hypothesis testing to optimize product designs, test system reliability, and evaluate new technologies. For example, testing a new manufacturing process to reduce defects.
Environmental Science: Environmental scientists use hypothesis testing to evaluate the impact of human activities, conservation efforts, and climate change effects.

Various tools are available for conducting hypothesis tests:

IBM SPSS Statistics : A user-friendly statistical software widely used for hypothesis testing.
R : An open-source programming language for statistical computing, offering packages like stats , ggplot2 , and dplyr for hypothesis testing.
Online Tools : Websites such as StatisticsHowTo.com offer hypothesis test calculators for quick analyses.

Hypothesis testing is a crucial tool for researchers across many disciplines. It allows them to make informed decisions, support or challenge theories, and contribute to knowledge advancement. By understanding and mastering hypothesis testing techniques, researchers can significantly enhance their data analysis impact.

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Evgeniy Riabenko is a data scientist with more than 10 years of experience in both industry and academia. He got his PhD in mathematical modelling from Moscow State University, and has expertise in statistics, machine learning, optimisation, time series analysis, topic modelling, and bioinformatics. For 7 years he taught statistics for data analysis courses at Moscow State University, Moscow Institute of Physics and Technology and Higher School of Economics; an adapted version of the course is available on Coursera.

After completing this course, a student will be able to:

• Identify cases where statistical analysis should be applied

• Select the most optimal statistical method for the analysis

• Check if the data in hand satisfies the underlying assumptions of the method

• Run the analysis using R

SKILLS: - Statistics

- Data Analysis

- Machine Learning

- Bioinformatics

DATE: 30 Apr - 18 May, 2018

DURATION: 3 Weeks

LECTURES: 3 Hours per day

LANGUAGE: English

LOCATION: Barcelona, Harbour.Space Campus

COURSE TYPE: Offline

STATISTICAL DATA ANALYSIS

This advanced course is devoted to the vast array of statistical analysis methods with focus on the applications. Instead of proving theorems or calculating Lebesgue integrals, we would consider various standard data analysis tasks that require statistics, study the taxonomy of statistical methods, learn their limits and assumptions, and, of course, apply them to different real-world datasets and problems using R.

Senior Data Scientist at Veon

We offer innovative university degrees taught in English by industry leaders from around the world, aimed at giving our students meaningful and creatively satisfying top-level professional futures. We think the future is bright if you make it so.

DATE: 30 Apr – 18 May, 2018