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Experimental Design: Definition and Types

By Jim Frost 3 Comments

What is Experimental Design?

An experimental design is a detailed plan for collecting and using data to identify causal relationships. Through careful planning, the design of experiments allows your data collection efforts to have a reasonable chance of detecting effects and testing hypotheses that answer your research questions.

An experiment is a data collection procedure that occurs in controlled conditions to identify and understand causal relationships between variables. Researchers can use many potential designs. The ultimate choice depends on their research question, resources, goals, and constraints. In some fields of study, researchers refer to experimental design as the design of experiments (DOE). Both terms are synonymous.

Ultimately, the design of experiments helps ensure that your procedures and data will evaluate your research question effectively. Without an experimental design, you might waste your efforts in a process that, for many potential reasons, can’t answer your research question. In short, it helps you trust your results.

Learn more about Independent and Dependent Variables .

Design of Experiments: Goals & Settings

Experiments occur in many settings, ranging from psychology, social sciences, medicine, physics, engineering, and industrial and service sectors. Typically, experimental goals are to discover a previously unknown effect , confirm a known effect, or test a hypothesis.

Effects represent causal relationships between variables. For example, in a medical experiment, does the new medicine cause an improvement in health outcomes? If so, the medicine has a causal effect on the outcome.

An experimental design’s focus depends on the subject area and can include the following goals:

• Understanding the relationships between variables.
• Identifying the variables that have the largest impact on the outcomes.
• Finding the input variable settings that produce an optimal result.

For example, psychologists have conducted experiments to understand how conformity affects decision-making. Sociologists have performed experiments to determine whether ethnicity affects the public reaction to staged bike thefts. These experiments map out the causal relationships between variables, and their primary goal is to understand the role of various factors.

Conversely, in a manufacturing environment, the researchers might use an experimental design to find the factors that most effectively improve their product’s strength, identify the optimal manufacturing settings, and do all that while accounting for various constraints. In short, a manufacturer’s goal is often to use experiments to improve their products cost-effectively.

In a medical experiment, the goal might be to quantify the medicine’s effect and find the optimum dosage.

Developing an Experimental Design

Developing an experimental design involves planning that maximizes the potential to collect data that is both trustworthy and able to detect causal relationships. Specifically, these studies aim to see effects when they exist in the population the researchers are studying, preferentially favor causal effects, isolate each factor’s true effect from potential confounders, and produce conclusions that you can generalize to the real world.

To accomplish these goals, experimental designs carefully manage data validity and reliability , and internal and external experimental validity. When your experiment is valid and reliable, you can expect your procedures and data to produce trustworthy results.

An excellent experimental design involves the following:

• Lots of preplanning.
• Developing experimental treatments.
• Determining how to assign subjects to treatment groups.

The remainder of this article focuses on how experimental designs incorporate these essential items to accomplish their research goals.

Learn more about Data Reliability vs. Validity and Internal and External Experimental Validity .

Preplanning, Defining, and Operationalizing for Design of Experiments

This phase of the design of experiments helps you identify critical variables, know how to measure them while ensuring reliability and validity, and understand the relationships between them. The review can also help you find ways to reduce sources of variability, which increases your ability to detect treatment effects. Notably, the literature review allows you to learn how similar studies designed their experiments and the challenges they faced.

Operationalizing a study involves taking your research question, using the background information you gathered, and formulating an actionable plan.

This process should produce a specific and testable hypothesis using data that you can reasonably collect given the resources available to the experiment.

• Null hypothesis : The jumping exercise intervention does not affect bone density.
• Alternative hypothesis : The jumping exercise intervention affects bone density.

To learn more about this early phase, read Five Steps for Conducting Scientific Studies with Statistical Analyses .

Formulating Treatments in Experimental Designs

In an experimental design, treatments are variables that the researchers control. They are the primary independent variables of interest. Researchers administer the treatment to the subjects or items in the experiment and want to know whether it causes changes in the outcome.

As the name implies, a treatment can be medical in nature, such as a new medicine or vaccine. But it’s a general term that applies to other things such as training programs, manufacturing settings, teaching methods, and types of fertilizers. I helped run an experiment where the treatment was a jumping exercise intervention that we hoped would increase bone density. All these treatment examples are things that potentially influence a measurable outcome.

Even when you know your treatment generally, you must carefully consider the amount. How large of a dose? If you’re comparing three different temperatures in a manufacturing process, how far apart are they? For my bone mineral density study, we had to determine how frequently the exercise sessions would occur and how long each lasted.

How you define the treatments in the design of experiments can affect your findings and the generalizability of your results.

Assigning Subjects to Experimental Groups

A crucial decision for all experimental designs is determining how researchers assign subjects to the experimental conditions—the treatment and control groups. The control group is often, but not always, the lack of a treatment. It serves as a basis for comparison by showing outcomes for subjects who don’t receive a treatment. Learn more about Control Groups .

How your experimental design assigns subjects to the groups affects how confident you can be that the findings represent true causal effects rather than mere correlation caused by confounders. Indeed, the assignment method influences how you control for confounding variables. This is the difference between correlation and causation .

Imagine a study finds that vitamin consumption correlates with better health outcomes. As a researcher, you want to be able to say that vitamin consumption causes the improvements. However, with the wrong experimental design, you might only be able to say there is an association. A confounder, and not the vitamins, might actually cause the health benefits.

Let’s explore some of the ways to assign subjects in design of experiments.

Completely Randomized Designs

A completely randomized experimental design randomly assigns all subjects to the treatment and control groups. You simply take each participant and use a random process to determine their group assignment. You can flip coins, roll a die, or use a computer. Randomized experiments must be prospective studies because they need to be able to control group assignment.

Random assignment in the design of experiments helps ensure that the groups are roughly equivalent at the beginning of the study. This equivalence at the start increases your confidence that any differences you see at the end were caused by the treatments. The randomization tends to equalize confounders between the experimental groups and, thereby, cancels out their effects, leaving only the treatment effects.

For example, in a vitamin study, the researchers can randomly assign participants to either the control or vitamin group. Because the groups are approximately equal when the experiment starts, if the health outcomes are different at the end of the study, the researchers can be confident that the vitamins caused those improvements.

Statisticians consider randomized experimental designs to be the best for identifying causal relationships.

If you can’t randomly assign subjects but want to draw causal conclusions about an intervention, consider using a quasi-experimental design .

Learn more about Randomized Controlled Trials and Random Assignment in Experiments .

Randomized Block Designs

Nuisance factors are variables that can affect the outcome, but they are not the researcher’s primary interest. Unfortunately, they can hide or distort the treatment results. When experimenters know about specific nuisance factors, they can use a randomized block design to minimize their impact.

This experimental design takes subjects with a shared “nuisance” characteristic and groups them into blocks. The participants in each block are then randomly assigned to the experimental groups. This process allows the experiment to control for known nuisance factors.

Blocking in the design of experiments reduces the impact of nuisance factors on experimental error. The analysis assesses the effects of the treatment within each block, which removes the variability between blocks. The result is that blocked experimental designs can reduce the impact of nuisance variables, increasing the ability to detect treatment effects accurately.

Suppose you’re testing various teaching methods. Because grade level likely affects educational outcomes, you might use grade level as a blocking factor. To use a randomized block design for this scenario, divide the participants by grade level and then randomly assign the members of each grade level to the experimental groups.

A standard guideline for an experimental design is to “Block what you can, randomize what you cannot.” Use blocking for a few primary nuisance factors. Then use random assignment to distribute the unblocked nuisance factors equally between the experimental conditions.

You can also use covariates to control nuisance factors. Learn about Covariates: Definition and Uses .

Observational Studies

In some experimental designs, randomly assigning subjects to the experimental conditions is impossible or unethical. The researchers simply can’t assign participants to the experimental groups. However, they can observe them in their natural groupings, measure the essential variables, and look for correlations. These observational studies are also known as quasi-experimental designs. Retrospective studies must be observational in nature because they look back at past events.

Imagine you’re studying the effects of depression on an activity. Clearly, you can’t randomly assign participants to the depression and control groups. But you can observe participants with and without depression and see how their task performance differs.

Observational studies let you perform research when you can’t control the treatment. However, quasi-experimental designs increase the problem of confounding variables. For this design of experiments, correlation does not necessarily imply causation. While special procedures can help control confounders in an observational study, you’re ultimately less confident that the results represent causal findings.

Learn more about Observational Studies .

For a good comparison, learn about the differences and tradeoffs between Observational Studies and Randomized Experiments .

Between-Subjects vs. Within-Subjects Experimental Designs

When you think of the design of experiments, you probably picture a treatment and control group. Researchers assign participants to only one of these groups, so each group contains entirely different subjects than the other groups. Analysts compare the groups at the end of the experiment. Statisticians refer to this method as a between-subjects, or independent measures, experimental design.

In a between-subjects design , you can have more than one treatment group, but each subject is exposed to only one condition, the control group or one of the treatment groups.

A potential downside to this approach is that differences between groups at the beginning can affect the results at the end. As you’ve read earlier, random assignment can reduce those differences, but it is imperfect. There will always be some variability between the groups.

In a  within-subjects experimental design , also known as repeated measures, subjects experience all treatment conditions and are measured for each. Each subject acts as their own control, which reduces variability and increases the statistical power to detect effects.

In this experimental design, you minimize pre-existing differences between the experimental conditions because they all contain the same subjects. However, the order of treatments can affect the results. Beware of practice and fatigue effects. Learn more about Repeated Measures Designs .

Design of Experiments Examples

For example, a bone density study has three experimental groups—a control group, a stretching exercise group, and a jumping exercise group.

In a between-subjects experimental design, scientists randomly assign each participant to one of the three groups.

In a within-subjects design, all subjects experience the three conditions sequentially while the researchers measure bone density repeatedly. The procedure can switch the order of treatments for the participants to help reduce order effects.

Matched Pairs Experimental Design

A matched pairs experimental design is a between-subjects study that uses pairs of similar subjects. Researchers use this approach to reduce pre-existing differences between experimental groups. It’s yet another design of experiments method for reducing sources of variability.

Researchers identify variables likely to affect the outcome, such as demographics. When they pick a subject with a set of characteristics, they try to locate another participant with similar attributes to create a matched pair. Scientists randomly assign one member of a pair to the treatment group and the other to the control group.

On the plus side, this process creates two similar groups, and it doesn’t create treatment order effects. While matched pairs do not produce the perfectly matched groups of a within-subjects design (which uses the same subjects in all conditions), it aims to reduce variability between groups relative to a between-subjects study.

On the downside, finding matched pairs is very time-consuming. Additionally, if one member of a matched pair drops out, the other subject must leave the study too.

Learn more about Matched Pairs Design: Uses & Examples .

Another consideration is whether you’ll use a cross-sectional design (one point in time) or use a longitudinal study to track changes over time .

A case study is a research method that often serves as a precursor to a more rigorous experimental design by identifying research questions, variables, and hypotheses to test. Learn more about What is a Case Study? Definition & Examples .

In conclusion, the design of experiments is extremely sensitive to subject area concerns and the time and resources available to the researchers. Developing a suitable experimental design requires balancing a multitude of considerations. A successful design is necessary to obtain trustworthy answers to your research question and to have a reasonable chance of detecting treatment effects when they exist.

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March 23, 2024 at 2:35 pm

Dear Jim You wrote a superb document, I will use it in my Buistatistics course, along with your three books. Thank you very much! Miguel

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Thanks so much, Miguel! Glad this post was helpful and I trust the books will be as well.

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What are the purpose and uses of experimental research design?

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Experimental design

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Data for statistical studies are obtained by conducting either experiments or surveys. Experimental design is the branch of statistics that deals with the design and analysis of experiments. The methods of experimental design are widely used in the fields of agriculture, medicine , biology , marketing research, and industrial production.

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In an experimental study, variables of interest are identified. One or more of these variables, referred to as the factors of the study , are controlled so that data may be obtained about how the factors influence another variable referred to as the response variable , or simply the response. As a case in point, consider an experiment designed to determine the effect of three different exercise programs on the cholesterol level of patients with elevated cholesterol. Each patient is referred to as an experimental unit , the response variable is the cholesterol level of the patient at the completion of the program, and the exercise program is the factor whose effect on cholesterol level is being investigated. Each of the three exercise programs is referred to as a treatment .

Three of the more widely used experimental designs are the completely randomized design, the randomized block design, and the factorial design. In a completely randomized experimental design, the treatments are randomly assigned to the experimental units. For instance, applying this design method to the cholesterol-level study, the three types of exercise program (treatment) would be randomly assigned to the experimental units (patients).

The use of a completely randomized design will yield less precise results when factors not accounted for by the experimenter affect the response variable. Consider, for example, an experiment designed to study the effect of two different gasoline additives on the fuel efficiency , measured in miles per gallon (mpg), of full-size automobiles produced by three manufacturers. Suppose that 30 automobiles, 10 from each manufacturer, were available for the experiment. In a completely randomized design the two gasoline additives (treatments) would be randomly assigned to the 30 automobiles, with each additive being assigned to 15 different cars. Suppose that manufacturer 1 has developed an engine that gives its full-size cars a higher fuel efficiency than those produced by manufacturers 2 and 3. A completely randomized design could, by chance , assign gasoline additive 1 to a larger proportion of cars from manufacturer 1. In such a case, gasoline additive 1 might be judged to be more fuel efficient when in fact the difference observed is actually due to the better engine design of automobiles produced by manufacturer 1. To prevent this from occurring, a statistician could design an experiment in which both gasoline additives are tested using five cars produced by each manufacturer; in this way, any effects due to the manufacturer would not affect the test for significant differences due to gasoline additive. In this revised experiment, each of the manufacturers is referred to as a block, and the experiment is called a randomized block design. In general, blocking is used in order to enable comparisons among the treatments to be made within blocks of homogeneous experimental units.

Factorial experiments are designed to draw conclusions about more than one factor, or variable. The term factorial is used to indicate that all possible combinations of the factors are considered. For instance, if there are two factors with a levels for factor 1 and b levels for factor 2, the experiment will involve collecting data on a b treatment combinations. The factorial design can be extended to experiments involving more than two factors and experiments involving partial factorial designs.

A computational procedure frequently used to analyze the data from an experimental study employs a statistical procedure known as the analysis of variance. For a single-factor experiment, this procedure uses a hypothesis test concerning equality of treatment means to determine if the factor has a statistically significant effect on the response variable. For experimental designs involving multiple factors, a test for the significance of each individual factor as well as interaction effects caused by one or more factors acting jointly can be made. Further discussion of the analysis of variance procedure is contained in the subsequent section.

Regression and correlation analysis

Regression analysis involves identifying the relationship between a dependent variable and one or more independent variables . A model of the relationship is hypothesized, and estimates of the parameter values are used to develop an estimated regression equation . Various tests are then employed to determine if the model is satisfactory. If the model is deemed satisfactory, the estimated regression equation can be used to predict the value of the dependent variable given values for the independent variables.

In simple linear regression , the model used to describe the relationship between a single dependent variable y and a single independent variable x is y = β 0 + β 1 x + ε. β 0 and β 1 are referred to as the model parameters, and ε is a probabilistic error term that accounts for the variability in y that cannot be explained by the linear relationship with x . If the error term were not present, the model would be deterministic; in that case, knowledge of the value of x would be sufficient to determine the value of y .

In multiple regression analysis , the model for simple linear regression is extended to account for the relationship between the dependent variable y and p independent variables x 1 , x 2 , . . ., x p . The general form of the multiple regression model is y = β 0 + β 1 x 1 + β 2 x 2 + . . . + β p x p + ε. The parameters of the model are the β 0 , β 1 , . . ., β p , and ε is the error term.

Either a simple or multiple regression model is initially posed as a hypothesis concerning the relationship among the dependent and independent variables. The least squares method is the most widely used procedure for developing estimates of the model parameters. For simple linear regression, the least squares estimates of the model parameters β 0 and β 1 are denoted b 0 and b 1 . Using these estimates, an estimated regression equation is constructed: ŷ = b 0 + b 1 x . The graph of the estimated regression equation for simple linear regression is a straight line approximation to the relationship between y and x .

As an illustration of regression analysis and the least squares method, suppose a university medical centre is investigating the relationship between stress and blood pressure . Assume that both a stress test score and a blood pressure reading have been recorded for a sample of 20 patients. The data are shown graphically in Figure 4 , called a scatter diagram . Values of the independent variable, stress test score, are given on the horizontal axis, and values of the dependent variable, blood pressure, are shown on the vertical axis. The line passing through the data points is the graph of the estimated regression equation: ŷ = 42.3 + 0.49 x . The parameter estimates, b 0 = 42.3 and b 1 = 0.49, were obtained using the least squares method.

A primary use of the estimated regression equation is to predict the value of the dependent variable when values for the independent variables are given. For instance, given a patient with a stress test score of 60, the predicted blood pressure is 42.3 + 0.49(60) = 71.7. The values predicted by the estimated regression equation are the points on the line in Figure 4 , and the actual blood pressure readings are represented by the points scattered about the line. The difference between the observed value of y and the value of y predicted by the estimated regression equation is called a residual . The least squares method chooses the parameter estimates such that the sum of the squared residuals is minimized.

A commonly used measure of the goodness of fit provided by the estimated regression equation is the coefficient of determination . Computation of this coefficient is based on the analysis of variance procedure that partitions the total variation in the dependent variable, denoted SST, into two parts: the part explained by the estimated regression equation, denoted SSR, and the part that remains unexplained, denoted SSE.

The measure of total variation, SST, is the sum of the squared deviations of the dependent variable about its mean: Σ( y − ȳ ) 2 . This quantity is known as the total sum of squares. The measure of unexplained variation, SSE, is referred to as the residual sum of squares. For the data in Figure 4 , SSE is the sum of the squared distances from each point in the scatter diagram (see Figure 4 ) to the estimated regression line: Σ( y − ŷ ) 2 . SSE is also commonly referred to as the error sum of squares. A key result in the analysis of variance is that SSR + SSE = SST.

The ratio r 2 = SSR/SST is called the coefficient of determination. If the data points are clustered closely about the estimated regression line, the value of SSE will be small and SSR/SST will be close to 1. Using r 2 , whose values lie between 0 and 1, provides a measure of goodness of fit; values closer to 1 imply a better fit. A value of r 2 = 0 implies that there is no linear relationship between the dependent and independent variables.

When expressed as a percentage , the coefficient of determination can be interpreted as the percentage of the total sum of squares that can be explained using the estimated regression equation. For the stress-level research study, the value of r 2 is 0.583; thus, 58.3% of the total sum of squares can be explained by the estimated regression equation ŷ = 42.3 + 0.49 x . For typical data found in the social sciences, values of r 2 as low as 0.25 are often considered useful. For data in the physical sciences, r 2 values of 0.60 or greater are frequently found.

In a regression study, hypothesis tests are usually conducted to assess the statistical significance of the overall relationship represented by the regression model and to test for the statistical significance of the individual parameters. The statistical tests used are based on the following assumptions concerning the error term: (1) ε is a random variable with an expected value of 0, (2) the variance of ε is the same for all values of x , (3) the values of ε are independent, and (4) ε is a normally distributed random variable.

The mean square due to regression, denoted MSR, is computed by dividing SSR by a number referred to as its degrees of freedom ; in a similar manner, the mean square due to error, MSE , is computed by dividing SSE by its degrees of freedom. An F-test based on the ratio MSR/MSE can be used to test the statistical significance of the overall relationship between the dependent variable and the set of independent variables. In general, large values of F = MSR/MSE support the conclusion that the overall relationship is statistically significant. If the overall model is deemed statistically significant, statisticians will usually conduct hypothesis tests on the individual parameters to determine if each independent variable makes a significant contribution to the model.

Statistical Analysis of Experimental Data

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Statistical methods are extremely important in engineering, because they provide a means for representing large amounts of data in a concise form that is easily interpreted and understood. Usually, the data are represented with a statistical distribution function that can be characterized by a measure of central tendency (the mean x ¯ ) and a measure of dispersion (the standard deviation  S x ). A normal or Gaussian probability distribution is by far the most commonly employed; however, in some cases, other distribution functions may have to be employed to adequately represent the data.

The most significant advantage resulting from the use of a probability distribution function in engineering applications is the ability to predict the occurrence of an event based on a relatively small sample. The effects of sampling error are accounted for by placing confidence limits on the predictions and establishing the associated confidence levels. Sampling error can be controlled if the sample size is adequate. Use of Studentʼs t distribution function, which characterizes sampling error, provides a basis for determining sample size consistent with specified levels of confidence. Studentʼs t distribution also permits a comparison to be made of two means to determine whether the observed difference is significant or whether it is due to random variation.

Statistical methods can also be employed to condition data and to eliminate an erroneous data point (one) from a series of measurements. This is a useful technique that improves the data base by providing strong evidence when something unanticipated is affecting an experiment.

Regression analysis can be used effectively to interpret data when the behavior of one quantity  y depends upon variations in one or more independent quantities x 1 , x 2 , ..., x n . Even though the functional relationship between quantities exhibiting variation remains unknown, it can be characterized statistically. Regression analysis provides a method to fit a straight line or a curve through a series of scattered data points on a graph. The adequacy of the regression analysis can be evaluated by determining a correlation coefficient. Methods for extending regression analysis to multivariate functions exist. In principle, these methods are identical to linear regression analysis; however, the analysis becomes much more complex. The increase in complexity is not a concern, because computer subroutines are available that solve the tedious equations and provide the results in a convenient format.

Many probability functions are used in statistical analyses to represent data and predict population properties. Once a probability function has been selected to represent a population, any series of measurements can be subjected to a chi-squared ( χ 2 ) test to check the validity of the assumed function. Accurate predictions can be made only if the proper probability function has been selected.

Finally, statistical methods for accessing error propagation are discussed. These methods provide a means for determining error in a quantity of interest y based on measurements of related quantities x 1 , x 2 , ..., x n and the functional relationship y  =  f ( x 1 ,  x 2 , ..., x n ).

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Teach yourself statistics

Experimental Design for ANOVA

There is a close relationship between experimental design and statistical analysis. The way that an experiment is designed determines the types of analyses that can be appropriately conducted.

In this lesson, we review aspects of experimental design that a researcher must understand in order to properly interpret experimental data with analysis of variance.

What Is an Experiment?

An experiment is a procedure carried out to investigate cause-and-effect relationships. For example, the experimenter may manipulate one or more variables (independent variables) to assess the effect on another variable (the dependent variable).

Conclusions are reached on the basis of data. If the dependent variable is unaffected by changes in independent variables, we conclude that there is no causal relationship between the dependent variable and the independent variables. On the other hand, if the dependent variable is affected, we conclude that a causal relationship exists.

Experimenter Control

One of the features that distinguish a true experiment from other types of studies is experimenter control of the independent variable(s).

In a true experiment, an experimenter controls the level of the independent variable administered to each subject. For example, dosage level could be an independent variable in a true experiment; because an experimenter can manipulate the dosage administered to any subject.

What is a Quasi-Experiment?

A quasi-experiment is a study that lacks a critical feature of a true experiment. Quasi-experiments can provide insights into cause-and-effect relationships; but evidence from a quasi-experiment is not as persuasive as evidence from a true experiment. True experiments are the gold standard for causal analysis.

A study that used gender or IQ as an independent variable would be an example of a quasi-experiment, because the study lacks experimenter control over the independent variable; that is, an experimenter cannot manipulate the gender or IQ of a subject.

As we discuss experimental design in the context of a tutorial on analysis of variance, it is important to point out that experimenter control is a requirement for a true experiment; but it is not a requirement for analysis of variance. Analysis of variance can be used with true experiments and with quasi-experiments that lack only experimenter control over the independent variable.

Note: Henceforth in this tutorial, when we refer to an experiment, we will be referring to a true experiment or to a quasi-experiment that is almost a true experiment, in the sense that it lacks only experimenter control over the independent variable.

What Is Experimental Design?

The term experimental design refers to a plan for conducting an experiment in such a way that research results will be valid and easy to interpret. This plan includes three interrelated activities:

• Write statistical hypotheses.
• Collect data.
• Analyze data.

Let's look in a little more detail at these three activities.

Statistical Hypotheses

A statistical hypothesis is an assumption about the value of a population parameter . There are two types of statistical hypotheses:

H 0: μ i = μ j

Here, μ i is the population mean for group i , and μ j is the population mean for group j . This hypothesis makes the assumption that population means in groups i and j are equal.

H 1: μ i ≠ μ j

This hypothesis makes the assumption that population means in groups i and j are not equal.

The null hypothesis and the alternative hypothesis are written to be mutually exclusive. If one is true, the other is not.

Experiments rely on sample data to test the null hypothesis. If experimental results, based on sample statistics , are consistent with the null hypothesis, the null hypothesis cannot be rejected; otherwise, the null hypothesis is rejected in favor of the alternative hypothesis.

Data Collection

The data collection phase of experimental design is all about methodology - how to run the experiment to produce valid, relevant statistics that can be used to test a null hypothesis.

Identify Variables

Every experiment exists to examine a cause-and-effect relationship. With respect to the relationship under investigation, an experimental design needs to account for three types of variables:

• Dependent variable. The dependent variable is the outcome being measured, the effect in a cause-and-effect relationship.
• Independent variables. An independent variable is a variable that is thought to be a possible cause in a cause-and-effect relationship.
• Extraneous variables. An extraneous variable is any other variable that could affect the dependent variable, but is not explicitly included in the experiment.

Note: The independent variables that are explicitly included in an experiment are also called factors .

Define Treatment Groups

In an experiment, treatment groups are built around factors, each group defined by a unique combination of factor levels.

For example, suppose that a drug company wants to test a new cholesterol medication. The dependent variable is total cholesterol level. One independent variable is dosage. And, since some drugs affect men and women differently, the researchers include an second independent variable - gender.

This experiment has two factors - dosage and gender. The dosage factor has three levels (0 mg, 50 mg, and 100 mg), and the gender factor has two levels (male and female). Given this combination of factors and levels, we can define six unique treatment groups, as shown below:

Note: The experiment described above is an example of a quasi-experiment, because the gender factor cannot be manipulated by the experimenter.

Select Factor Levels

A factor in an experiment can be described by the way in which factor levels are chosen for inclusion in the experiment:

• Fixed factor. The experiment includes all factor levels about which inferences are to be made.
• Random factor. The experiment includes a random sample of levels from a much bigger population of factor levels.

Experiments can be described by the presence or absence of fixed or random factors:

• Fixed-effects model. All of the factors in the experiment are fixed.
• Random-effects model. All of the factors in the experiment are random.
• Mixed model. At least one factor in the experiment is fixed, and at least one factor is random.

The use of fixed factors versus random factors has implications for how experimental results are interpreted. With a fixed factor, results apply only to factor levels that are explicitly included in the experiment. With a random factor, results apply to every factor level from the population.

For example, consider the blood pressure experiment described above. Suppose the experimenter only wanted to test the effect of three particular dosage levels - 0 mg, 50 mg, and 100 mg. He would include those dosage levels in the experiment, and any research conclusions would apply to only those particular dosage levels. This would be an example of a fixed-effects model.

On the other hand, suppose the experimenter wanted to test the effect of any dosage level. Since it is not practical to test every dosage level, the experimenter might choose three dosage levels at random from the population of possible dosage levels. Any research conclusions would apply not only to the selected dosage levels, but also to other dosage levels that were not included explicitly in the experiment. This would be an example of a random-effects model.

Select Experimental Units

The experimental unit is the entity that provides values for the dependent variable. Depending on the needs of the study, an experimental unit may be a person, animal, plant, product - anything. For example, in the cholesterol study described above, researchers measured cholesterol level (the dependent variable) of people; so the experimental units were people.

Note: When the experimental units are people, they are often referred to as subjects . Some researchers prefer the term participant , because subject has a connotation that the person is subservient.

If time and money were no object, you would include the entire population of experimental units in your experiment. In the real world, where there is never enough time or money, you will usually select a sample of experimental units from the population.

Ultimately, you want to use sample data to make inferences about population parameters. With that in mind, it is best practice to draw a random sample of experimental units from the population. This provides a defensible, statistical basis for generalizing from sample findings to the larger population.

Finally, it is important to consider sample size. The larger the sample, the greater the statistical power ; and the more confidence you can have in your results.

Assign Experimental Units to Treatments

Having selected a sample of experimental units, we need to assign each unit to one or more treatment groups. Here are two ways that you might assign experimental units to groups:

• Independent groups design. Each experimental unit is randomly assigned to one, and only one, treatment group. This is also known as a between-subjects design .
• Repeated measures design. Experimental units are assigned to more than one treatment group. This is also known as a within-subjects design .

Control for Extraneous Variables

Extraneous variables can mask effects of independent variables. Therefore, a good experimental design controls potential effects of extraneous variables. Here are a few strategies for controlling extraneous variables:

• Randomization Assign subjects randomly to treatment groups. This tends to distribute effects of extraneous variables evenly across groups.
• Repeated measures design. To control for individual differences between subjects (age, attitude, religion, etc.), assign each subject to multiple treatments. This strategy is called using subjects as their own control.
• Counterbalancing. In repeated measures designs, randomize or reverse the order of treatments among subjects to control for order effects (e.g., fatigue, practice).

As we describe specific experimental designs in upcoming lessons, we will point out the strategies that are used with each design to control the confounding effects of extraneous variables.

Data Analysis

Researchers follow a formal process to determine whether to reject a null hypothesis, based on sample data. This process, called hypothesis testing, consists of five steps:

• Formulate hypotheses. This involves stating the null and alternative hypotheses. Because the hypotheses are mutually exclusive, if one is true, the other must be false.
• Choose the test statistic. This involves specifying the statistic that will be used to assess the validity of the null hypothesis. Typically, in analysis of variance studies, researchers compute a F ratio to test hypotheses.
• Compute a P-value, based on sample data. Suppose the observed test statistic is equal to S . The P-value is the probability that the experiment would yield a test statistic as extreme as S , assuming the null hypothesis is true.
• Choose a significance level. The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is really true. Researchers often choose a significance level of 0.05 or 0.01.
• Test the null hypothesis. If the P-value is smaller than the significance level, we reject the null hypothesis; if it is larger, we fail to reject.

A good experimental design includes a precise plan for data analysis. Before the first data point is collected, a researcher should know how experimental data will be processed to accept or reject the null hypotheses.

Test Your Understanding

In a well-designed experiment, which of the following statements is true?

I. The null hypothesis and the alternative hypothesis are mutually exclusive. II. The null hypothesis is subjected to statistical test. III. The alternative hypothesis is subjected to statistical test.

(A) I only (B) II only (C) III only (D) I and II (E) I and III

The correct answer is (D). The null hypothesis and the alternative hypothesis are mutually exclusive; if one is true, the other must be false. Only the null hypothesis is subjected to statistical test. When the null hypothesis is accepted, the alternative hypothesis is rejected. The alternative hypothesis is not tested explicitly.

In a true experiment, each subject is assigned to only one treatment group. What type of design is this?

(A) Independent groups design (B) Repeated measures design (C) Within-subjects design (D) None of the above (E) All of the above

The correct answer is (A). In an independent groups design, each experimental unit is assigned to one treatment group. In the other two designs, each experimental unit is assigned to more than one treatment group.

In a true experiment, which of the following does the experimenter control?

(A) How to manipulate independent variables. (B) How to assign subjects to treatment conditions. (C) How to control for extraneous variables. (D) None of the above (E) All of the above

The correct answer is (E). The experimenter chooses factors and factor levels for the experiment, assigns experimental units to treatment groups (often through a random process), and implements strategies (randomization, counterbalancing, etc.) to control the influence of extraneous variables.

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Experimental Design – Types, Methods, Guide

Table of Contents

Experimental Design

Experimental design is a process of planning and conducting scientific experiments to investigate a hypothesis or research question. It involves carefully designing an experiment that can test the hypothesis, and controlling for other variables that may influence the results.

Experimental design typically includes identifying the variables that will be manipulated or measured, defining the sample or population to be studied, selecting an appropriate method of sampling, choosing a method for data collection and analysis, and determining the appropriate statistical tests to use.

Types of Experimental Design

Here are the different types of experimental design:

Completely Randomized Design

In this design, participants are randomly assigned to one of two or more groups, and each group is exposed to a different treatment or condition.

Randomized Block Design

This design involves dividing participants into blocks based on a specific characteristic, such as age or gender, and then randomly assigning participants within each block to one of two or more treatment groups.

Factorial Design

In a factorial design, participants are randomly assigned to one of several groups, each of which receives a different combination of two or more independent variables.

Repeated Measures Design

In this design, each participant is exposed to all of the different treatments or conditions, either in a random order or in a predetermined order.

Crossover Design

This design involves randomly assigning participants to one of two or more treatment groups, with each group receiving one treatment during the first phase of the study and then switching to a different treatment during the second phase.

Split-plot Design

In this design, the researcher manipulates one or more variables at different levels and uses a randomized block design to control for other variables.

Nested Design

This design involves grouping participants within larger units, such as schools or households, and then randomly assigning these units to different treatment groups.

Laboratory Experiment

Laboratory experiments are conducted under controlled conditions, which allows for greater precision and accuracy. However, because laboratory conditions are not always representative of real-world conditions, the results of these experiments may not be generalizable to the population at large.

Field Experiment

Field experiments are conducted in naturalistic settings and allow for more realistic observations. However, because field experiments are not as controlled as laboratory experiments, they may be subject to more sources of error.

Experimental Design Methods

Experimental design methods refer to the techniques and procedures used to design and conduct experiments in scientific research. Here are some common experimental design methods:

Randomization

This involves randomly assigning participants to different groups or treatments to ensure that any observed differences between groups are due to the treatment and not to other factors.

Control Group

The use of a control group is an important experimental design method that involves having a group of participants that do not receive the treatment or intervention being studied. The control group is used as a baseline to compare the effects of the treatment group.

Blinding involves keeping participants, researchers, or both unaware of which treatment group participants are in, in order to reduce the risk of bias in the results.

Counterbalancing

This involves systematically varying the order in which participants receive treatments or interventions in order to control for order effects.

Replication

Replication involves conducting the same experiment with different samples or under different conditions to increase the reliability and validity of the results.

This experimental design method involves manipulating multiple independent variables simultaneously to investigate their combined effects on the dependent variable.

This involves dividing participants into subgroups or blocks based on specific characteristics, such as age or gender, in order to reduce the risk of confounding variables.

Data Collection Method

Experimental design data collection methods are techniques and procedures used to collect data in experimental research. Here are some common experimental design data collection methods:

Direct Observation

This method involves observing and recording the behavior or phenomenon of interest in real time. It may involve the use of structured or unstructured observation, and may be conducted in a laboratory or naturalistic setting.

Self-report Measures

Self-report measures involve asking participants to report their thoughts, feelings, or behaviors using questionnaires, surveys, or interviews. These measures may be administered in person or online.

Behavioral Measures

Behavioral measures involve measuring participants’ behavior directly, such as through reaction time tasks or performance tests. These measures may be administered using specialized equipment or software.

Physiological Measures

Physiological measures involve measuring participants’ physiological responses, such as heart rate, blood pressure, or brain activity, using specialized equipment. These measures may be invasive or non-invasive, and may be administered in a laboratory or clinical setting.

Archival Data

Archival data involves using existing records or data, such as medical records, administrative records, or historical documents, as a source of information. These data may be collected from public or private sources.

Computerized Measures

Computerized measures involve using software or computer programs to collect data on participants’ behavior or responses. These measures may include reaction time tasks, cognitive tests, or other types of computer-based assessments.

Video Recording

Video recording involves recording participants’ behavior or interactions using cameras or other recording equipment. This method can be used to capture detailed information about participants’ behavior or to analyze social interactions.

Data Analysis Method

Experimental design data analysis methods refer to the statistical techniques and procedures used to analyze data collected in experimental research. Here are some common experimental design data analysis methods:

Descriptive Statistics

Descriptive statistics are used to summarize and describe the data collected in the study. This includes measures such as mean, median, mode, range, and standard deviation.

Inferential Statistics

Inferential statistics are used to make inferences or generalizations about a larger population based on the data collected in the study. This includes hypothesis testing and estimation.

Analysis of Variance (ANOVA)

ANOVA is a statistical technique used to compare means across two or more groups in order to determine whether there are significant differences between the groups. There are several types of ANOVA, including one-way ANOVA, two-way ANOVA, and repeated measures ANOVA.

Regression Analysis

Regression analysis is used to model the relationship between two or more variables in order to determine the strength and direction of the relationship. There are several types of regression analysis, including linear regression, logistic regression, and multiple regression.

Factor Analysis

Factor analysis is used to identify underlying factors or dimensions in a set of variables. This can be used to reduce the complexity of the data and identify patterns in the data.

Structural Equation Modeling (SEM)

SEM is a statistical technique used to model complex relationships between variables. It can be used to test complex theories and models of causality.

Cluster Analysis

Cluster analysis is used to group similar cases or observations together based on similarities or differences in their characteristics.

Time Series Analysis

Time series analysis is used to analyze data collected over time in order to identify trends, patterns, or changes in the data.

Multilevel Modeling

Multilevel modeling is used to analyze data that is nested within multiple levels, such as students nested within schools or employees nested within companies.

Applications of Experimental Design 

Experimental design is a versatile research methodology that can be applied in many fields. Here are some applications of experimental design:

• Medical Research: Experimental design is commonly used to test new treatments or medications for various medical conditions. This includes clinical trials to evaluate the safety and effectiveness of new drugs or medical devices.
• Agriculture : Experimental design is used to test new crop varieties, fertilizers, and other agricultural practices. This includes randomized field trials to evaluate the effects of different treatments on crop yield, quality, and pest resistance.
• Environmental science: Experimental design is used to study the effects of environmental factors, such as pollution or climate change, on ecosystems and wildlife. This includes controlled experiments to study the effects of pollutants on plant growth or animal behavior.
• Psychology : Experimental design is used to study human behavior and cognitive processes. This includes experiments to test the effects of different interventions, such as therapy or medication, on mental health outcomes.
• Engineering : Experimental design is used to test new materials, designs, and manufacturing processes in engineering applications. This includes laboratory experiments to test the strength and durability of new materials, or field experiments to test the performance of new technologies.
• Education : Experimental design is used to evaluate the effectiveness of teaching methods, educational interventions, and programs. This includes randomized controlled trials to compare different teaching methods or evaluate the impact of educational programs on student outcomes.
• Marketing : Experimental design is used to test the effectiveness of marketing campaigns, pricing strategies, and product designs. This includes experiments to test the impact of different marketing messages or pricing schemes on consumer behavior.

Examples of Experimental Design 

Here are some examples of experimental design in different fields:

• Example in Medical research : A study that investigates the effectiveness of a new drug treatment for a particular condition. Patients are randomly assigned to either a treatment group or a control group, with the treatment group receiving the new drug and the control group receiving a placebo. The outcomes, such as improvement in symptoms or side effects, are measured and compared between the two groups.
• Example in Education research: A study that examines the impact of a new teaching method on student learning outcomes. Students are randomly assigned to either a group that receives the new teaching method or a group that receives the traditional teaching method. Student achievement is measured before and after the intervention, and the results are compared between the two groups.
• Example in Environmental science: A study that tests the effectiveness of a new method for reducing pollution in a river. Two sections of the river are selected, with one section treated with the new method and the other section left untreated. The water quality is measured before and after the intervention, and the results are compared between the two sections.
• Example in Marketing research: A study that investigates the impact of a new advertising campaign on consumer behavior. Participants are randomly assigned to either a group that is exposed to the new campaign or a group that is not. Their behavior, such as purchasing or product awareness, is measured and compared between the two groups.
• Example in Social psychology: A study that examines the effect of a new social intervention on reducing prejudice towards a marginalized group. Participants are randomly assigned to either a group that receives the intervention or a control group that does not. Their attitudes and behavior towards the marginalized group are measured before and after the intervention, and the results are compared between the two groups.

When to use Experimental Research Design 

Experimental research design should be used when a researcher wants to establish a cause-and-effect relationship between variables. It is particularly useful when studying the impact of an intervention or treatment on a particular outcome.

Here are some situations where experimental research design may be appropriate:

• When studying the effects of a new drug or medical treatment: Experimental research design is commonly used in medical research to test the effectiveness and safety of new drugs or medical treatments. By randomly assigning patients to treatment and control groups, researchers can determine whether the treatment is effective in improving health outcomes.
• When evaluating the effectiveness of an educational intervention: An experimental research design can be used to evaluate the impact of a new teaching method or educational program on student learning outcomes. By randomly assigning students to treatment and control groups, researchers can determine whether the intervention is effective in improving academic performance.
• When testing the effectiveness of a marketing campaign: An experimental research design can be used to test the effectiveness of different marketing messages or strategies. By randomly assigning participants to treatment and control groups, researchers can determine whether the marketing campaign is effective in changing consumer behavior.
• When studying the effects of an environmental intervention: Experimental research design can be used to study the impact of environmental interventions, such as pollution reduction programs or conservation efforts. By randomly assigning locations or areas to treatment and control groups, researchers can determine whether the intervention is effective in improving environmental outcomes.
• When testing the effects of a new technology: An experimental research design can be used to test the effectiveness and safety of new technologies or engineering designs. By randomly assigning participants or locations to treatment and control groups, researchers can determine whether the new technology is effective in achieving its intended purpose.

How to Conduct Experimental Research

Here are the steps to conduct Experimental Research:

• Identify a Research Question : Start by identifying a research question that you want to answer through the experiment. The question should be clear, specific, and testable.
• Develop a Hypothesis: Based on your research question, develop a hypothesis that predicts the relationship between the independent and dependent variables. The hypothesis should be clear and testable.
• Design the Experiment : Determine the type of experimental design you will use, such as a between-subjects design or a within-subjects design. Also, decide on the experimental conditions, such as the number of independent variables, the levels of the independent variable, and the dependent variable to be measured.
• Select Participants: Select the participants who will take part in the experiment. They should be representative of the population you are interested in studying.
• Randomly Assign Participants to Groups: If you are using a between-subjects design, randomly assign participants to groups to control for individual differences.
• Conduct the Experiment : Conduct the experiment by manipulating the independent variable(s) and measuring the dependent variable(s) across the different conditions.
• Analyze the Data: Analyze the data using appropriate statistical methods to determine if there is a significant effect of the independent variable(s) on the dependent variable(s).
• Draw Conclusions: Based on the data analysis, draw conclusions about the relationship between the independent and dependent variables. If the results support the hypothesis, then it is accepted. If the results do not support the hypothesis, then it is rejected.
• Communicate the Results: Finally, communicate the results of the experiment through a research report or presentation. Include the purpose of the study, the methods used, the results obtained, and the conclusions drawn.

Purpose of Experimental Design 

The purpose of experimental design is to control and manipulate one or more independent variables to determine their effect on a dependent variable. Experimental design allows researchers to systematically investigate causal relationships between variables, and to establish cause-and-effect relationships between the independent and dependent variables. Through experimental design, researchers can test hypotheses and make inferences about the population from which the sample was drawn.

Experimental design provides a structured approach to designing and conducting experiments, ensuring that the results are reliable and valid. By carefully controlling for extraneous variables that may affect the outcome of the study, experimental design allows researchers to isolate the effect of the independent variable(s) on the dependent variable(s), and to minimize the influence of other factors that may confound the results.

Experimental design also allows researchers to generalize their findings to the larger population from which the sample was drawn. By randomly selecting participants and using statistical techniques to analyze the data, researchers can make inferences about the larger population with a high degree of confidence.

Overall, the purpose of experimental design is to provide a rigorous, systematic, and scientific method for testing hypotheses and establishing cause-and-effect relationships between variables. Experimental design is a powerful tool for advancing scientific knowledge and informing evidence-based practice in various fields, including psychology, biology, medicine, engineering, and social sciences.

Advantages of Experimental Design 

Experimental design offers several advantages in research. Here are some of the main advantages:

• Control over extraneous variables: Experimental design allows researchers to control for extraneous variables that may affect the outcome of the study. By manipulating the independent variable and holding all other variables constant, researchers can isolate the effect of the independent variable on the dependent variable.
• Establishing causality: Experimental design allows researchers to establish causality by manipulating the independent variable and observing its effect on the dependent variable. This allows researchers to determine whether changes in the independent variable cause changes in the dependent variable.
• Replication : Experimental design allows researchers to replicate their experiments to ensure that the findings are consistent and reliable. Replication is important for establishing the validity and generalizability of the findings.
• Random assignment: Experimental design often involves randomly assigning participants to conditions. This helps to ensure that individual differences between participants are evenly distributed across conditions, which increases the internal validity of the study.
• Precision : Experimental design allows researchers to measure variables with precision, which can increase the accuracy and reliability of the data.
• Generalizability : If the study is well-designed, experimental design can increase the generalizability of the findings. By controlling for extraneous variables and using random assignment, researchers can increase the likelihood that the findings will apply to other populations and contexts.

Limitations of Experimental Design

Experimental design has some limitations that researchers should be aware of. Here are some of the main limitations:

• Artificiality : Experimental design often involves creating artificial situations that may not reflect real-world situations. This can limit the external validity of the findings, or the extent to which the findings can be generalized to real-world settings.
• Ethical concerns: Some experimental designs may raise ethical concerns, particularly if they involve manipulating variables that could cause harm to participants or if they involve deception.
• Participant bias : Participants in experimental studies may modify their behavior in response to the experiment, which can lead to participant bias.
• Limited generalizability: The conditions of the experiment may not reflect the complexities of real-world situations. As a result, the findings may not be applicable to all populations and contexts.
• Cost and time : Experimental design can be expensive and time-consuming, particularly if the experiment requires specialized equipment or if the sample size is large.
• Researcher bias : Researchers may unintentionally bias the results of the experiment if they have expectations or preferences for certain outcomes.
• Lack of feasibility : Experimental design may not be feasible in some cases, particularly if the research question involves variables that cannot be manipulated or controlled.

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Statistical Design and Analysis of Biological Experiments

Chapter 1 principles of experimental design, 1.1 introduction.

The validity of conclusions drawn from a statistical analysis crucially hinges on the manner in which the data are acquired, and even the most sophisticated analysis will not rescue a flawed experiment. Planning an experiment and thinking about the details of data acquisition is so important for a successful analysis that R. A. Fisher—who single-handedly invented many of the experimental design techniques we are about to discuss—famously wrote

To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of. ( Fisher 1938 )

(Statistical) design of experiments provides the principles and methods for planning experiments and tailoring the data acquisition to an intended analysis. Design and analysis of an experiment are best considered as two aspects of the same enterprise: the goals of the analysis strongly inform an appropriate design, and the implemented design determines the possible analyses.

The primary aim of designing experiments is to ensure that valid statistical and scientific conclusions can be drawn that withstand the scrutiny of a determined skeptic. Good experimental design also considers that resources are used efficiently, and that estimates are sufficiently precise and hypothesis tests adequately powered. It protects our conclusions by excluding alternative interpretations or rendering them implausible. Three main pillars of experimental design are randomization , replication , and blocking , and we will flesh out their effects on the subsequent analysis as well as their implementation in an experimental design.

An experimental design is always tailored towards predefined (primary) analyses and an efficient analysis and unambiguous interpretation of the experimental data is often straightforward from a good design. This does not prevent us from doing additional analyses of interesting observations after the data are acquired, but these analyses can be subjected to more severe criticisms and conclusions are more tentative.

In this chapter, we provide the wider context for using experiments in a larger research enterprise and informally introduce the main statistical ideas of experimental design. We use a comparison of two samples as our main example to study how design choices affect an analysis, but postpone a formal quantitative analysis to the next chapters.

1.2 A Cautionary Tale

For illustrating some of the issues arising in the interplay of experimental design and analysis, we consider a simple example. We are interested in comparing the enzyme levels measured in processed blood samples from laboratory mice, when the sample processing is done either with a kit from a vendor A, or a kit from a competitor B. For this, we take 20 mice and randomly select 10 of them for sample preparation with kit A, while the blood samples of the remaining 10 mice are prepared with kit B. The experiment is illustrated in Figure 1.1 A and the resulting data are given in Table 1.1 .

One option for comparing the two kits is to look at the difference in average enzyme levels, and we find an average level of 10.32 for vendor A and 10.66 for vendor B. We would like to interpret their difference of -0.34 as the difference due to the two preparation kits and conclude whether the two kits give equal results or if measurements based on one kit are systematically different from those based on the other kit.

Such interpretation, however, is only valid if the two groups of mice and their measurements are identical in all aspects except the sample preparation kit. If we use one strain of mice for kit A and another strain for kit B, any difference might also be attributed to inherent differences between the strains. Similarly, if the measurements using kit B were conducted much later than those using kit A, any observed difference might be attributed to changes in, e.g., mice selected, batches of chemicals used, device calibration, or any number of other influences. None of these competing explanations for an observed difference can be excluded from the given data alone, but good experimental design allows us to render them (almost) arbitrarily implausible.

A second aspect for our analysis is the inherent uncertainty in our calculated difference: if we repeat the experiment, the observed difference will change each time, and this will be more pronounced for a smaller number of mice, among others. If we do not use a sufficient number of mice in our experiment, the uncertainty associated with the observed difference might be too large, such that random fluctuations become a plausible explanation for the observed difference. Systematic differences between the two kits, of practically relevant magnitude in either direction, might then be compatible with the data, and we can draw no reliable conclusions from our experiment.

In each case, the statistical analysis—no matter how clever—was doomed before the experiment was even started, while simple ideas from statistical design of experiments would have provided correct and robust results with interpretable conclusions.

1.3 The Language of Experimental Design

By an experiment we understand an investigation where the researcher has full control over selecting and altering the experimental conditions of interest, and we only consider investigations of this type. The selected experimental conditions are called treatments . An experiment is comparative if the responses to several treatments are to be compared or contrasted. The experimental units are the smallest subdivision of the experimental material to which a treatment can be assigned. All experimental units given the same treatment constitute a treatment group . Especially in biology, we often compare treatments to a control group to which some standard experimental conditions are applied; a typical example is using a placebo for the control group, and different drugs for the other treatment groups.

The values observed are called responses and are measured on the response units ; these are often identical to the experimental units but need not be. Multiple experimental units are sometimes combined into groupings or blocks , such as mice grouped by litter, or samples grouped by batches of chemicals used for their preparation. More generally, we call any grouping of the experimental material (even with group size one) a unit .

In our example, we selected the mice, used a single sample per mouse, deliberately chose the two specific vendors, and had full control over which kit to assign to which mouse. In other words, the two kits are the treatments and the mice are the experimental units. We took the measured enzyme level of a single sample from a mouse as our response, and samples are therefore the response units. The resulting experiment is comparative, because we contrast the enzyme levels between the two treatment groups.

Figure 1.1: Three designs to determine the difference between two preparation kits A and B based on four mice. A: One sample per mouse. Comparison between averages of samples with same kit. B: Two samples per mouse treated with the same kit. Comparison between averages of mice with same kit requires averaging responses for each mouse first. C: Two samples per mouse each treated with different kit. Comparison between two samples of each mouse, with differences averaged.

In this example, we can coalesce experimental and response units, because we have a single response per mouse and cannot distinguish a sample from a mouse in the analysis, as illustrated in Figure 1.1 A for four mice. Responses from mice with the same kit are averaged, and the kit difference is the difference between these two averages.

By contrast, if we take two samples per mouse and use the same kit for both samples, then the mice are still the experimental units, but each mouse now groups the two response units associated with it. Now, responses from the same mouse are first averaged, and these averages are used to calculate the difference between kits; even though eight measurements are available, this difference is still based on only four mice (Figure 1.1 B).

If we take two samples per mouse, but apply each kit to one of the two samples, then the samples are both the experimental and response units, while the mice are blocks that group the samples. Now, we calculate the difference between kits for each mouse, and then average these differences (Figure 1.1 C).

If we only use one kit and determine the average enzyme level, then this investigation is still an experiment, but is not comparative.

To summarize, the design of an experiment determines the logical structure of the experiment ; it consists of (i) a set of treatments (the two kits); (ii) a specification of the experimental units (animals, cell lines, samples) (the mice in Figure 1.1 A,B and the samples in Figure 1.1 C); (iii) a procedure for assigning treatments to units; and (iv) a specification of the response units and the quantity to be measured as a response (the samples and associated enzyme levels).

1.4 Experiment Validity

Before we embark on the more technical aspects of experimental design, we discuss three components for evaluating an experiment’s validity: construct validity , internal validity , and external validity . These criteria are well-established in areas such as educational and psychological research, and have more recently been discussed for animal research ( Würbel 2017 ) where experiments are increasingly scrutinized for their scientific rationale and their design and intended analyses.

1.4.1 Construct Validity

Construct validity concerns the choice of the experimental system for answering our research question. Is the system even capable of providing a relevant answer to the question?

Studying the mechanisms of a particular disease, for example, might require careful choice of an appropriate animal model that shows a disease phenotype and is accessible to experimental interventions. If the animal model is a proxy for drug development for humans, biological mechanisms must be sufficiently similar between animal and human physiologies.

Another important aspect of the construct is the quantity that we intend to measure (the measurand ), and its relation to the quantity or property we are interested in. For example, we might measure the concentration of the same chemical compound once in a blood sample and once in a highly purified sample, and these constitute two different measurands, whose values might not be comparable. Often, the quantity of interest (e.g., liver function) is not directly measurable (or even quantifiable) and we measure a biomarker instead. For example, pre-clinical and clinical investigations may use concentrations of proteins or counts of specific cell types from blood samples, such as the CD4+ cell count used as a biomarker for immune system function.

1.4.2 Internal Validity

The internal validity of an experiment concerns the soundness of the scientific rationale, statistical properties such as precision of estimates, and the measures taken against risk of bias. It refers to the validity of claims within the context of the experiment. Statistical design of experiments plays a prominent role in ensuring internal validity, and we briefly discuss the main ideas before providing the technical details and an application to our example in the subsequent sections.

Scientific Rationale and Research Question

The scientific rationale of a study is (usually) not immediately a statistical question. Translating a scientific question into a quantitative comparison amenable to statistical analysis is no small task and often requires careful consideration. It is a substantial, if non-statistical, benefit of using experimental design that we are forced to formulate a precise-enough research question and decide on the main analyses required for answering it before we conduct the experiment. For example, the question: is there a difference between placebo and drug? is insufficiently precise for planning a statistical analysis and determine an adequate experimental design. What exactly is the drug treatment? What should the drug’s concentration be and how is it administered? How do we make sure that the placebo group is comparable to the drug group in all other aspects? What do we measure and what do we mean by “difference?” A shift in average response, a fold-change, change in response before and after treatment?

The scientific rationale also enters the choice of a potential control group to which we compare responses. The quote

The deep, fundamental question in statistical analysis is ‘Compared to what?’ ( Tufte 1997 )

highlights the importance of this choice.

There are almost never enough resources to answer all relevant scientific questions. We therefore define a few questions of highest interest, and the main purpose of the experiment is answering these questions in the primary analysis . This intended analysis drives the experimental design to ensure relevant estimates can be calculated and have sufficient precision, and tests are adequately powered. This does not preclude us from conducting additional secondary analyses and exploratory analyses , but we are not willing to enlarge the experiment to ensure that strong conclusions can also be drawn from these analyses.

Risk of Bias

Experimental bias is a systematic difference in response between experimental units in addition to the difference caused by the treatments. The experimental units in the different groups are then not equal in all aspects other than the treatment applied to them. We saw several examples in Section 1.2 .

Minimizing the risk of bias is crucial for internal validity and we look at some common measures to eliminate or reduce different types of bias in Section 1.5 .

Precision and Effect Size

Another aspect of internal validity is the precision of estimates and the expected effect sizes. Is the experimental setup, in principle, able to detect a difference of relevant magnitude? Experimental design offers several methods for answering this question based on the expected heterogeneity of samples, the measurement error, and other sources of variation: power analysis is a technique for determining the number of samples required to reliably detect a relevant effect size and provide estimates of sufficient precision. More samples yield more precision and more power, but we have to be careful that replication is done at the right level: simply measuring a biological sample multiple times as in Figure 1.1 B yields more measured values, but is pseudo-replication for analyses. Replication should also ensure that the statistical uncertainties of estimates can be gauged from the data of the experiment itself, without additional untestable assumptions. Finally, the technique of blocking , shown in Figure 1.1 C, can remove a substantial proportion of the variation and thereby increase power and precision if we find a way to apply it.

1.4.3 External Validity

The external validity of an experiment concerns its replicability and the generalizability of inferences. An experiment is replicable if its results can be confirmed by an independent new experiment, preferably by a different lab and researcher. Experimental conditions in the replicate experiment usually differ from the original experiment, which provides evidence that the observed effects are robust to such changes. A much weaker condition on an experiment is reproducibility , the property that an independent researcher draws equivalent conclusions based on the data from this particular experiment, using the same analysis techniques. Reproducibility requires publishing the raw data, details on the experimental protocol, and a description of the statistical analyses, preferably with accompanying source code. Many scientific journals subscribe to reporting guidelines to ensure reproducibility and these are also helpful for planning an experiment.

A main threat to replicability and generalizability are too tightly controlled experimental conditions, when inferences only hold for a specific lab under the very specific conditions of the original experiment. Introducing systematic heterogeneity and using multi-center studies effectively broadens the experimental conditions and therefore the inferences for which internal validity is available.

For systematic heterogeneity , experimental conditions are systematically altered in addition to the treatments, and treatment differences estimated for each condition. For example, we might split the experimental material into several batches and use a different day of analysis, sample preparation, batch of buffer, measurement device, and lab technician for each batch. A more general inference is then possible if effect size, effect direction, and precision are comparable between the batches, indicating that the treatment differences are stable over the different conditions.

In multi-center experiments , the same experiment is conducted in several different labs and the results compared and merged. Multi-center approaches are very common in clinical trials and often necessary to reach the required number of patient enrollments.

Generalizability of randomized controlled trials in medicine and animal studies can suffer from overly restrictive eligibility criteria. In clinical trials, patients are often included or excluded based on co-medications and co-morbidities, and the resulting sample of eligible patients might no longer be representative of the patient population. For example, Travers et al. ( 2007 ) used the eligibility criteria of 17 random controlled trials of asthma treatments and found that out of 749 patients, only a median of 6% (45 patients) would be eligible for an asthma-related randomized controlled trial. This puts a question mark on the relevance of the trials’ findings for asthma patients in general.

1.5 Reducing the Risk of Bias

1.5.1 randomization of treatment allocation.

If systematic differences other than the treatment exist between our treatment groups, then the effect of the treatment is confounded with these other differences and our estimates of treatment effects might be biased.

We remove such unwanted systematic differences from our treatment comparisons by randomizing the allocation of treatments to experimental units. In a completely randomized design , each experimental unit has the same chance of being subjected to any of the treatments, and any differences between the experimental units other than the treatments are distributed over the treatment groups. Importantly, randomization is the only method that also protects our experiment against unknown sources of bias: we do not need to know all or even any of the potential differences and yet their impact is eliminated from the treatment comparisons by random treatment allocation.

Randomization has two effects: (i) differences unrelated to treatment become part of the ‘statistical noise’ rendering the treatment groups more similar; and (ii) the systematic differences are thereby eliminated as sources of bias from the treatment comparison.

Randomization transforms systematic variation into random variation.

In our example, a proper randomization would select 10 out of our 20 mice fully at random, such that the probability of any one mouse being picked is 1/20. These ten mice are then assigned to kit A, and the remaining mice to kit B. This allocation is entirely independent of the treatments and of any properties of the mice.

To ensure random treatment allocation, some kind of random process needs to be employed. This can be as simple as shuffling a pack of 10 red and 10 black cards or using a software-based random number generator. Randomization is slightly more difficult if the number of experimental units is not known at the start of the experiment, such as when patients are recruited for an ongoing clinical trial (sometimes called rolling recruitment ), and we want to have reasonable balance between the treatment groups at each stage of the trial.

Seemingly random assignments “by hand” are usually no less complicated than fully random assignments, but are always inferior. If surprising results ensue from the experiment, such assignments are subject to unanswerable criticism and suspicion of unwanted bias. Even worse are systematic allocations; they can only remove bias from known causes, and immediately raise red flags under the slightest scrutiny.

The Problem of Undesired Assignments

Even with a fully random treatment allocation procedure, we might end up with an undesirable allocation. For our example, the treatment group of kit A might—just by chance—contain mice that are all bigger or more active than those in the other treatment group. Statistical orthodoxy recommends using the design nevertheless, because only full randomization guarantees valid estimates of residual variance and unbiased estimates of effects. This argument, however, concerns the long-run properties of the procedure and seems of little help in this specific situation. Why should we care if the randomization yields correct estimates under replication of the experiment, if the particular experiment is jeopardized?

Another solution is to create a list of all possible allocations that we would accept and randomly choose one of these allocations for our experiment. The analysis should then reflect this restriction in the possible randomizations, which often renders this approach difficult to implement.

The most pragmatic method is to reject highly undesirable designs and compute a new randomization ( Cox 1958 ) . Undesirable allocations are unlikely to arise for large sample sizes, and we might accept a small bias in estimation for small sample sizes, when uncertainty in the estimated treatment effect is already high. In this approach, whenever we reject a particular outcome, we must also be willing to reject the outcome if we permute the treatment level labels. If we reject eight big and two small mice for kit A, then we must also reject two big and eight small mice. We must also be transparent and report a rejected allocation, so that critics may come to their own conclusions about potential biases and their remedies.

1.5.2 Blinding

Bias in treatment comparisons is also introduced if treatment allocation is random, but responses cannot be measured entirely objectively, or if knowledge of the assigned treatment affects the response. In clinical trials, for example, patients might react differently when they know to be on a placebo treatment, an effect known as cognitive bias . In animal experiments, caretakers might report more abnormal behavior for animals on a more severe treatment. Cognitive bias can be eliminated by concealing the treatment allocation from technicians or participants of a clinical trial, a technique called single-blinding .

If response measures are partially based on professional judgement (such as a clinical scale), patient or physician might unconsciously report lower scores for a placebo treatment, a phenomenon known as observer bias . Its removal requires double blinding , where treatment allocations are additionally concealed from the experimentalist.

Blinding requires randomized treatment allocation to begin with and substantial effort might be needed to implement it. Drug companies, for example, have to go to great lengths to ensure that a placebo looks, tastes, and feels similar enough to the actual drug. Additionally, blinding is often done by coding the treatment conditions and samples, and effect sizes and statistical significance are calculated before the code is revealed.

In clinical trials, double-blinding creates a conflict of interest. The attending physicians do not know which patient received which treatment, and thus accumulation of side-effects cannot be linked to any treatment. For this reason, clinical trials have a data monitoring committee not involved in the final analysis, that performs intermediate analyses of efficacy and safety at predefined intervals. If severe problems are detected, the committee might recommend altering or aborting the trial. The same might happen if one treatment already shows overwhelming evidence of superiority, such that it becomes unethical to withhold this treatment from the other patients.

1.5.3 Analysis Plan and Registration

An often overlooked source of bias has been termed the researcher degrees of freedom or garden of forking paths in the data analysis. For any set of data, there are many different options for its analysis: some results might be considered outliers and discarded, assumptions are made on error distributions and appropriate test statistics, different covariates might be included into a regression model. Often, multiple hypotheses are investigated and tested, and analyses are done separately on various (overlapping) subgroups. Hypotheses formed after looking at the data require additional care in their interpretation; almost never will \(p\) -values for these ad hoc or post hoc hypotheses be statistically justifiable. Many different measured response variables invite fishing expeditions , where patterns in the data are sought without an underlying hypothesis. Only reporting those sub-analyses that gave ‘interesting’ findings invariably leads to biased conclusions and is called cherry-picking or \(p\) -hacking (or much less flattering names).

The statistical analysis is always part of a larger scientific argument and we should consider the necessary computations in relation to building our scientific argument about the interpretation of the data. In addition to the statistical calculations, this interpretation requires substantial subject-matter knowledge and includes (many) non-statistical arguments. Two quotes highlight that experiment and analysis are a means to an end and not the end in itself.

There is a boundary in data interpretation beyond which formulas and quantitative decision procedures do not go, where judgment and style enter. ( Abelson 1995 )

Often, perfectly reasonable people come to perfectly reasonable decisions or conclusions based on nonstatistical evidence. Statistical analysis is a tool with which we support reasoning. It is not a goal in itself. ( Bailar III 1981 )

There is often a grey area between exploiting researcher degrees of freedom to arrive at a desired conclusion, and creative yet informed analyses of data. One way to navigate this area is to distinguish between exploratory studies and confirmatory studies . The former have no clearly stated scientific question, but are used to generate interesting hypotheses by identifying potential associations or effects that are then further investigated. Conclusions from these studies are very tentative and must be reported honestly as such. In contrast, standards are much higher for confirmatory studies, which investigate a specific predefined scientific question. Analysis plans and pre-registration of an experiment are accepted means for demonstrating lack of bias due to researcher degrees of freedom, and separating primary from secondary analyses allows emphasizing the main goals of the study.

Analysis Plan

The analysis plan is written before conducting the experiment and details the measurands and estimands, the hypotheses to be tested together with a power and sample size calculation, a discussion of relevant effect sizes, detection and handling of outliers and missing data, as well as steps for data normalization such as transformations and baseline corrections. If a regression model is required, its factors and covariates are outlined. Particularly in biology, handling measurements below the limit of quantification and saturation effects require careful consideration.

In the context of clinical trials, the problem of estimands has become a recent focus of attention. An estimand is the target of a statistical estimation procedure, for example the true average difference in enzyme levels between the two preparation kits. A main problem in many studies are post-randomization events that can change the estimand, even if the estimation procedure remains the same. For example, if kit B fails to produce usable samples for measurement in five out of ten cases because the enzyme level was too low, while kit A could handle these enzyme levels perfectly fine, then this might severely exaggerate the observed difference between the two kits. Similar problems arise in drug trials, when some patients stop taking one of the drugs due to side-effects or other complications.

Registration

Registration of experiments is an even more severe measure used in conjunction with an analysis plan and is becoming standard in clinical trials. Here, information about the trial, including the analysis plan, procedure to recruit patients, and stopping criteria, are registered in a public database. Publications based on the trial then refer to this registration, such that reviewers and readers can compare what the researchers intended to do and what they actually did. Similar portals for pre-clinical and translational research are also available.

1.6 Notes and Summary

The problem of measurements and measurands is further discussed for statistics in Hand ( 1996 ) and specifically for biological experiments in Coxon, Longstaff, and Burns ( 2019 ) . A general review of methods for handling missing data is Dong and Peng ( 2013 ) . The different roles of randomization are emphasized in Cox ( 2009 ) .

Two well-known reporting guidelines are the ARRIVE guidelines for animal research ( Kilkenny et al. 2010 ) and the CONSORT guidelines for clinical trials ( Moher et al. 2010 ) . Guidelines describing the minimal information required for reproducing experimental results have been developed for many types of experimental techniques, including microarrays (MIAME), RNA sequencing (MINSEQE), metabolomics (MSI) and proteomics (MIAPE) experiments; the FAIRSHARE initiative provides a more comprehensive collection ( Sansone et al. 2019 ) .

The problems of experimental design in animal experiments and particularly translation research are discussed in Couzin-Frankel ( 2013 ) . Multi-center studies are now considered for these investigations, and using a second laboratory already increases reproducibility substantially ( Richter et al. 2010 ; Richter 2017 ; Voelkl et al. 2018 ; Karp 2018 ) and allows standardizing the treatment effects ( Kafkafi et al. 2017 ) . First attempts are reported of using designs similar to clinical trials ( Llovera and Liesz 2016 ) . Exploratory-confirmatory research and external validity for animal studies is discussed in Kimmelman, Mogil, and Dirnagl ( 2014 ) and Pound and Ritskes-Hoitinga ( 2018 ) . Further information on pilot studies is found in Moore et al. ( 2011 ) , Sim ( 2019 ) , and Thabane et al. ( 2010 ) .

The deliberate use of statistical analyses and their interpretation for supporting a larger argument was called statistics as principled argument ( Abelson 1995 ) . Employing useless statistical analysis without reference to the actual scientific question is surrogate science ( Gigerenzer and Marewski 2014 ) and adaptive thinking is integral to meaningful statistical analysis ( Gigerenzer 2002 ) .

In an experiment, the investigator has full control over the experimental conditions applied to the experiment material. The experimental design gives the logical structure of an experiment: the units describing the organization of the experimental material, the treatments and their allocation to units, and the response. Statistical design of experiments includes techniques to ensure internal validity of an experiment, and methods to make inference from experimental data efficient.

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• Choosing the Right Statistical Test | Types & Examples

Choosing the Right Statistical Test | Types & Examples

Published on January 28, 2020 by Rebecca Bevans . Revised on June 22, 2023.

Statistical tests are used in hypothesis testing . They can be used to:

• determine whether a predictor variable has a statistically significant relationship with an outcome variable.
• estimate the difference between two or more groups.

Statistical tests assume a null hypothesis of no relationship or no difference between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis.

If you already know what types of variables you’re dealing with, you can use the flowchart to choose the right statistical test for your data.

Statistical tests flowchart

Table of contents

What does a statistical test do, when to perform a statistical test, choosing a parametric test: regression, comparison, or correlation, choosing a nonparametric test, flowchart: choosing a statistical test, other interesting articles, frequently asked questions about statistical tests.

Statistical tests work by calculating a test statistic – a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship.

It then calculates a p value (probability value). The p -value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true.

If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a statistically significant relationship between the predictor and outcome variables.

If the value of the test statistic is less extreme than the one calculated from the null hypothesis, then you can infer no statistically significant relationship between the predictor and outcome variables.

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You can perform statistical tests on data that have been collected in a statistically valid manner – either through an experiment , or through observations made using probability sampling methods .

For a statistical test to be valid , your sample size needs to be large enough to approximate the true distribution of the population being studied.

To determine which statistical test to use, you need to know:

• whether your data meets certain assumptions.
• the types of variables that you’re dealing with.

Statistical assumptions

Statistical tests make some common assumptions about the data they are testing:

• Independence of observations (a.k.a. no autocorrelation): The observations/variables you include in your test are not related (for example, multiple measurements of a single test subject are not independent, while measurements of multiple different test subjects are independent).
• Homogeneity of variance : the variance within each group being compared is similar among all groups. If one group has much more variation than others, it will limit the test’s effectiveness.
• Normality of data : the data follows a normal distribution (a.k.a. a bell curve). This assumption applies only to quantitative data .

If your data do not meet the assumptions of normality or homogeneity of variance, you may be able to perform a nonparametric statistical test , which allows you to make comparisons without any assumptions about the data distribution.

If your data do not meet the assumption of independence of observations, you may be able to use a test that accounts for structure in your data (repeated-measures tests or tests that include blocking variables).

Types of variables

The types of variables you have usually determine what type of statistical test you can use.

Quantitative variables represent amounts of things (e.g. the number of trees in a forest). Types of quantitative variables include:

• Continuous (aka ratio variables): represent measures and can usually be divided into units smaller than one (e.g. 0.75 grams).
• Discrete (aka integer variables): represent counts and usually can’t be divided into units smaller than one (e.g. 1 tree).

Categorical variables represent groupings of things (e.g. the different tree species in a forest). Types of categorical variables include:

• Ordinal : represent data with an order (e.g. rankings).
• Nominal : represent group names (e.g. brands or species names).
• Binary : represent data with a yes/no or 1/0 outcome (e.g. win or lose).

Choose the test that fits the types of predictor and outcome variables you have collected (if you are doing an experiment , these are the independent and dependent variables ). Consult the tables below to see which test best matches your variables.

Parametric tests usually have stricter requirements than nonparametric tests, and are able to make stronger inferences from the data. They can only be conducted with data that adheres to the common assumptions of statistical tests.

The most common types of parametric test include regression tests, comparison tests, and correlation tests.

Regression tests

Regression tests look for cause-and-effect relationships . They can be used to estimate the effect of one or more continuous variables on another variable.

Comparison tests

Comparison tests look for differences among group means . They can be used to test the effect of a categorical variable on the mean value of some other characteristic.

T-tests are used when comparing the means of precisely two groups (e.g., the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups (e.g., the average heights of children, teenagers, and adults).

Correlation tests

Correlation tests check whether variables are related without hypothesizing a cause-and-effect relationship.

These can be used to test whether two variables you want to use in (for example) a multiple regression test are autocorrelated.

Non-parametric tests don’t make as many assumptions about the data, and are useful when one or more of the common statistical assumptions are violated. However, the inferences they make aren’t as strong as with parametric tests.

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This flowchart helps you choose among parametric tests. For nonparametric alternatives, check the table above.

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
• Null hypothesis

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

Statistical tests commonly assume that:

• the data are normally distributed
• the groups that are being compared have similar variance
• the data are independent

If your data does not meet these assumptions you might still be able to use a nonparametric statistical test , which have fewer requirements but also make weaker inferences.

A test statistic is a number calculated by a  statistical test . It describes how far your observed data is from the  null hypothesis  of no relationship between  variables or no difference among sample groups.

The test statistic tells you how different two or more groups are from the overall population mean , or how different a linear slope is from the slope predicted by a null hypothesis . Different test statistics are used in different statistical tests.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g. the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g. water volume or weight).

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What Is the Difference Between Data Analysis and Statistical Analysis?

By Alex Kuo - 8 min read

Though they started as clearly separate fields, the lines between data analysis and statistical analysis have since blurred. So much so that the terms “data analysis” and “statistical analysis” are often used interchangeably. But they shouldn’t be. 

With this in mind, let’s dive into the data analysis vs. statistical analysis conundrum and explore their differences.

What Is Data Analysis?

Data analysis can be defined as both a branch of data science and a distinctive field in its own right. The term “data analysis” essentially encompasses all the processes and methods used to extract value from data. These include different approaches to inspecting, cleaning, transforming, visualizing, modeling, and interpreting data.

The individual whose job is to analyze data is referred to as a data analyst. Using their expertise in various data analytics tools and techniques to interpret data trends, data analysts identify correlations and present their findings to their employers, who will then use these findings to inform their decision-making processes and strategic planning and solve business problems.

The exact nature of these findings will depend on the type of data analytics performed.

Descriptive data analysis aims to describe or summarize data to understand its characteristics and provide insights into what has happened (or is currently happening). And that’s where its purpose ends. There are no attempts to make predictions or determine causality.

Making predictions is the purpose of the aptly named branch known as predictive data analysis. Use this analysis on historical data, and you’ll easily extrapolate likely outcomes for the future.

Now, if you want to act based on these predictions, you need prescriptive data analysis. This type goes beyond predicting future outcomes by recommending actions or strategies to achieve specific goals. 

What Is Statistical Analysis?

Statistical analysis has the same general goal as data analysis – to make sense of the raw data.

However, to achieve this goal, statistical analysis relies on different statistical methods and techniques . Common statistical methods include descriptive statistics, regression analysis, correlation analysis, and hypothesis testing. The statistical techniques these methods employ are more specialized tasks, such as the mean, linear regression, and the Pearson correlation coefficient.

Now, if you’re a novice, these terms won’t mean much to you. However, they serve to demonstrate how heavily statistical analysis relies on, well, statistics.

Until a few decades ago, only statisticians employed these techniques while performing statistical analysis. Now, data scientists use them, too, in specific fields, such as data visualization . 

That’s how the whole data analysis vs. statistical analysis debate started in the first place. However, the statistical methods and techniques performed under the umbrella of data analysis are just a tiny fraction of everything that the field of statistical analysis encompasses. 

Data Analysis vs. Statistical Analysis: What Are the Differences?

By now, it’s clear that data analysis and statistical analysis aren’t the same from their scope alone. A better way to view these analyses is through a Venn diagram. Sure, there is an overlap where both data analysts and statistical analysts share common ground – the methods and techniques they use. However, both circles also contain a broader range of activities that distinguishes them clearly. However, the scope of activities isn’t the only difference between data analysis and statistical analysis.

Most commonly, the role of a data analyst is to sift through vast amounts of data (i.e., big data) to inspect it, clean it, model it, or present it in a non-technical way.

A statistician, on the other hand, will receive a limited amount of relevant data collected (i.e., a sample) to analyze it using rigorous statistical techniques. 

The Approach

As mentioned, both data analysis and statistical analysis have the same goal – to gain valuable insights from raw data. However, both fields approach this goal differently.

A data analyst will use a data science toolbox consisting of programming languages (e.g., Python) and analytics engines (e.g., Apache Spark) to process and analyze data. While a statistical analyst can also make use of similar statistical programs (e.g., R), their approach to analysis is more methodical and targeted. Basically, statistical analysis aims to understand one particular aspect of the analyzed sample at a time. 

The Purpose

From the approach to analyzing data, we can infer another important difference between data analysis and statistical analysis – their very purpose. Broadly speaking, data analysis aims to observe trends and patterns in large sets of data. 

In contrast, statistical analysis tries to validate these observations to ensure they are significant and reliable. In this process, some observations and explanations will be confirmed, while others will be refuted or require further validation. Think of it as separating the wheat from the chaff.

The Skill Set

To do their job correctly, data analysts will need to be skilled in query language and have a decent grasp of business applications. 

For statisticians, it’s all about mathematical knowledge and experience . That’s why organizations typically have many data analysts (attached to every department), while statisticians are more challenging to find. Once hired, they are usually centralized in the core data team.

Common Applications of Data Analytics and Statistics

Learning about the most common applications of data analytics and statistics will also help you differentiate between them better, as each of these disciplines is integral to separate fields.

Data analytics is extensively used in the following fields:

-  E-commerce ( optimizing marketing campaigns and increasing sales)

- Healthcare (promoting better patient care, preventing diseases, and optimizing resources)

- Cybersecurity (detecting and preventing cyberattacks)

- Banking (handling risks and customizing financial services)

As for statistics, it dominates the following sectors:

-  Government sectors (virtually all decision-making)

- Political campaigns (curating campaigns and winning votes)

- Medicine (discovering and testing new treatments and drugs)

- Sports (improving the effectiveness of particular sports)

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If you struggle with one of them (or both), don’t worry. Julius AI is here to help. This handy AI-powered tool doesn’t concern itself with the data analysis vs. statistical analysis discourse. It simply gets the job done, whatever that job might be.

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Study/Experimental/Research Design: Much More Than Statistics

Kenneth l. knight.

Brigham Young University, Provo, UT

The purpose of study, experimental, or research design in scientific manuscripts has changed significantly over the years. It has evolved from an explanation of the design of the experiment (ie, data gathering or acquisition) to an explanation of the statistical analysis. This practice makes “Methods” sections hard to read and understand.

To clarify the difference between study design and statistical analysis, to show the advantages of a properly written study design on article comprehension, and to encourage authors to correctly describe study designs.

Description:

The role of study design is explored from the introduction of the concept by Fisher through modern-day scientists and the AMA Manual of Style . At one time, when experiments were simpler, the study design and statistical design were identical or very similar. With the complex research that is common today, which often includes manipulating variables to create new variables and the multiple (and different) analyses of a single data set, data collection is very different than statistical design. Thus, both a study design and a statistical design are necessary.

Advantages:

Scientific manuscripts will be much easier to read and comprehend. A proper experimental design serves as a road map to the study methods, helping readers to understand more clearly how the data were obtained and, therefore, assisting them in properly analyzing the results.

Study, experimental, or research design is the backbone of good research. It directs the experiment by orchestrating data collection, defines the statistical analysis of the resultant data, and guides the interpretation of the results. When properly described in the written report of the experiment, it serves as a road map to readers, 1 helping them negotiate the “Methods” section, and, thus, it improves the clarity of communication between authors and readers.

A growing trend is to equate study design with only the statistical analysis of the data. The design statement typically is placed at the end of the “Methods” section as a subsection called “Experimental Design” or as part of a subsection called “Data Analysis.” This placement, however, equates experimental design and statistical analysis, minimizing the effect of experimental design on the planning and reporting of an experiment. This linkage is inappropriate, because some of the elements of the study design that should be described at the beginning of the “Methods” section are instead placed in the “Statistical Analysis” section or, worse, are absent from the manuscript entirely.

Have you ever interrupted your reading of the “Methods” to sketch out the variables in the margins of the paper as you attempt to understand how they all fit together? Or have you jumped back and forth from the early paragraphs of the “Methods” section to the “Statistics” section to try to understand which variables were collected and when? These efforts would be unnecessary if a road map at the beginning of the “Methods” section outlined how the independent variables were related, which dependent variables were measured, and when they were measured. When they were measured is especially important if the variables used in the statistical analysis were a subset of the measured variables or were computed from measured variables (such as change scores).

The purpose of this Communications article is to clarify the purpose and placement of study design elements in an experimental manuscript. Adopting these ideas may improve your science and surely will enhance the communication of that science. These ideas will make experimental manuscripts easier to read and understand and, therefore, will allow them to become part of readers' clinical decision making.

WHAT IS A STUDY (OR EXPERIMENTAL OR RESEARCH) DESIGN?

The terms study design, experimental design, and research design are often thought to be synonymous and are sometimes used interchangeably in a single paper. Avoid doing so. Use the term that is preferred by the style manual of the journal for which you are writing. Study design is the preferred term in the AMA Manual of Style , 2 so I will use it here.

A study design is the architecture of an experimental study 3 and a description of how the study was conducted, 4 including all elements of how the data were obtained. 5 The study design should be the first subsection of the “Methods” section in an experimental manuscript (see the Table ). “Statistical Design” or, preferably, “Statistical Analysis” or “Data Analysis” should be the last subsection of the “Methods” section.

Table. Elements of a “Methods” Section

The “Study Design” subsection describes how the variables and participants interacted. It begins with a general statement of how the study was conducted (eg, crossover trials, parallel, or observational study). 2 The second element, which usually begins with the second sentence, details the number of independent variables or factors, the levels of each variable, and their names. A shorthand way of doing so is with a statement such as “A 2 × 4 × 8 factorial guided data collection.” This tells us that there were 3 independent variables (factors), with 2 levels of the first factor, 4 levels of the second factor, and 8 levels of the third factor. Following is a sentence that names the levels of each factor: for example, “The independent variables were sex (male or female), training program (eg, walking, running, weight lifting, or plyometrics), and time (2, 4, 6, 8, 10, 15, 20, or 30 weeks).” Such an approach clearly outlines for readers how the various procedures fit into the overall structure and, therefore, enhances their understanding of how the data were collected. Thus, the design statement is a road map of the methods.

The dependent (or measurement or outcome) variables are then named. Details of how they were measured are not given at this point in the manuscript but are explained later in the “Instruments” and “Procedures” subsections.

Next is a paragraph detailing who the participants were and how they were selected, placed into groups, and assigned to a particular treatment order, if the experiment was a repeated-measures design. And although not a part of the design per se, a statement about obtaining written informed consent from participants and institutional review board approval is usually included in this subsection.

The nuts and bolts of the “Methods” section follow, including such things as equipment, materials, protocols, etc. These are beyond the scope of this commentary, however, and so will not be discussed.

The last part of the “Methods” section and last part of the “Study Design” section is the “Data Analysis” subsection. It begins with an explanation of any data manipulation, such as how data were combined or how new variables (eg, ratios or differences between collected variables) were calculated. Next, readers are told of the statistical measures used to analyze the data, such as a mixed 2 × 4 × 8 analysis of variance (ANOVA) with 2 between-groups factors (sex and training program) and 1 within-groups factor (time of measurement). Researchers should state and reference the statistical package and procedure(s) within the package used to compute the statistics. (Various statistical packages perform analyses slightly differently, so it is important to know the package and specific procedure used.) This detail allows readers to judge the appropriateness of the statistical measures and the conclusions drawn from the data.

STATISTICAL DESIGN VERSUS STATISTICAL ANALYSIS

Avoid using the term statistical design . Statistical methods are only part of the overall design. The term gives too much emphasis to the statistics, which are important, but only one of many tools used in interpreting data and only part of the study design:

The most important issues in biostatistics are not expressed with statistical procedures. The issues are inherently scientific, rather than purely statistical, and relate to the architectural design of the research, not the numbers with which the data are cited and interpreted. 6

Stated another way, “The justification for the analysis lies not in the data collected but in the manner in which the data were collected.” 3 “Without the solid foundation of a good design, the edifice of statistical analysis is unsafe.” 7 (pp4–5)

The intertwining of study design and statistical analysis may have been caused (unintentionally) by R.A. Fisher, “… a genius who almost single-handedly created the foundations for modern statistical science.” 8 Most research did not involve statistics until Fisher invented the concepts and procedures of ANOVA (in 1921) 9 , 10 and experimental design (in 1935). 11 His books became standard references for scientists in many disciplines. As a result, many ANOVA books were titled Experimental Design (see, for example, Edwards 12 ), and ANOVA courses taught in psychology and education departments included the words experimental design in their course titles.

Before the widespread use of computers to analyze data, designs were much simpler, and often there was little difference between study design and statistical analysis. So combining the 2 elements did not cause serious problems. This is no longer true, however, for 3 reasons: (1) Research studies are becoming more complex, with multiple independent and dependent variables. The procedures sections of these complex studies can be difficult to understand if your only reference point is the statistical analysis and design. (2) Dependent variables are frequently measured at different times. (3) How the data were collected is often not directly correlated with the statistical design.

For example, assume the goal is to determine the strength gain in novice and experienced athletes as a result of 3 strength training programs. Rate of change in strength is not a measurable variable; rather, it is calculated from strength measurements taken at various time intervals during the training. So the study design would be a 2 × 2 × 3 factorial with independent variables of time (pretest or posttest), experience (novice or advanced), and training (isokinetic, isotonic, or isometric) and a dependent variable of strength. The statistical design , however, would be a 2 × 3 factorial with independent variables of experience (novice or advanced) and training (isokinetic, isotonic, or isometric) and a dependent variable of strength gain. Note that data were collected according to a 3-factor design but were analyzed according to a 2-factor design and that the dependent variables were different. So a single design statement, usually a statistical design statement, would not communicate which data were collected or how. Readers would be left to figure out on their own how the data were collected.

MULTIVARIATE RESEARCH AND THE NEED FOR STUDY DESIGNS

With the advent of electronic data gathering and computerized data handling and analysis, research projects have increased in complexity. Many projects involve multiple dependent variables measured at different times, and, therefore, multiple design statements may be needed for both data collection and statistical analysis. Consider, for example, a study of the effects of heat and cold on neural inhibition. The variables of H max and M max are measured 3 times each: before, immediately after, and 30 minutes after a 20-minute treatment with heat or cold. Muscle temperature might be measured each minute before, during, and after the treatment. Although the minute-by-minute data are important for graphing temperature fluctuations during the procedure, only 3 temperatures (time 0, time 20, and time 50) are used for statistical analysis. A single dependent variable H max :M max ratio is computed to illustrate neural inhibition. Again, a single statistical design statement would tell little about how the data were obtained. And in this example, separate design statements would be needed for temperature measurement and H max :M max measurements.

As stated earlier, drawing conclusions from the data depends more on how the data were measured than on how they were analyzed. 3 , 6 , 7 , 13 So a single study design statement (or multiple such statements) at the beginning of the “Methods” section acts as a road map to the study and, thus, increases scientists' and readers' comprehension of how the experiment was conducted (ie, how the data were collected). Appropriate study design statements also increase the accuracy of conclusions drawn from the study.

CONCLUSIONS

The goal of scientific writing, or any writing, for that matter, is to communicate information. Including 2 design statements or subsections in scientific papers—one to explain how the data were collected and another to explain how they were statistically analyzed—will improve the clarity of communication and bring praise from readers. To summarize:

• Purge from your thoughts and vocabulary the idea that experimental design and statistical design are synonymous.
• Study or experimental design plays a much broader role than simply defining and directing the statistical analysis of an experiment.
• A properly written study design serves as a road map to the “Methods” section of an experiment and, therefore, improves communication with the reader.
• Study design should include a description of the type of design used, each factor (and each level) involved in the experiment, and the time at which each measurement was made.
• Clarify when the variables involved in data collection and data analysis are different, such as when data analysis involves only a subset of a collected variable or a resultant variable from the mathematical manipulation of 2 or more collected variables.

Acknowledgments

Thanks to Thomas A. Cappaert, PhD, ATC, CSCS, CSE, for suggesting the link between R.A. Fisher and the melding of the concepts of research design and statistics.

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Nominal Vs Ordinal Data: Key Differences and Similarities

Are you curious about differentiating between Nominal and Ordinal Data? Nominal Data organises information without a specific order, whereas Ordinal Data arranges items meaningfully. This blog examines Nominal vs Ordinal Data, applications, instances of these two data forms and their importance in Statistical and Data Analysis.

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Have you ever questioned how data is classified and analysed in Statistics? Understanding the distinction between Nominal Data vs Ordinal Data is crucial for Data Analysis. Nominal Data organises information without sequence, like gender, colour, or animal categories. It revolves around categories. Ordinal Data presents a hierarchy or sequence, such as education levels, satisfaction ratings, or competition rankings.   

Each form of data has a distinct role in structuring and evaluating information. Grasping the difference between Nominal vs Ordinal Data can greatly improve your analytical abilities. Thus, helping you interpret datasets accurately and make informed decisions. Ready to enhance your Data Analysis skills? Let’s begin!  

Table of Contents

1) What is Nominal Data?   

2) What is Ordinal Data?   

3) Key Differences Between Nominal and Ordinal Data  

4) Similarities Between Nominal and Ordinal Data  

5) Conclusion  

What is Nominal Data?     

Nominal Data, also known as categorical data, plays a crucial role in research, statistics, and Data Analysis. It consists of groupings or tags that categorise and sort information. Categorical data is characterised by the absence of a predefined order or hierarchy among its categories. These categories are separate and do not overlap.  

Nominal Data organises data into distinct labels or categories with no inherent ranking. These labels are shown through names or terms without any hierarchy. Nominal Data is valuable for qualitative categorisation, enabling researchers to categorise data points by specific characteristics without suggesting any numerical connections.  

"Blue" or "green" eye colour falls under the category of Nominal Data, as an illustration. 

Every category is unique, without any specific arrangement or hierarchy. Brands of smartphones such as "iPhone" and "Samsung" are considered Nominal Data. There is no ranking system among brands. Modes of transportation such as "car" or "bicycle" are considered Nominal Data. They are distinct classifications with no intrinsic ranking.  

Characteristics of Nominal Data    

Nominal Data comprises different, descriptive categories that can’t be ordered or ranked hierarchically. Let’s explore some of the characteristics of Nominal Data here:  

1) Different Groups   

Nominal Data is made up of unique and unrelated groups. Every category is distinct and does not intersect with any other. This distinct separation enables easy categorisation and organisation of data points according to certain attributes or characteristics.  

2) Labels That Give Detailed Descriptions  

Descriptive labels, not numeric or quantitative values, are used to identify Nominal Data. These tags assign significant titles to groupings, which helps simplify the comprehension and analysis of the information. Instances include titles, tags, or phrases that characterise the group, like "green" for eye tint or "Samsung" for phone manufacturer.  

3) Absence of a Hierarchical Structure    

Nominal Data cannot be organised in a ranking or hierarchical order. No category is inherently better or worse than another, as no defined order or hierarchy exists among them. This feature sets Nominal Data apart from Ordinal Data, which does possess a logical order.  

4) Categorical Sorting   

Nominal Data is utilised to categorise qualitative data, allowing for the organization of data based on attributes that are not numerical. This data is important for categorising data points based on specific traits without suggesting numerical connections, which is crucial for qualitative research and analysis.  

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Examples of Nominal Data  

Below are some examples of how Nominal Data is applied to group and organise data into separate and unordered categories:  

a) Eye Colours : Eye colours such as "blue," "green," and "brown" are categorised as Nominal Data. Every colour is a separate group without any natural sequence or hierarchy.  

b) Types of Pets : Types such as "dog," "cat," and "bird" are examples of Nominal Data. Every kind of pet belongs to its distinct group with no ranking.  

c) Beverage Brands : Labels of drinks like "Coca-Cola," "Pepsi," and "Sprite" are considered Nominal Data. These groups are distinct and do not have any numerical or sequential connection.  

d) Countries : Countries such as "France," "Japan," and "Brazil" are examples of Nominal Data. Every country is unique, and no ranking is assigned to them.  

e) Marital Status : Labels such as "single," "married," "divorced," and "widowed" are considered Nominal Data. They categorise people without suggesting any ranking or sequence.  

What is Ordinal Data?     

Ordinal Data is a form of qualitative data that sorts variables into descriptive categories in a meaningful sequence. These categories are arranged in a hierarchy, ranging from top to bottom. Ordinal Data is more intricate than Nominal Data because it has a built-in order but is still straightforward.  

Ordinal Data allows for the comparison and ranking of accomplishments, positions, or performance despite varying intervals between them. This data type is beneficial for comprehending ranked selections or preferences and evaluating relative variances.  

Characteristics of Ordinal Data    

Ordinal Data is characterised by its ability to rank categories in a meaningful order while maintaining qualitative distinctions.  

1) Categories Organised in a Hierarchical Manner   

Ordinal Data consists of categories with a distinct and meaningful sequence or ranking. Categories can be compared to one another, for instance, in terms of satisfaction levels or levels of education achieved. This arrangement assists in comparing and grasping relative positions in the dataset.  

2) Uneven Gaps   

Although ordinal data order categories, the gaps between them may not be uniform, and the distinction between a 'good' and 'excellent' rating may not be as similar as between 'poor' and 'average.' This feature sets Ordinal Data apart from interval or ratio data.  

3) Nature With Qualities   

Although it has a ranking system, Ordinal Data remains qualitative. It explains qualities and features that are not numerical. This is beneficial for recording preferences, rankings, and ordered choices without needing exact numerical values.  

4) Differences Among Relatives   

Ordinal Data is perfect for evaluating the comparative distinctions among categories. It permits comparisons like superior, inferior, increased, or decreased. This is especially beneficial in sectors such as education, market research, and performance assessment, where grasping the hierarchy of categories holds more significance than quantifying precise disparities.  

5) Basic yet Enlightening    

Ordinal Data finds a middle ground between being straightforward and informative. Although it contains more information than Nominal Data because of its natural sequence, it is still simpler when compared to interval and ratio data. This feature allows it to be a flexible instrument for different analytical situations.  

Examples of Ordinal Data    

Below are some instances showcasing the application of Ordinal Data across different fields and sectors:  

a) Levels of Education : Ordinal Data is frequently utilised to portray educational attainment levels, including "high school," "bachelor's degree," "master's degree," and "Ph.D." These levels have a specific sequence.  

b) Customer Satisfaction Ratings : In surveys on customer satisfaction, people typically rate their experience on a scale ranging from "poor" to "excellent." These ratings represent data in a specific order with a well-defined ranking.  

c) Economic Classes : Social classes based on ranking, such as "lower class," "middle class," and "upper class", are categorised as Ordinal Data. Every class holds a unique rank in the hierarchy.  

d) Employee Performance Ratings : Ratings such as "needs improvement," "satisfactory," "good," and "excellent" are considered Ordinal Data. These ratings establish a ranking of performance levels.  

e) Levels of Pain Intensity : Within healthcare, pain levels are commonly assessed using a range from "no pain" to "severe pain." These levels have a specific sequence but varying intervals, classifying them as Ordinal Data.  

These instances show how Ordinal Data is used in different fields and areas to classify information into specific, organised categories.  

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Key Differences Between Nominal and Ordinal Data    

Understanding the main distinctions between nominal and Ordinal Data is crucial for individuals involved in Data Analysis, research, or statistics. Both kinds of data are vital for structuring and understanding information, although they have distinct functions and necessitate distinct methodologies. Let's explore their meanings, traits, uses, and distinctions thoroughly.  

Similarities Between Nominal and Ordinal Data  

Nominal and Ordinal Data are crucial types of qualitative data used in statistics, research, and analysis. They have multiple similarities, which are helpful in categorising and analysing non-numeric data. Comprehending these likenesses aids researchers and analysts in efficiently utilising both forms of data in their tasks.  

1) Qualitative Nature    

Nominal and Ordinal Data are qualitative data types that describe attributes that cannot be measured using numerical values. They record qualitative data like groups, descriptors, and orders. Categorical data categorises various animals, whereas Ordinal Data orders levels of satisfaction. Both offer an understanding of characteristics and choices.  

2) Utilise for Classification   

Both nominal and Ordinal Data classify information into separate categories. This aids in structuring data, simplifying the process of analysing and interpreting it. Each data point is only assigned to a single category, as categories do not overlap. This distinct classification enables easy comparison and assessment of diverse groups.  

3) Data Collection Methods    

Nominal or ordinal data is gathered using comparable techniques, including surveys, questionnaires, interviews, and observations. Surveys could inquire about favourite pet choices (nominal) or satisfaction levels (ordinal). Both data categories require individuals to provide details on what they like, their qualities, or their past encounters.  

4) Visual Representation   

Nominal and Ordinal Data are displayed through comparable charts and graphs. Both categories frequently utilise bar graphs and pie charts to display the distribution of categories. These visuals differentiate categories without suggesting an order for Nominal Data, whereas Ordinal Data charts showcase a hierarchical structure.  

5) Statistical Analysis   

Non-parametric methods can be used to analyse both nominal and Ordinal Data. Non-parametric tests are appropriate for qualitative data because they do not make assumptions about data distribution. The chi-square test is utilised for Nominal Data, whereas the Mann-Whitney U and Kruskal-Wallis tests examine Ordinal Data ranks.   

6) Flexibility in Application     

Nominal and Ordinal Data provide versatility in different fields and domains. They are used to capture and evaluate qualitative data in fields such as social sciences, marketing, healthcare, and education. For instance, in marketing, Nominal Data is used to classify preferences, while Ordinal Data is used to determine satisfaction levels.  

7) Ease of Understanding   

Nominal and Ordinal Data are simple to comprehend and interpret, making them understandable for many people. Descriptive labels and categories assist researchers, analysts, and stakeholders in quickly understanding the meaning of data, enabling better communication and collaboration and improving the effectiveness of Data Analysis overall. 

8) Support for Descriptive Statistics   

Descriptive statistics can be used to outline and describe dataset features for both nominal and Ordinal Data. Nominal Data relies on frequency counts and mode, whereas Ordinal Data relies on median and range to emphasise central tendency and variability. Descriptive statistics aid researchers in recognising essential patterns and trends.   

9) Complementary Use in Research    

Both nominal and Ordinal Data can be combined in research to gain a thorough understanding of a topic. For instance, research on customer likes could use Nominal Data for types of products and Ordinal Data for levels of satisfaction. The melding of both data types enriches and deepens qualitative research.  

Conclusion   

Categorising and examining qualitative information is essential for nominal and ordinal data. Nominal Data categorises specific, unordered groups, whereas Ordinal Data organises categories in a meaningful sequence. Both categories facilitate qualitative analysis and visualisation, assisting various research disciplines. Enhancing data interpretation and decision-making comes from understanding Nominal vs Ordinal Data and where they are applied. By utilising both effectively, researchers can gain a thorough understanding and make educated decisions.  

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Frequently Asked Questions

They are gathered via questionnaires, observations, surveys, and interviews. Nominal Data involves picking various categories, whereas Ordinal Data involves rating items and ranking.   

They are used to categorise and analyse non-numeric data. Nominal Data sets out distinct categories, whereas Ordinal Data ranks categories. Thus, aiding in analysis in various fields.   

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The Knowledge Academy’s Knowledge Pass , a prepaid voucher, adds another layer of flexibility, allowing course bookings over a 12-month period. Join us on a journey where education knows no bounds. 

The Knowledge Academy offers various Business Analyst Course , including the Statistics Course, Business Analyst Fundamentals Training, and Introduction To Business Analytics Training. These courses cater to different skill levels and provide comprehensive insights into What is Data Collection .   

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The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

Statistical analysis means investigating trends, patterns, and relationships using quantitative data . It is an important research tool used by scientists, governments, businesses, and other organisations.

To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process . You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure.

After collecting data from your sample, you can organise and summarise the data using descriptive statistics . Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalise your findings.

This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

Table of contents

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarise your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, frequently asked questions about statistics.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

• Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
• Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
• Null hypothesis: Parental income and GPA have no relationship with each other in college students.
• Alternative hypothesis: Parental income and GPA are positively correlated in college students.

Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

• In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
• In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
• In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

• In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
• In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
• In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
• Experimental
• Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

Measuring variables

When planning a research design, you should operationalise your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

• Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
• Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

Sampling for statistical analysis

There are two main approaches to selecting a sample.

• Probability sampling: every member of the population has a chance of being selected for the study through random selection.
• Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalisable findings, you should use a probability sampling method. Random selection reduces sampling bias and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to be biased, they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

• your sample is representative of the population you’re generalising your findings to.
• your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalise your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialised, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalised in your discussion section .

Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

• Will you have resources to advertise your study widely, including outside of your university setting?
• Will you have the means to recruit a diverse sample that represents a broad population?
• Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

• Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
• Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
• Expected effect size : a standardised indication of how large the expected result of your study will be, usually based on other similar studies.
• Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarise them.

Inspect your data

There are various ways to inspect your data, including the following:

• Organising data from each variable in frequency distribution tables .
• Displaying data from a key variable in a bar chart to view the distribution of responses.
• Visualising the relationship between two variables using a scatter plot .

By visualising your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

• Mode : the most popular response or value in the data set.
• Median : the value in the exact middle of the data set when ordered from low to high.
• Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

• Range : the highest value minus the lowest value of the data set.
• Interquartile range : the range of the middle half of the data set.
• Standard deviation : the average distance between each value in your data set and the mean.
• Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

• Estimation: calculating population parameters based on sample statistics.
• Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

• A point estimate : a value that represents your best guess of the exact parameter.
• An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

• A test statistic tells you how much your data differs from the null hypothesis of the test.
• A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

• Comparison tests assess group differences in outcomes.
• Regression tests assess cause-and-effect relationships between variables.
• Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

• A simple linear regression includes one predictor variable and one outcome variable.
• A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

• A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
• A z test is for exactly 1 or 2 groups when the sample is large.
• An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

• If you have only one sample that you want to compare to a population mean, use a one-sample test .
• If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
• If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
• If you expect a difference between groups in a specific direction, use a one-tailed test .
• If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

• a t value (test statistic) of 3.00
• a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

• a t value of 3.08
• a p value of 0.001

The final step of statistical analysis is interpreting your results.

Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

Decision errors

Type I and Type II errors are mistakes made in research conclusions. A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false.

You can aim to minimise the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasises null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

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.

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts, and meanings, use qualitative methods .
• If you want to analyse a large amount of readily available data, use secondary data. If you want data specific to your purposes with control over how they are generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

Statistical analysis is the main method for analyzing quantitative research data . It uses probabilities and models to test predictions about a population from sample data.

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• Central Limit Theorem | Formula, Definition & Examples
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What are the Benefits of Data Analytics in the Business World?

By UOnline News 08-08-2024

In today's fast-paced, data-driven world, businesses are increasingly relying on data analytics to gain a competitive edge. In such highly competitive business environments, data analytics has emerged as a powerful tool for all kinds of businesses. More than ever before, the benefits of data analytics to businesses have become vast and far-reaching.

This blog post explores the various benefits of data analytics in business, illustrating how it can transform operations and drive growth.

How Does Data Analytics Help Business?

Data analytics, the process of examining large datasets to uncover hidden patterns, correlations, and insights, has become a cornerstone of modern business strategy. From enhancing decision-making to improving operational efficiency, the benefits of data analytics in business are multifaceted and profound.

By leveraging the advantages of data analytics, businesses can make more informed decisions, improve operational efficiency, enhance customer experiences, and drive innovation. Data analytics has the potential to transform every aspect of a business.

Leveraging data analytics is no longer just an advantage but a necessity for sustainable growth and success. By investing in data analytics capabilities, businesses can unlock new opportunities, mitigate risks, and achieve their strategic objectives more effectively.

Read on to delve into the myriad benefits of data analytics, including how it can transform your business and drive sustainable growth.

Understanding Data Analytics

Data analytics refers to the process of examining data sets to draw conclusions about the information they contain. It involves applying algorithms, statistical techniques, and machine learning models to uncover patterns, correlations, and insights that can inform decision-making. Data analytics can be categorized into four main types: descriptive, diagnostic, predictive, and prescriptive analytics.

Descriptive Analytics: This involves summarizing historical data to understand what has happened in the past. It includes data aggregation and data mining to provide insights into past performance.

Diagnostic Analytics: This focuses on understanding why something happened. It involves data discovery, drill-down, and correlations to identify the root causes of past outcomes.

Predictive Analytics: This type of analytics uses historical data to forecast future events. Techniques such as regression analysis, time series analysis, and machine learning are employed to predict future trends and behaviors.

Prescriptive Analytics: This goes a step further by recommending actions to achieve desired outcomes. It involves optimization and simulation algorithms to suggest the best course of action based on the predictive analysis.

Data Analytics Benefits for Business

Enhanced Decision-Making

One of the most significant benefits of data analytics is its ability to enhance decision-making. By analyzing historical data, businesses can identify trends and patterns that inform strategic decisions. This data-driven approach minimizes the reliance on gut feelings and intuition, leading to more accurate and reliable outcomes.

For example, a retail company can analyze sales data to determine which products are performing well and adjust their inventory accordingly. This not only reduces the risk of stockouts but also ensures that capital is not tied up in slow-moving products.

Improved Operational Efficiency

In terms of operational efficiency, the importance of data analytics in business cannot be overstated. Data analytics can streamline operations by identifying bottlenecks and inefficiencies within business processes. By examining process data, businesses can pinpoint areas where resources are being wasted and implement changes to enhance efficiency.

For instance, a manufacturing company can use data analytics to monitor machine performance and predict maintenance needs, reducing downtime and increasing productivity. Similarly, logistics companies can optimize delivery routes based on traffic patterns and delivery schedules, resulting in faster deliveries and lower fuel costs.

Personalized Customer Experiences

In an era where customer experience is paramount, data analytics provides businesses with the tools to deliver personalized experiences. By analyzing customer data, businesses can gain insights into individual preferences, behaviors, and purchase histories. This enables the creation of targeted marketing campaigns and personalized product recommendations, enhancing customer satisfaction and loyalty.

For example, an e-commerce platform can analyze browsing and purchase data to recommend products that align with a customer's interests, increasing the likelihood of repeat purchases.

Risk Management and Mitigation

Every business faces risks, whether they are financial, operational, or market-related. The benefits of big data analytics include helping businesses identify and mitigate these risks by providing a comprehensive understanding of potential threats. For instance, financial institutions can use data analytics to detect fraudulent activities by analyzing transaction patterns and flagging anomalies. Similarly, businesses can analyze market data to anticipate changes in demand and adjust their strategies accordingly, reducing the impact of market volatility.

Optimized Marketing Campaigns

Marketing is a critical area where data analytics’ importance is significant. By analyzing data from various sources such as social media, website traffic, and customer interactions, businesses can gain insights into the effectiveness of their marketing campaigns. This allows for the optimization of marketing strategies, ensuring that resources are allocated to the most effective channels.

For example, a company can analyze the performance of different ad campaigns to determine which ones are generating the highest return on investment (ROI) and adjust their budget allocation accordingly.

Cost Reduction

Data analytics can lead to significant cost reductions by identifying areas where expenses can be minimized without compromising quality. For instance, by analyzing procurement data, businesses can identify suppliers that offer the best value for money and negotiate better contracts.

Additionally, data analytics can help optimize inventory management, reducing carrying costs and minimizing waste. For example, a company can use data analytics to forecast demand accurately, ensuring that they order the right amount of stock and avoid overproduction.

Competitive Advantage

In a competitive business environment, gaining an edge over rivals is crucial. Data analytics provides businesses with insights that can drive innovation and differentiate them from the competition. By analyzing market trends and customer feedback, businesses can identify unmet needs and develop new products or services to address them. Additionally, data analytics can help businesses benchmark their performance against competitors, identifying areas where they can improve and capitalize on opportunities.

Enhanced Employee Performance and Satisfaction

Data analytics is not only beneficial for external operations but also for internal processes. By analyzing employee performance data, businesses can identify top performers and areas where additional training may be needed. This enables the implementation of targeted development programs that enhance employee skills and productivity.

Additionally, data analytics can help improve employee satisfaction by analyzing feedback and identifying factors that contribute to a positive work environment. For example, by analyzing survey data, a company can identify common employee concerns and implement changes to address them, leading to higher retention rates.

Innovation and Product Development

Data analytics can drive innovation by providing insights into customer needs and market trends. By analyzing data from various sources, businesses can identify gaps in the market and develop new products or services to meet those needs.

This data-driven approach to innovation ensures that new offerings are aligned with customer preferences and have a higher likelihood of success. For instance, a tech company can analyze user feedback and usage data to develop new features for their software products, enhancing user satisfaction and driving adoption.

Supply Chain Optimization

Data analytics can significantly enhance supply chain management by providing visibility into every stage of the supply chain. Businesses can analyze data related to suppliers, inventory levels, transportation, and demand forecasts to optimize their supply chain operations.

For example, a logistics company can use data analytics to optimize delivery routes, reduce fuel consumption, and improve delivery times. This not only lowers operational costs but also enhances customer satisfaction by ensuring timely deliveries.

Human Resources Management

Data analytics can transform human resources management by providing insights into employee performance, engagement, and retention. By analyzing HR data, businesses can identify trends and patterns that inform hiring decisions, employee development programs, and retention strategies. For example, an organization can use data analytics to identify the factors that contribute to high employee turnover. By addressing these factors, the organization can improve employee satisfaction and retention rates.

Regulatory Compliance

In many industries, regulatory compliance is a critical concern. Data analytics can help businesses ensure compliance with various regulations by providing a comprehensive view of their operations and identifying areas where they may be falling short.

For example, in the healthcare industry, data analytics can be used to monitor patient records and ensure that they are being handled in accordance with privacy regulations. Similarly, in the financial sector, data analytics can help monitor transactions for compliance with anti-money laundering (AML) regulations.

Real-World Examples of How Data Analytics Help Business

Walmart, the world's largest retailer, uses data analytics extensively to optimize its operations and enhance customer experience. The company collects vast amounts of data from its stores and online channels, which it analyzes to make data-driven decisions. For example, Walmart uses predictive analytics to forecast demand and manage inventory levels, ensuring that products are available when customers need them. This has helped Walmart reduce stockouts and improve customer satisfaction.

Kaiser Permanente

Kaiser Permanente, a leading healthcare provider, leverages data analytics to improve patient care and operational efficiency. The organization uses data analytics to monitor patient outcomes, identify trends, and develop personalized treatment plans. By analyzing patient data, Kaiser Permanente can identify high-risk patients and intervene early to prevent complications. This has led to improved patient outcomes and reduced healthcare costs.

Capital One

Capital One, a major financial institution, uses data analytics to enhance its risk management and customer experience. The company analyzes transaction data to detect fraudulent activities and prevent financial losses. Additionally, Capital One uses data analytics to create personalized offers and recommendations for its customers, improving customer satisfaction and loyalty.

Final Thoughts on Data Analytics in Business

Data analytics offers many benefits for businesses across various industries. From enhanced decision-making and operational efficiency to improved customer experiences and risk management, data analytics has the potential to transform business operations and drive growth. By leveraging the power of data, businesses can uncover new opportunities, innovate, and gain a competitive edge in the market.

As the volume of data continues to grow, the importance of data analytics in business will only increase, making it an essential tool for success in the modern business landscape. Businesses that embrace this powerful tool will be well-positioned to navigate the complexities of the modern business landscape and thrive in an ever-evolving market. Whether you are a small startup or a large enterprise, the insights gained from data analytics can provide the foundation for informed decision-making, strategic planning, and long-term success.

Learn more about the University of Miami UOnline Master of Science in Data Analytics and Program Evaluation .

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Analysis of Weibull progressively first-failure censored data with beta-binomial removals

• Refah Alotaibi 1 , 
• Mazen Nassar 2 ,  ,  , 
• Zareen A. Khan 1 , 
• Ahmed Elshahhat 3
• 1. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
• 2. Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
• 3. Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt
• Received: 06 June 2024 Revised: 28 July 2024 Accepted: 31 July 2024 Published: 14 August 2024

MSC : 62F10, 62F15, 62N01, 62N02, 62N05

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This study examined the estimations of Weibull distribution using progressively first-failure censored data, under the assumption that removals follow the beta-binomial distribution. Classical and Bayesian approaches for estimating unknown model parameters have been established. The estimations included scale and shape parameters, reliability and failure rate metrics as well as beta-binomial parameters. Estimations were considered from both point and interval viewpoints. The Bayes estimates were developed by using the squared error loss and generating samples for the posterior distribution through the Markov Chain Monte Carlo technique. Two interval estimation approaches are considered: approximate confidence intervals based on asymptotic normality of likelihood estimates and Bayes credible intervals. To investigate the performance of classical and Bayesian estimations, a simulation study was considered by various kinds of experimental settings. Furthermore, two examples related to real datasets were thoroughly investigated to verify the practical importance of the suggested methodologies.

• Weibull distribution ,
• progressive first-failure censoring ,
• beta-binomial removals ,
• classical estimation ,
• Bayesian estimation

Citation: Refah Alotaibi, Mazen Nassar, Zareen A. Khan, Ahmed Elshahhat. Analysis of Weibull progressively first-failure censored data with beta-binomial removals[J]. AIMS Mathematics, 2024, 9(9): 24109-24142. doi: 10.3934/math.20241172

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• This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/4.0/ -->

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• © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/4.0 )

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• Figure 1. The log-likelihood curves of $ \alpha $ (left) and $ \theta $ (right) from the simulated data
• Figure 2. Fitting diagrams of the WD from BCRTs dataset
• Figure 3. The log-likelihoods of $ \alpha $, $ \theta $, $ a $, and $ b $ from BCRTs data
• Figure 4. The density (left) and trace (right) plots of $ \alpha $, $ \theta $, $ R(t) $, $ h(t) $, $ a $, and $ b $ from BCRTs data
• Figure 5. Fitting diagrams of the WD from vinyl chloride dataset
• Figure 6. The log-likelihoods of $ \alpha $, $ \theta $, $ a $, and $ b $ from vinyl chloride data
• Figure 7. The density (left) and trace (right) plots of $ \alpha $, $ \theta $, $ R(t) $, $ h(t) $, $ a $, and $ b $ from vinyl chloride data

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Title: efficient variance-based reliability sensitivity analysis for monte carlo methods.

Abstract: In this paper, a Monte Carlo based approach for the quantification of the importance of the scattering input parameters with respect to the failure probability is presented. Using the basic idea of the alpha-factors of the First Order Reliability Method, this approach was developed to analyze correlated input variables as well as arbitrary marginal parameter distributions. Based on an efficient transformation scheme using the importance sampling principle, only a single analysis run by a plain or variance-reduced Monte Carlo method is required to give a sufficient estimate of the introduced parameter sensitivities. Several application examples are presented and discussed in the paper.

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New results in the CTEQ-TEA global analysis of parton distributions in the nucleon

• Courtoy, A.
• Hobbs, T. J.
• Hou, T. -J.
• Lin, H. -W.
• Nadolsky, P.
• Sitiwaldi, I.
• Yuan, C. -P.

This report summarizes the latest developments in the CTEQ-TEA global analysis of parton distribution functions (PDFs) in the nucleon. The focus is on recent NNLO fits to high-precision LHC data at 8 and 13 TeV, including Drell-Yan, jet, and top-quark pair production, pursued on the way toward the release of the new generation of CTEQ-TEA general-purpose PDFs. The report also discusses advancements in statistical and numerical methods for PDF determination and uncertainty quantification, highlighting the importance of robust and replicable uncertainties for high-stakes observables. Additionally, it covers phenomenological studies related to PDF determination, such as the interplay of experimental constraints, exploration of correlations between high-$x$ nucleon sea and low-energy parity-violating measurements, fitted charm in the nucleon, the photon PDF in the neutron, and simultaneous SMEFT-PDF analyses.

• High Energy Physics - Phenomenology

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• Business and industry

Economic activity and social change in the UK, real-time indicators : 15 August 2024

Early experimental data and analysis on economic activity and social change in the UK. These real-time indicators are created using rapid response surveys, novel data sources and experimental methods.

https://www.ons.gov.uk/releases/economicactivityandsocialchangeintheukrealtimeindicators15august2024

Official statistics are produced impartially and free from political influence.

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