Understanding Model Assumptions in Statistical Analysis

Statistical models like the t-test, ANOVA, and linear regression rest on specific assumptions about the data being analyzed. When those assumptions are violated, test results can mislead you, producing incorrect conclusions about treatment effects, group differences, or relationships between variables. This article explains the core assumptions behind common statistical tests, shows you how to check them with diagnostic tools, and provides a practical checklist you can apply before running your own analyses. The guidance applies to students analyzing course data, researchers preparing manuscripts, and life-science professionals who use statistics to support decisions in clinical, agricultural, or laboratory settings.

What Are Model Assumptions and Why Do They Matter

Model assumptions are the mathematical conditions that must hold for a statistical test to produce valid results. Think of them as the operating requirements for a piece of laboratory equipment. If you run a centrifuge outside its specified speed range, the results are unreliable. Similarly, if you apply a t-test to data that grossly violate its assumptions, the p-values and confidence intervals you obtain may not reflect the true state of the world.

The consequences of violated assumptions are also academic. In clinical research, a test that produces too many false positives could lead investigators to declare a treatment effective when it is not. In agricultural trials, an ANOVA performed on non-normal data could mask a real difference between feed formulations or fertilizer treatments. Understanding assumptions helps you avoid both types of errors.

The National Institute of Standards and Technology maintains a Research Data Framework that emphasizes the importance of documenting data quality and analysis methods throughout the research lifecycle. Part of that documentation involves knowing which statistical assumptions apply to your data and how you verified them.

Core Assumptions for Common Statistical Tests

Different tests require different assumptions, but several appear repeatedly across the most common procedures. The sections below describe the assumptions for the t-test, ANOVA, and linear regression, which are the workhorses of statistical analysis in many fields.

Independence of Observations

The independence assumption requires that each observation in your dataset provides unique information and is not influenced by other observations in the same sample. This assumption is violated when measurements come from the same subject over time, from animals in the same litter, or from plants in the same plot, unless the analysis accounts for that structure.

The biasing effects of violating the independence assumption upon the power of the t-test have been documented in the educational psychology literature. When observations are not independent, the effective sample size is smaller than the number of rows in your spreadsheet, and your test may declare significance when none exists or miss real effects.

Independence is often established by design instead of by statistical testing. Random assignment to treatment groups, proper randomization of experimental units, and appropriate spacing of field plots are design decisions that protect independence. If your data have a nested structure, such as multiple measurements per animal or repeated sampling from the same field, you may need mixed models or repeated measures ANOVA instead of simple tests.

Normality of Data or Residuals

The normality assumption states that the data, or more precisely the residuals from your model, follow a normal distribution. For the t-test and ANOVA, this means the outcome variable is normally distributed within each group. For regression, it means the errors around the regression line are normally distributed.

A common misconception holds that the t-test and linear regression are valid only for normally distributed outcomes. This belief is incorrect. The t-test and linear regression compare the mean of an outcome variable across different subjects, and while they are valid even in very small samples when the outcome is normally distributed, their major usefulness comes from the fact that in large samples they are valid for any distribution. Simulation studies with extremely non-normal data demonstrate this validity. The major limitation on the t-test and linear regression for inference about associations is not distributional, but whether detecting and estimating a difference in the mean of the outcome answers the scientific question at hand.

This point matters for practitioners. If your research question is about group means, the t-test and regression may serve you well even with skewed data, provided your sample is large enough. If your question concerns medians, quantiles, or the shape of the distribution itself, other methods may be more appropriate.

Homogeneity of Variance

The homogeneity of variance assumption, also called homoscedasticity, requires that the spread of the outcome variable is similar across groups or across the range of predictor values. For a t-test comparing two groups, this means the variances in both groups should be roughly equal. For ANOVA with three or more groups, all groups should have similar variances. For regression, the variability of residuals should be constant across all fitted values.

The conditions required to conduct the t-test include measured values on an interval or ratio scale, simple random extraction, normal distribution of data, appropriate sample size, and homogeneity of variance. When variances are unequal, the standard t-test can produce incorrect results, and alternatives like the Welch test may be more appropriate.

Linearity for Regression

Linear regression assumes that the relationship between each predictor and the outcome is linear. If the true relationship is curved, such as a U-shaped dose-response curve, a linear model will systematically under-predict in some regions and over-predict in others. The residuals will show a pattern that reflects the misspecified functional form.

Non-linear regression analysis is often sophisticated because model coefficients can be partially correlated and fitting procedures can be sensitive to initial values. Machine learning approaches can recognize non-linear patterns that are difficult to represent in classical models without explicit physical assumptions, and they offer greater robustness against measurement errors. However, these methods require training to identify the optimal number and combination of hidden layers and neurons for the specific problem.

No Influential Outliers

Outliers are extreme values that do not fit the pattern of the rest of the data. A single outlier can shift a regression line, inflate the variance estimate, and change the conclusion of a hypothesis test. Some tests are more robust to outliers than others, but all common parametric tests can be affected by extreme values.

At a Glance: Assumption Checklist for Common Tests

The table below summarizes the key assumptions for the most frequently used statistical tests and the primary diagnostic methods for checking each one.

How to Check Normality Assumptions

Normality checking is a common source of confusion because the available methods have important limitations. The normality test is itself a kind of hypothesis test with Type I and Type II errors, similar to other hypothesis tests. This means the sample size influences the power of the normality test and its reliability. As the sample size decreases, sufficient power is not guaranteed even with the same significance level.

Graphical Methods

Graphical methods are often the first step in assessing normality. A histogram of the data can reveal obvious skewness or bimodality. A QQ plot, which compares the quantiles of your data to the quantiles of a normal distribution, is more informative. Points that fall roughly along the diagonal line suggest normality. Systematic deviations, such as an S-shape or a curve bending away from the line, indicate skewness or heavy tails.

Graphical techniques for checking assumptions are widely used in statistical practice. They have the advantage of showing also whether a violation exists but also the nature of the violation, which can guide the choice of remedy.

Statistical Tests of Normality

Statistical tests like the Shapiro-Wilk test and the Kolmogorov-Smirnov test provide a formal assessment of normality. The null hypothesis is that the data come from a normal distribution. A small p-value suggests the data are not normal.

However, these tests have a well-documented limitation. In small samples, they may lack the power to detect meaningful departures from normality. In large samples, they may flag trivial departures that have no practical impact on the validity of your analysis. The sample size must influence the power of the normality test and its reliability, and it is hard to find an established sample size for satisfying the power of the normality test.

The Problem with Pre-Testing Assumptions

Some researchers advocate testing assumptions first and then choosing a test based on the outcome. This approach has been examined critically. Research on the two-sample t-test has asked whether pre-testing its assumptions pays off, and the evidence suggests it does not. The sequential procedure of testing normality and then choosing between a parametric and non-parametric test introduces additional uncertainty that is not captured in the final p-value.

A related concern is that null hypothesis significance testing does not provide a sufficient basis for evaluating statistical model assumptions. While NHST-based tests can provide some degree of confirmation for the model assumption that is evaluated, these tests do not inform you of the degree of support that the data provide for the null hypothesis or to what extent the null hypothesis should be considered plausible after taking the data into account. Addressing the prior plausibility of the model assumption is unavoidable if the goal is to determine how plausible it is that the model assumption holds. Without assessing the prior plausibility of the model assumptions, it remains fully uncertain whether the model of interest gives an adequate description of the data and thus whether it can be considered valid for the application at hand.

How to Check Homogeneity of Variance

Homogeneity of variance can be assessed graphically and statistically. A box plot of the outcome variable by group shows the spread of each group side by side. If the boxes have very different heights, the variances may be unequal. A residual plot from an ANOVA or regression model can also reveal variance patterns.

Statistical tests for homogeneity of variance include Levene test and the Brown-Forsythe test. These tests are less sensitive to departures from normality than older tests like the F-test for variance ratios. When variances are unequal, the Welch test for two groups or the Welch ANOVA for multiple groups provides an alternative that does not require equal variances.

How to Check Independence

Independence is primarily a design issue instead of a data issue. You should ask whether the data collection process could have introduced dependencies between observations. Common sources of dependence include repeated measurements on the same subject, clustering of subjects within groups, spatial correlation in field trials, and temporal correlation in time series data.

If your data have a hierarchical structure, you may need to account for it in the analysis. Mixed effects models include random intercepts for clusters, which acknowledges that observations within a cluster are correlated. Repeated measures ANOVA handles designs where each subject is measured multiple times.

The independence assumption is particularly important because violations can bias the power of the t-test. When observations are not independent, the effective sample size is smaller than the nominal sample size, and the test may have inflated Type I error rates or reduced power.

Practical Workflow for Checking Assumptions

The following workflow provides a structured approach to verifying model assumptions before conducting statistical tests. This checklist is designed for students and researchers who need a practical method that balances rigor with efficiency.

Step 1: Document Your Design

Before looking at any data, write down the design of your study. Identify the experimental units, the treatment structure, and any blocking or nesting factors. This documentation helps you determine whether independence is plausible and whether your analysis should include random effects.

The NC3Rs Experimental Design Assistant provides a tool for planning experiments that includes guidance on randomization, blinding, and sample size calculation. Using such tools at the design stage can prevent assumption violations before data collection begins.

Step 2: Visualize the Data

Create histograms or box plots of the outcome variable for each group. Look for obvious skewness, outliers, or differences in spread between groups. Create a QQ plot for each group to assess normality visually.

For regression, plot the outcome against each predictor to check for linearity. A scatter plot that shows a clear curve suggests that a linear model may not fit well.

Step 3: Run Formal Diagnostic Tests

Use statistical tests to supplement the graphical assessment. The Shapiro-Wilk test assesses normality of the data or residuals. Levene test assesses homogeneity of variance. These tests provide quantitative evidence that you can report in your methods section.

Remember that these tests have limitations. They are influenced by sample size, and they do not tell you whether a violation is severe enough to matter for your analysis. Interpret them in the context of your graphical displays and your sample size.

Step 4: Examine Residuals for Regression Models

For linear regression, the residuals are the differences between the observed values and the values predicted by the model. Plot the residuals against the fitted values. The plot should show a random scatter with no pattern. A funnel shape, where the spread of residuals increases with the fitted values, suggests heteroscedasticity. A curve in the plot suggests that the model is misspecified.

The QQ plot of residuals assesses normality. Cook distance identifies influential points that have a disproportionate effect on the regression coefficients.

Step 5: Decide Whether Violations Matter

Not all assumption violations are equally serious. The t-test and linear regression are robust to some departures from normality, particularly in large samples. The robustness of the t-test when applied to ordinal scaled data has been demonstrated for samples of sizes 5 to 20, where the maximum actual level of significance is close to the declared level even though the normality assumption is clearly violated.

The key question is whether the violation is severe enough to change your conclusions. If your data are mildly skewed and your sample is large, the t-test may still be valid. If your data are extremely skewed or contain severe outliers, you may need an alternative approach.

Step 6: Choose an Appropriate Remedy

If assumption violations are severe, you have several options. Transformations such as the logarithm or square root can reduce skewness and stabilize variances. Non-parametric tests like the Wilcoxon rank sum test do not require normality, though they test different hypotheses. The bootstrap t-test provides an alternative that does not rely on the normality assumption.

The bootstrap t-test has been shown to outperform Student t-test under normality in data. With fixed true-positive rate, the bootstrap t-test maintained equivalent accuracy in true-positive rate but significantly improved the true-negative rate compared to the Student t-test. The bootstrap t-test is recommended to replace Student t-test in medical data analysis regardless of sample size.

Options and Tradeoffs When Assumptions Are Violated

When your data violate model assumptions, you face a decision about how to proceed. Each option has advantages and disadvantages, and the best choice depends on your research question, your sample size, and the nature of the violation.

Transformation

Transforming the outcome variable can address skewness and unequal variances. The logarithmic transformation is common for right-skewed data, such as concentrations or counts. The square root transformation is useful for count data. The Box-Cox family of transformations provides a systematic way to choose a transformation parameter.

The tradeoff is that the analysis is then conducted on the transformed scale, and results must be interpreted in that scale. Differences between group means on the log scale correspond to ratios on the original scale, which may or may not be what you want to report.

Non-Parametric Tests

Non-parametric tests like the Wilcoxon rank sum test for two independent samples and the Kruskal-Wallis test for multiple groups do not require normality. They are based on ranks instead of raw values, which makes them robust to outliers and skewed distributions.

The tradeoff is that these tests answer different questions. The Wilcoxon-Mann-Whitney test is often used when a researcher wants to know which of two groups generally has the larger responses, and either a t-test or a Wilcoxon-Mann-Whitney test could be acceptable. Although both tests are usually associated with quite different hypotheses, the decision rule and p-value from either test could be associated with many different sets of assumptions. Each perspective allows a different interpretation of the associated p-value.

For paired data, the Wilcoxon signed-rank test is often considered the non-parametric alternative to the paired t-test. However, the Wilcoxon signed-rank test is not a proper test for central tendencies as a replacement of the conventional t-test for paired samples whenever assumptions about the dependent variable are in doubt. Researchers should choose statistical procedures on the basis of the null hypothesis to be tested and not primarily on the basis of the type of data.

Robust Methods

Robust statistical methods are designed to perform well even when assumptions are violated. The Welch t-test does not require equal variances. Robust regression methods down-weight influential observations. The bootstrap provides a general approach to inference that does not rely on parametric assumptions.

The Welch t-test has been compared to the Student t-test in terms of sensitivity to real world violations of distributional assumptions. Logistic regression has been found to be more robust than either t-test in some situations.

Bayesian Approaches

Bayesian methods offer an alternative framework that can handle assumption violations more flexibly. Bayesian t-tests quantify evidence instead of producing p-values, and they can incorporate models with different assumptions simultaneously.

A comprehensive t-test framework based on Bayesian model averaging simultaneously takes into account models that assume equal and unequal variances, and models that use t-likelihoods to improve robustness to outliers. The resulting inference is based on a weighted average across the entire model ensemble, with higher weights assigned to models that predicted the observed data well. This integrated approach provides robustness without having to commit to a single model following a series of assumption checks.

Records and Measurements for Assumption Checking

Good statistical practice involves documenting your assumption checks so that others can evaluate your decisions. The following records are useful for this purpose.

Data Dictionary

Maintain a data dictionary that describes each variable, its measurement scale, and any transformations applied. This documentation helps readers understand what the analysis actually tested.

Diagnostic Test Results

Record the results of your normality and variance tests, including the test statistic, degrees of freedom, and p-value. Report these in your methods section or supplementary materials.

Diagnostic Plots

Save the QQ plots, residual plots, and other diagnostic graphics. These provide visual evidence that supports your choice of statistical methods.

Analysis Decisions

Document any decisions you made in response to assumption violations, such as choosing the Welch test over the Student t-test or applying a transformation. Explain the rationale for each decision.

The EQUATOR Network provides reporting guidelines for many study types, and these guidelines often require authors to describe their statistical methods in sufficient detail that others can replicate the analysis. Following these guidelines improves the transparency and reproducibility of your work.

Common Failure Patterns in Assumption Checking

Several recurring problems appear when researchers check model assumptions. Recognizing these patterns can help you avoid them.

Over-Reliance on Normality Tests

Many researchers treat the Shapiro-Wilk test as a gatekeeper, refusing to use parametric tests unless the test is non-significant. This approach is problematic because the test has low power in small samples and excessive power in large samples. A non-significant result in a small sample does not confirm normality, and a significant result in a large sample may flag a trivial departure.

Ignoring the Research Question

The choice between parametric and non-parametric methods should depend on the null hypothesis being tested, not primarily on the type of data. If your research question concerns group means, the t-test may be appropriate even with non-normal data. If your question concerns medians or the shape of the distribution, other methods are needed.

Confusing Residuals with Raw Data

For regression and ANOVA, the normality assumption applies to the residuals, not to the raw outcome variable. It is possible for the outcome to be non-normal while the residuals are approximately normal, particularly when the model includes important predictors. Checking normality of the raw data when the assumption applies to residuals can lead to unnecessary transformations.

Failing to Account for Design Structure

Independence violations are often missed because researchers do not document the design structure. If you have multiple measurements per subject, repeated sampling from the same location, or animals from the same litter, your observations are not independent. Failing to account for this structure can inflate Type I error rates.

Using Pre-Testing Without Understanding Its Limitations

The practice of testing assumptions and then choosing a test based on the outcome introduces additional uncertainty. Research has shown that pre-testing assumptions does not pay off for the two-sample t-test. The sequential procedure can produce p-values that do not have their nominal properties.

Limitations of Assumption Checking

Assumption checking has inherent limitations that you should understand before relying on it heavily.

Tests Have Their Own Assumptions

The tests used to check assumptions have their own assumptions and limitations. The Shapiro-Wilk test assumes that the data are a random sample from some population. Levene test is less sensitive to non-normality than some alternatives, but it is not assumption-free.

Sample Size Affects Everything

The power of normality tests depends on sample size. In small samples, normality tests may fail to detect meaningful departures from normality. In large samples, they may detect trivial departures. The same issue affects tests of homogeneity of variance.

Statistical Significance Does Not Equal Practical Significance

A statistically significant test of normality does not tell you whether the departure from normality is large enough to affect your analysis. The t-test is robust to moderate departures from normality, particularly in large samples. The question is not whether the data are perfectly normal, but whether the departure is severe enough to invalidate the inference.

Assumption Checking Is Not a Substitute for Good Design

The best way to satisfy model assumptions is to design your study carefully. Randomization promotes independence. Adequate sample sizes provide power for both the primary analysis and the assumption checks. Careful measurement reduces outliers. The Research Data Framework from the National Institute of Standards and Technology emphasizes the importance of planning for data quality throughout the research lifecycle.

Welfare and Safety Context for Life-Science Applications

In life-science research, statistical decisions can have welfare and safety implications. A study that incorrectly concludes a treatment is effective may expose patients or animals to unnecessary risk. A study that incorrectly concludes a treatment is ineffective may deny patients or animals a beneficial intervention.

The NC3Rs Experimental Design Assistant was developed to improve experimental design in animal research, with the goal of reducing the number of animals needed while maintaining scientific rigor. Proper statistical analysis is part of this effort, because underpowered or misanalyzed studies waste animal lives and produce unreliable results.

When your analysis involves animal subjects, human patients, or environmental samples, consider the broader context of your statistical decisions. An assumption violation that changes a conclusion from significant to non-significant, or vice versa, can have real consequences for the populations you study.

Professional Escalation Criteria

Some situations call for consultation with a professional statistician. Consider seeking expert advice in the following circumstances.

Complex Design Structures

If your study involves multiple levels of nesting, crossed factors, or repeated measures with complex correlation structures, a statistician can help you specify an appropriate model and check its assumptions.

Severe Assumption Violations

If your data are extremely skewed, contain many outliers, or show patterns that no simple transformation can fix, a statistician can recommend robust methods or alternative modeling approaches.

High-Stakes Decisions

If your analysis will inform regulatory submissions, clinical treatment decisions, or policy recommendations, the cost of a statistical error is high. Professional review of your methods and assumptions is warranted.

Unfamiliar Methods

If you are considering a method you have not used before, such as Bayesian model averaging or bootstrap inference, consult someone with experience in that method. The PubMed database maintained by the National Library of Medicine can help you find methodological papers, but interpreting them correctly often requires expertise.

Publication or Grant Review

If your manuscript or grant proposal will undergo statistical review, having a statistician review your methods before submission can save time and improve your chances of success. The NCBI Literature Resources provide access to the scientific literature that can help you understand reporting standards in your field.

Frequently Asked Questions

What is the difference between checking normality of the data and checking normality of residuals?

For regression and ANOVA, the normality assumption applies to the residuals, which are the differences between observed values and model predictions. The raw outcome variable may be non-normal while the residuals are approximately normal, particularly when the model includes important predictors. For the t-test comparing two groups, the normality assumption applies to the outcome variable within each group, which is equivalent to checking the residuals from a model that includes only the group indicator.

Can I use a t-test if my data are not normally distributed?

Yes, in many cases. The t-test and linear regression compare the mean of an outcome variable for different subjects, and in large samples they are valid for any distribution. Simulation studies demonstrate this validity in extremely non-normal data. The major limitation is not distributional, but whether detecting and estimating a difference in the mean of the outcome answers the scientific question at hand. In small samples with severe non-normality, alternative methods may be more appropriate.

What sample size do I need for a normality test to be reliable?

There is no established sample size that guarantees adequate power for a normality test. The power of the normality test depends on the sample size, the significance level, and the magnitude of the departure from normality. As the sample size decreases, sufficient power is not guaranteed even with the same significance level. In practice, graphical methods like QQ plots are often more informative than formal tests, especially in small samples.

When should I use the Welch t-test instead of the Student t-test?

The Welch t-test does not require equal variances between groups, while the Student t-test assumes homogeneity of variance. If your data show unequal variances between groups, the Welch test is a safer choice. Some statisticians recommend using the Welch test by default because it performs well even when variances are equal, and it protects against the consequences of unequal variances.

Is the Wilcoxon rank sum test always a good alternative to the t-test?

The Wilcoxon rank sum test does not require normality, but it tests a different hypothesis than the t-test. The t-test compares group means, while the Wilcoxon test is often interpreted as comparing the distributions of the two groups. The decision rule and p-value from either test could be associated with many different sets of assumptions, and each perspective allows a different interpretation of the associated p-value. Choose the test based on the null hypothesis you want to test, not primarily on the type of data.

What should I do if my regression residuals show a clear pattern?

A pattern in the residuals, such as a curve or a funnel shape, suggests that the model is misspecified. A curve indicates that the relationship between the predictor and outcome is not linear. A funnel shape indicates that the variance of the residuals changes with the fitted values. Consider adding non-linear terms, transforming variables, or using a different modeling approach. Machine learning methods can recognize non-linear patterns that are difficult to represent in classical models without explicit physical assumptions.

How do I handle outliers in my data?

First, check whether the outliers are data entry errors. If they are, correct them. If they are legitimate values, consider whether they are influential, meaning they have a disproportionate effect on the analysis. Cook distance is a common measure of influence in regression. Options for handling influential outliers include robust regression methods, transformations, or analyzing the data with and without the outliers to see how much the conclusions change.

Should I test assumptions before or after running my primary analysis?

The workflow described in this article suggests checking assumptions as part of the analysis process, before interpreting the final results. However, pre-testing assumptions and then choosing a test based on the outcome has been shown not to pay off for the two-sample t-test. A better approach is to examine your data graphically, consider the design of your study, and choose an analysis plan that is appropriate for your research question and robust to plausible assumption violations.

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References and Further Reading

• Research Data Framework. National Institute of Standards and Technology.
• EQUATOR Network. EQUATOR Network.
• Experimental Design Assistant. NC3Rs.
• NCBI Literature Resources. National Center for Biotechnology Information.
• PubMed. National Library of Medicine.
• The importance of the normality assumption in large public health data sets.. Annual review of public health, 2002.
• More about the basic assumptions of t-test: normality and sample size.. Korean journal of anesthesiology, 2019.
• Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules.. Statistics surveys, 2010.
• Attach importance of the bootstrap t test against Student's t test in clinical epidemiology: a demonstrative comparison using COVID-19 as an example.. Epidemiology and infection, 2021.
• Improving lesion-symptom mapping.. Journal of cognitive neuroscience, 2007.
• Robustness of the two independent samples t-test when applied to ordinal scaled data.. Statistics in medicine, 1987.
• Model-averaged Bayesian t tests.. Psychonomic bulletin & review, 2025.
• The paired t test and beyond: Recommendations for testing the central tendencies of two paired samples in research on speech, language and hearing pathology.. Journal of communication disorders, 2017.
• Prediction of formaldehyde emissions from wood-based panels containing amino plastic resins using non-linear regression analysis and machine learning.. 2026.
• Static thresholds and limitations of linear assumptions in reservoir-induced seismicity assessment: Toward a dynamic machine learning framework. 2026.
• Microbiome mediation analysis: methods, assumptions, and practical considerations.. 2026.
• Retraction: Do Magnetic murmurs guide birds? A directional statistical investigation for influence of Earth's Magnetic field on bird navigation.. 2026.
• Why checking model assumptions using null hypothesis significance tests does not suffice: A plea for plausibility. Psychonomic Bulletin & Review, 2018.
• Checking Model Assumptions. 2017.
• Checking model assumptions. 2018.
• Why checking model assumptions using null hypothesis significance tests does not suffice: Supplementary materials. 2017.
• Linear Models (continued) Model Checking Model Assumptions Graphical Techniques for Checking Assumptions
• Model Building Process Part 1 : Checking Model Assumptions V 1 . 1
• The biasing effects of violating the independence assumption upon the power of t test. Japanese Journal of Educational Psychology, 1996.
• The two-sample t test: Pre-testing its assumptions does not pay off. Statistical Papers, 2011.
• Type I error inflation of the separate-variances Welch t test with very small sample sizes when assumptions are met. Journal of Modern Applied Statistical Methods, 2011.
• Welch’s t test is more sensitive to real world violations of distributional assumptions than student’s t test but logistic regression is more robust than either. Statistical Papers, 2024.

This article is educational and does not replace institutional policy, professional advice, or applicable safety and regulatory requirements.