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1Scan for outdated or missing drivers - takes under a minute2Repair Windows errors before they cause bigger problems3Fix the driver behind crashes, sound loss and screen glitchesChoose a statistical test by the quantity you want to estimate or compare, the study design, and the method’s assumptions—not by whether a normality test rejects. Parametric methods such as t tests and ANOVA make inferences using a model described by parameters; nonparametric methods often use ranks, signs, or resampling and can suit ordinal data or settings where a conventional model is unsuitable. Neither label tells you, by itself, what effect a test measures or whether its assumptions fit your data.
What “parametric” and “nonparametric” mean
A parametric method specifies a model in terms of a limited set of parameters and uses that model to make inferences. A t test, for example, is commonly used to assess a difference in means; ANOVA is commonly used to compare means across groups. These procedures rely on assumptions tied to their model and design.
Nonparametric methods commonly use ranks, signs, or other procedures that make less specific assumptions about the outcome’s distribution. They can be useful with ordinal or ranked observations, skewed data, or when a conventional parametric model is not appropriate. “Nonparametric” does not mean assumption-free: independence, symmetry, continuity, or other conditions may still matter, depending on the procedure. Penn State’s STAT 500 Lesson 11 introduces nonparametric tests and bootstrap resampling, while its STAT 415 Wilcoxon lesson describes assumptions for signed-rank testing.
Why a nonnormal result does not automatically call for a nonparametric test
A normality check alone cannot choose the analysis. The relevant question is whether the assumptions of the intended method are reasonable for the study design and target quantity. Some parametric tests can be robust to certain departures from normality under suitable conditions; the degree of robustness depends on the setting. Conversely, a rank-based procedure has its own assumptions and may address a different target.
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For example, a t test typically evaluates a difference in means. A rank test evaluates ranks or relative ordering, and its result is not automatically a test of medians. Jim Frost explains that parametric and nonparametric results can differ while both are valid if they answer different questions, such as a difference in means versus a difference in medians. See Statistics By Jim’s comparison of nonparametric and parametric tests.
Match the method to the design and question
The methods below are common starting points, not interchangeable substitutes. Confirm that the procedure matches the outcome, sampling structure, and hypothesis you actually want to test.
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| Study setup | Parametric example | Nonparametric example | Interpretation to check |
|---|---|---|---|
| One sample or paired measurements | One-sample or paired t test | Sign test; Wilcoxon signed-rank test | The signed-rank test is not assumption-free. In its one-sample setting, Penn State specifies a continuous random variable and a symmetric population distribution. |
| Two independent groups | Two-sample t test | Mann–Whitney U / Wilcoxon rank-sum test | Do not automatically interpret the rank test as a median comparison; its meaning depends on distributional conditions. |
| More than two groups | One-way ANOVA | Kruskal–Wallis test; Mood’s median test | These procedures do not necessarily test the same effect. State the target and assumptions. |
| Repeated measures or blocked comparisons | Factorial-design methods, where appropriate | Friedman test, where the design and hypothesis fit | Check the precise repeated or blocked structure before selecting a procedure. |
| Monotonic association or ordinal data | Pearson correlation, in suitable settings | Spearman correlation | Spearman assesses monotonic association; it is not a test for every kind of nonlinear relationship. |
Penn State’s STAT 800 Lesson 11 includes an applied Mann–Whitney example and discusses alternatives including Fisher’s exact test, Kruskal–Wallis, and one-sample Wilcoxon procedures. The appropriate choice still depends on the question and design.
A practical checklist for choosing a test
- Name the target. Decide whether you want a difference in means, a median comparison, a rank tendency, a probability of superiority, or an association. Do not select a method before clarifying what its result should mean.
- Map the design. Distinguish independent groups from paired observations, repeated measures, or blocked comparisons. Identify whether the outcome is categorical, quantitative, or ordinal.
- Check the measurement scale. Rank-based methods may be suitable for ordinal outcomes, but ordinal measurement alone does not settle the choice. Consider what distinctions the scale supports and what effect is meaningful.
- Review method-specific assumptions. Assess independence and any relevant conditions involving distributions, symmetry, variance, or shape. For instance, Penn State’s STAT 415 lesson says the one-sample Wilcoxon signed-rank procedure assumes continuity and a symmetric population distribution.
- Inspect the data in context. Look at the outcome’s distribution, outliers, group sizes, and design. Do not infer the method solely from a raw-data normality test; evaluate whether the selected method’s assumptions are plausible for the analysis.
- Plan the interpretation. Decide what effect the procedure can detect and how you will report it. A nonparametric procedure can have lower power in some comparable settings, but there is no universal penalty; power depends on the data and the alternative of interest.
How to interpret different results
Two methods applied to the same dataset can produce different p-values without either calculation being inherently wrong. They may target different quantities, rely on different assumptions, or respond differently to the data’s shape and outliers. Before comparing results, identify each method’s target effect, outcome scale, design, assumptions, robustness, and power for the alternative that matters.
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Report the procedure, the effect or contrast it addresses, and the assumptions that support its use. Avoid describing a Mann–Whitney result as a median difference unless the conditions needed for that interpretation are justified. Likewise, do not claim that a nonsignificant result proves there is no effect; it indicates that the analysis did not provide sufficient evidence against its specified null hypothesis at the chosen threshold.
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