Written by Dackohn; last reviewed November 2026.
Parametric tests such as the t-test compare means and assume a roughly normal distribution. Nonparametric tests such as Mann–Whitney compare ranks and make weaker assumptions. Use parametric tests for roughly normal data or moderately large samples. Use nonparametric tests for ordinal data, strong skew or outliers in small samples.
The difference in one sentence
A parametric test assumes the data follow a particular distribution and estimates its parameters, usually the mean. A nonparametric test replaces the values with their ranks, so it only uses their order and is not affected by how extreme a value is.
Which test replaces which
| Situation | Parametric | Nonparametric |
|---|---|---|
| Two independent groups | Independent t-test | Mann–Whitney U |
| Two paired measurements | Paired t-test | Wilcoxon signed-rank |
| Three or more groups | One-way ANOVA | Kruskal–Wallis |
| Relationship between two variables | Pearson correlation | Spearman correlation |
Worked example: one outlier changes the answer
Group A: 12, 14, 15, 13, 16, 14, 15, 13. Group B: 15, 17, 16, 18, 17, 16, 19, 60. Nearly every value in B is above nearly every value in A, but one value of 60 is far from the rest.
- Welch’s t-test gives p = .172, not significant. The 60 raises B’s mean to 22.25, but it inflates B’s variance so much that the difference looks uncertain.
- Mann–Whitney U gives p = .001. Ranks are not affected by how far away the 60 is, only by its position at the top.
The medians (14 and 17) describe these groups better than the means (14 and 22.25). Before choosing a test, check whether the 60 is a typing error.
When each is the better choice
Choose a parametric test when data are roughly normal, or when samples are moderately large, since the Central Limit Theorem makes means approximately normal anyway. You also get an estimate in the original units with a confidence interval.
Choose a nonparametric test when the data are ordinal, such as ratings on a 1–5 scale; when samples are small and clearly skewed; or when outliers are genuine and you want results that do not hinge on them.
Does a nonparametric test lose much power?
Less than many people assume. For normal data, Mann–Whitney is about 95% as efficient as the t-test, and for heavy-tailed data it can be far more powerful, as the example shows.
Common mistakes
- Assuming nonparametric means “no assumptions”. Observations must still be independent, and Wilcoxon assumes symmetric differences.
- Trying both tests and reporting the one that is significant. That is a form of p-hacking. Choose in advance.
- Relying only on a normality test. In small samples it rarely detects a problem, and in large ones it flags trivial departures.
Try it yourself
Normality Test →Check your data with Shapiro–Wilk and a Q-Q plot. Which Test Should I Use? →Answer a few questions and get a recommendation.See also: The Friedman test · Sign test vs Wilcoxon
Frequently asked questions
What is the main difference between parametric and nonparametric tests?
Parametric tests compare means and assume a distribution, usually normal. Nonparametric tests use ranks and make weaker assumptions.
Are nonparametric tests less powerful?
Slightly for truly normal data: Mann-Whitney is about 95% as efficient as the t-test. For heavy-tailed data they can be much more powerful.
Can I use a t-test on Likert data?
It is common and often gives similar answers with enough respondents, but a single Likert item is ordinal, so a rank-based test is the safer default.
Related reading: Choosing a statistical test · Skewness and kurtosis · How to detect outliers
Sources & further reading: NIST/SEMATECH e-Handbook of Statistical Methods · OpenStax Introductory Statistics. How we compute & validate: methodology. Written & reviewed by Dackohn; last reviewed August 2026.