Definition
Nonparametric tests do not assume a normal distribution — they work with the ranks of values rather than the values themselves. The Mann–Whitney U test replaces the two-sample t-test, the Wilcoxon signed-rank test the paired t-test, Kruskal–Wallis ANOVA one-way ANOVA and the Friedman test repeated-measures ANOVA. They suit small samples, ordinal data and outliers.
Statistical tests
The price for robustness is slightly lower power when the data really are normal (a loss of roughly 5 %) — with skewed data or extremes, nonparametric tests are actually more powerful. They test differences in distributions (typically medians), not means, so phrase your conclusion accordingly.
For correlations of ordinal data use Spearman's ρ or Kendall's τ; for binary paired outcomes the sign test and McNemar's test. A significant Kruskal–Wallis ANOVA is followed by multiple comparisons of mean ranks.
In Statistica
Statistics → Nonparametrics contains all the tests above including multiple comparisons after Kruskal–Wallis ANOVA, the two-sample Kolmogorov–Smirnov test, Spearman and Kendall correlations, and box plots by group straight from the results dialog.
Related terms
- t-testThe t-test compares means: the one-sample version compares a mean with a fixed value, the two-sample version the means…
- ANOVA (analysis of variance)ANOVA (analysis of variance) tests whether the means of three or more groups differ.
- Normality testA normality test checks whether data come from a normal distribution — an assumption of the t-test, ANOVA, regression and capability indices.
- Normal distributionThe normal (Gaussian) distribution is a symmetric bell-shaped distribution described by its mean and standard deviation.
- CorrelationCorrelation measures the strength and direction of a linear relationship between two quantities with a number from −1 to 1.
Knowledgebase guides
FAQ
- When should I reach for a nonparametric test?
- When data are ordinal (rating scales), samples are small and clearly non-normal, or outliers drive the result. For large samples of continuous data a t-test is usually fine.
- What is the nonparametric counterpart of ANOVA?
- Kruskal–Wallis ANOVA for independent groups and the Friedman test for repeated measures.
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Statistical tests
Updated: September 2026.