🔎 Nonparametric Tests Calculator

Select a distribution-free test, paste your data, and receive the test statistic, p-value, critical interpretation, effect size, and a transparent step-by-step explanation. Covers Mann–Whitney U, Wilcoxon signed-rank, Kruskal–Wallis H, and Shapiro–Wilk normality checks.

1. Choose Your Test

Mann–Whitney U Wilcoxon signed-rank Kruskal–Wallis H Shapiro–Wilk W

Tail Direction (U / Wilcoxon)

Two-tailed (≠) Left-tailed (<) Right-tailed (>)

Tail choice applies to Mann–Whitney U and Wilcoxon tests. Kruskal–Wallis and Shapiro–Wilk are inherently two-tailed.

Significance Level (α)

Custom α must lie between 0.001 and 0.25.

2. Enter Data

Sample 1 values

Sample 2 values

Formula Reference

Mann–Whitney U

\\[ U = \min(U_1, U_2), \quad U_1 = n_1 n_2 + \frac{n_1 (n_1 + 1)}{2} - R_1 \\]

Wilcoxon signed-rank

\\[ T = \min(W^+, W^-), \quad W^+ = \sum \text{ranks on positive differences} \\]

Kruskal–Wallis H

\\[ H = \frac{12}{N(N+1)} \sum_{i=1}^{k} \frac{R_i^2}{n_i} - 3(N + 1) \\]

Shapiro–Wilk W

\\[ W = \frac{\left(\sum_{i=1}^{n} a_i x_{(n+1-i)}\right)^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2} \\]

How to Use This Calculator

Select the appropriate nonparametric test for your design and data.
Paste raw data into the fields provided (two groups, paired observations, multiple groups, or a single sample).
Choose tail direction (if relevant) and confirm the significance level α.
Run the test to obtain the statistic, p-value, decision, effect size, and workflow notes.
For small samples (n < 10) consult exact critical value tables per textbook references when available.

References

Hollander, M., Wolfe, D. A., & Chicken, E. (2013). Nonparametric Statistical Methods (3rd ed.). Wiley.
Shapiro, S. S., & Wilk, M. B. (1965). “An analysis of variance test for normality (complete samples).” Biometrika, 52(3/4), 591–611.
Conover, W. J. (1999). Practical Nonparametric Statistics (3rd ed.). Wiley.

Disclaimer

These tests assume independent observations (except paired designs) and are most accurate when using exact tables for small sample sizes. The calculator uses large-sample approximations and tie corrections; verify assumptions before reporting findings.