Does this match SPSS?

Yes. U, z, and the asymptotic p value follow the same tie-corrected formulas as SPSS and R. For small samples without ties, the exact p value is shown.

Can I use the Mann-Whitney U test for Likert scale data?

Yes. It is the standard choice for comparing two independent groups on a single Likert item, because single items are ordinal.

What is a good effect size r?

Common guidelines are about .10 small, .30 medium, and .50 large (Cohen, 1988). r is calculated as |z| ÷ √N.

MANN-WHITNEY U TEST CALCULATOR

Mann-Whitney U test calculator with exact p values and effect size.

Compare two independent groups when the data are ordinal (such as Likert items) or not normally distributed. You get U, z, the p value (exact for small samples without ties), medians, mean ranks, effect size r, and an APA sentence.

DATA

Two independent groups

NON-PARAMETRIC

GROUP A NAMEGROUP B NAME

GROUP A VALUESGROUP B VALUES

Separate values with commas, spaces, or new lines. Paste a column from Excel.

Mann-Whitney U test: when to use it, formula, and reporting

What is the Mann-Whitney U test?

It compares two independent groups by ranking all values together and checking whether one group tends to have higher ranks. It is the non-parametric alternative to the independent-samples t-test, also called the Wilcoxon rank-sum test.

Formula

U₁ = R₁ − n₁(n₁ + 1) ÷ 2, U₂ = n₁n₂ − U₁, U = min(U₁, U₂)

R₁ is the sum of ranks in group 1. Tied values share the average rank. For larger samples, z = (U₁ − n₁n₂/2) ÷ σ_U, with a tie correction in σ_U.

Mann-Whitney U vs t-test

Use the t-test when the outcome is numeric and roughly normal in each group
Use Mann-Whitney for single Likert items, ranks, or skewed data with outliers
Mann-Whitney compares distributions (often summarised as medians); the t-test compares means
With very small groups (under about 10 each), Mann-Whitney is usually the safer choice

Mann-Whitney U vs Wilcoxon signed-rank

Mann-Whitney is for two different groups of people. Wilcoxon signed-rank is for the same people measured twice, such as a pre-test and post-test.

How to report it (APA style)

“A Mann-Whitney U test indicated that satisfaction was significantly higher for in-person students (Mdn = 7.5) than for online students (Mdn = 3.5), U = 2, z = −2.58, p = .013, r = .74.” Report medians, U, z, p, and an effect size.

References

Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics, 18(1), 50–60.
Fritz, C. O., Morris, P. E., & Richler, J. J. (2012). Effect size estimates: Current use, calculations, and interpretation. Journal of Experimental Psychology: General, 141(1), 2–18.

Mann-Whitney U Test Calculator

Run the non-parametric alternative to the independent t-test for Likert items or skewed data, with exact p values for small samples and a ready-to-use write-up.

Compare two groups on a single Likert item

Compare skewed scores between two independent groups

Report U, z, p, medians, and effect size r

KEY FUNCTIONS

Exact p value for small samples without tiesTie-corrected normal approximationMedians and mean ranksEffect size rAPA report sentence

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