Mann-Whitney U Test Calculator

The Mann-Whitney U test (also called the Wilcoxon rank-sum test) compares two independent groups when the data are ordinal or not normally distributed, for example urban and rural students’ answers on a 5-point Likert item. It is the non-parametric alternative to the independent samples t test. Paste the two groups to get SPSS-style rank and test statistics tables, the effect size r and a ready APA 7 sentence.

How to use this calculator

  1. Put each group in its own column (group sizes can differ).
  2. Copy both columns, with group names in the first row if you like, and paste them.
  3. Click Calculate.
  4. Report the medians of both groups, U, z, p and the effect size r.

Formula

Rank all N = n₁ + n₂ values together (ties get the average rank)
U₁ = R₁ − n₁(n₁ + 1)/2,   U₂ = n₁n₂ − U₁,   U = min(U₁, U₂)
z = (U₁ − n₁n₂/2) / √[(n₁n₂/12)((N + 1) − Σ(t³ − t)/(N(N − 1)))]
Effect size r = |z| / √N

Step-by-step example

  1. Likert item scores: Urban (n = 8) and Rural (n = 10) students (click Load example).
  2. Sum of ranks: Urban R₁ = 109.5, Rural R₂ = 61.5.
  3. U₁ = 109.5 − 8 × 9 / 2 = 73.5; U = min(73.5, 6.5) = 6.5.
  4. z = 3.05, p = .002, r = .72 (a large effect).

How to interpret the results

If p is below .05, the two groups differ in their distributions; when the two distributions have a similar shape, this can be read as a difference in medians. Report medians rather than means. The effect size r = |z|/√N is about .10 for a small, .30 for a medium and .50 for a large effect.

How to report it in APA 7 style

A Mann-Whitney U test indicated that urban students (Mdn = 4.00, n = 8) scored significantly higher than rural students (Mdn = 2.00, n = 10), U = 6.5, z = 3.05, p = .002, r = .72.

Statistical symbols (t, F, p, r, M, SD, N, d) should be italicised in your thesis.

Assumptions

  • The dependent variable is ordinal or continuous.
  • The two groups are independent (different participants).
  • Observations are independent within each group.
  • To interpret the result as a difference in medians, the two distributions should have a similar shape.

How to do it in SPSS, R or Excel

SPSS: Analyze → Nonparametric Tests → Legacy Dialogs → 2 Independent Samples → Mann-Whitney U. R: wilcox.test(y ~ group, correct = FALSE, exact = FALSE). Python: scipy.stats.mannwhitneyu(..., method='asymptotic', use_continuity=False), which ScholarCalc’s results were validated against.

Roman Urdu mein khulasa

Mann-Whitney U test do alag groups ko compare karta hai jab data normal na ho ya ordinal ho, jaise aik Likert item (1–5). Ye independent t test ka non-parametric mutabadil hai. Ye means ke bajaye ranks compare karta hai, is liye thesis mein medians report karein. p 0.05 se kam ho to farq significant hai, aur effect size r farq ki taqat batata hai.

Frequently asked questions

When should I use Mann-Whitney U instead of an independent t test?

Use it when the outcome is ordinal (such as a single Likert item), when the data are clearly skewed with small samples, or when there are extreme outliers.

Is the Mann-Whitney U test the same as the Wilcoxon rank-sum test?

Yes. They are equivalent tests; SPSS reports both U and Wilcoxon W in the same table.

Does the test compare medians?

It compares whole distributions (whether values in one group tend to be larger). It can be read as a comparison of medians only when both groups’ distributions have a similar shape.

How are ties handled?

Tied values receive the average of their ranks, and the z statistic includes a tie correction, as in SPSS’s asymptotic significance.

What effect size should I report?

Report r = |z| / √N. Values of about .10, .30 and .50 are commonly read as small, medium and large.

How do I report the Mann-Whitney U test in APA?

Give both medians and group sizes, then U, z, p and r, for example: U = 6.5, z = 3.05, p = .002, r = .72.

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Cite this calculator

If ScholarCalc helped your analysis, you can cite it in APA 7 format:

ScholarCalc. (2026). Mann-Whitney U Test Calculator [Web application]. https://scholarcalc.com/mann-whitney-u-test-calculator/

Written and maintained by the ScholarCalc team. Last reviewed: November 2026.

Accuracy: results are computed in your browser and were validated against Python scipy, statsmodels and pingouin on test datasets. See Methodology and accuracy.