Mann-Whitney U test calculator

Mann-Whitney: comparing two groups without assuming normality

The Mann-Whitney test is the non-parametric alternative to the independent t test. It ranks all scores together and compares the rank sums of the two groups, so it does not assume normality and suits ordinal data such as Likert totals, small samples and skewed distributions. It tests whether one group tends to have higher scores, and equals a comparison of medians only if the two distributions have the same shape.

Enter the scores of both groups and the calculator shows the ranks, U, z, p and an effect size as the rank-biserial correlation, with the median and mean rank of each group. Interactive diagrams show how the ranks are distributed, with an APA sentence and R, Python and SPSS code.

When to use it

• Comparing ordinal Likert scores between two groups
• Analysing small or skewed samples where a t test is doubtful
• Comparing reaction times that contain outliers

Statistics calculators

The statistics calculators are free tools from ArabPsychology for psychology students and researchers. Each calculator does more than give a number: it shows the formula with your own numbers, explains the result in plain language, checks the assumptions, draws interactive diagrams that show how the formula works, and writes the results sentence in APA 7 style, ready to copy.

How to use the calculators

1. Pick a calculator from the list; each one starts with example data that shows how to enter yours.
2. Type or paste your data from Excel or SPSS, or enter summary statistics (mean, SD and sample size).
3. Read the results and the explanation, hover over parts of the formula to see them in the diagram, and try the sliders to see how the result changes.
4. Copy the APA sentence, download the diagrams as SVG or PNG, or send the result to another calculator or to the Diagram Builder.

Available calculators

Start here

• Which statistical test should I use? — Answer a few questions about your variables and groups to find the right statistical test, with the reason, then open its calculator. Runs in your browser.

Describe your data

• Descriptive statistics — Free descriptive statistics calculator: mean, median, SD, variance, quartiles, skewness, kurtosis, normality test and outliers, with histogram and box plot.
• z-score and percentile — Convert a raw score to a z score, percentile and area under the normal curve, and to T scores, IQ-type standard scores and stanines, with a draggable normal curve.
• Test score converter — Convert a test score between z, T, IQ-type (100/15), stanine, sten and percentile, from a raw score or any scale, with an SEM band and normal curve.
• Confidence interval — Confidence interval of a mean (t) and a proportion (Wilson, Wald), margin of error, and how n and confidence level change the width, with a simulation of many samples.

Compare groups

• t test — Run a one-sample, independent or paired t test: t, df, p, the confidence interval and Cohen's d, with an explanation, interactive diagrams and an APA sentence.
• One-way ANOVA — One-way ANOVA calculator: F, p, sums of squares, eta and omega squared, Levene, Welch ANOVA and Tukey HSD post-hoc, with an interactive variance partition diagram.
• Repeated-measures ANOVA — Repeated-measures ANOVA: F, p, sphericity correction (Greenhouse-Geisser, Huynh-Feldt), effect size and paired post hoc tests, with diagrams and an APA sentence.
• Chi-square test — Chi-square calculator for independence (contingency tables) and goodness of fit: expected counts, standardized residuals, Cramér's V, phi and Fisher's exact test for 2×2.
• McNemar test — McNemar test for paired yes/no data, such as before and after: 2×2 table, discordant pairs, χ² and p, with diagrams, an APA sentence and R/Python/SPSS code.

Non-parametric tests

• Mann-Whitney U test — Mann-Whitney U test for two independent groups: U, z, p, rank-biserial correlation, mean ranks and medians, with diagrams and an APA sentence.
• Wilcoxon signed-rank test — Wilcoxon signed-rank test for paired scores or one sample against a median: W, z, p, effect size and signed ranks, with diagrams and an APA sentence.
• Kruskal-Wallis test — Kruskal-Wallis H test for three or more independent groups: H, df, p, effect size, mean ranks and Dunn post hoc with Holm, plus diagrams and APA.
• Friedman test — Friedman test for three or more related conditions: χ², df, p, effect size, mean ranks and pairwise Wilcoxon post hoc, with diagrams and an APA sentence.

Relationships

• Correlation — Calculate Pearson r and Spearman rho, p, the confidence interval by Fisher z and r², with a draggable scatter plot and a Venn diagram of shared variance.
• Partial correlation — Partial correlation controlling for one or more variables, Pearson or Spearman: r, df and p, with interactive diagrams and an APA sentence.
• Simple linear regression — Simple linear regression: slope, intercept, R², F, standard errors, prediction with CI and PI, with least squares drawn as squares and draggable points.
• Mediation analysis — Simple mediation X → M → Y: paths a, b, c and c′, the indirect effect a×b with a bootstrap CI, an interactive path diagram and an APA sentence.

Measurement and reliability

• Cronbach's alpha — Get Cronbach's alpha, standardized alpha, item-total correlations, alpha if item deleted and the Feldt confidence interval, with a heatmap of inter-item correlations.
• Cohen's kappa — Cohen's kappa for two raters: κ, standard error, CI, percent agreement and weighted kappa (linear, quadratic), with diagrams and an APA sentence.
• Intraclass correlation (ICC) — Intraclass correlation (ICC) for rater and test-retest reliability: one-way, two-way models, single or average, agreement or consistency, with CI.
• Split-half reliability and KR-20 — Split-half reliability with Spearman-Brown correction (odd-even or first half), and KR-20 and KR-21 for 0/1 items, with diagrams and an APA sentence.

Planning and reporting

• Effect size converter — Convert between d, r, odds ratio and eta squared, and get effect sizes from t, F and χ², with Hedges' g, U3, overlap, probability of superiority, NNT and an overlap plot.
• Sample size and power — A-priori sample size and post-hoc power for t tests, correlation, one-way ANOVA and chi-square in the style of G*Power, with an α, β and power diagram and power curve.
• Survey sample size and margin of error — Survey sample size for a chosen margin of error and confidence level, or the margin of error of a sample, with finite population and response rate adjustment.
• Meta-analysis — Meta-analysis with fixed and random effects (DerSimonian–Laird): pooled effect, Q, I², τ², prediction interval, forest and funnel plots, from effect sizes or means.

Why these calculators

• Completely free, no sign-up, and your data never leaves your browser.
• Exact distributions (t, F, chi-square and normal), matching SPSS and R.
• The calculators are connected: enter your data once and use it everywhere, and send an effect size to the power analysis in one click.
• Available in six languages: Arabic, English, French, German, Spanish and Japanese.

Frequently asked questions