Evaluate independent groups with ranked evidence and summaries. Review medians, mean ranks, z, and p-values. Export results, inspect plots, and explain findings with confidence.
| Observation | Group A | Group B |
|---|---|---|
| 1 | 5 | 2 |
| 2 | 7 | 3 |
| 3 | 8 | 4 |
| 4 | 9 | 6 |
| 5 | 12 | 10 |
| 6 | 13 | 11 |
| 7 | 15 | 14 |
This sample lets you test the form quickly and inspect rank behavior, U values, p estimation, effect size, export output, and the generated plot.
The Mann-Whitney U test compares two independent groups by ranking all observations together. It is useful when data are ordinal, skewed, or not comfortably modeled by a normal distribution.
Combine both groups, sort the values, and assign ranks. When ties occur, assign the average rank to each tied observation.
Let R1 be the rank sum for Group A and R2 for Group B.
U₁ = R₁ − n₁(n₁ + 1) / 2 U₂ = R₂ − n₂(n₂ + 1) / 2 U = min(U₁, U₂)
When exact calculation is not used, the calculator estimates the p-value from the normal approximation with tie correction.
Mean(U₁) = n₁n₂ / 2 Var(U₁) = (n₁n₂ / 12) × [ N + 1 − Σ(t³ − t) / (N(N − 1)) ]
Here, N = n₁ + n₂ and t is each tie block size.
Rank-biserial correlation = (2U₁ / (n₁n₂)) − 1 Common-language effect size = U₁ / (n₁n₂)
This calculator also reports the median of all pairwise differences, Group A minus Group B, when the pair count stays reasonable for browser computation.
This tool is designed for practical nonparametric comparison of two independent samples. It calculates the Mann-Whitney U statistic, shows both directional U values, and reports a p-value using either exact logic for small untied samples or a tie-corrected normal approximation when data are larger or tied. It also adds descriptive summaries so you can review sample size, median, mean, spread, quartiles, and rank behavior without moving to another page.
The result area explains whether the observed difference is statistically meaningful at your chosen alpha level and gives an effect size interpretation. Rank-biserial correlation helps describe direction and strength, while the common-language effect size gives an intuitive probability-style reading. A Hodges-Lehmann shift estimate is also included when the number of pairwise differences remains manageable in the browser.
The plot section uses an interactive graph so you can inspect the distributions visually. Export tools let you save a CSV file with summary and rank detail, or a PDF report for documentation and sharing. This makes the page useful for education, audits, reports, research notes, quality reviews, and quick checks during analysis workflows.
Use it when two independent groups are compared with ordinal data, skewed measurements, outliers, or uncertain normality assumptions. It is a strong alternative to a two-sample t test.
Not directly. It compares rank behavior between groups. Under similar distribution shapes, it is often interpreted as a location or median shift comparison.
It means the alternative hypothesis expects Group A values to be smaller overall than Group B values, which usually produces smaller ranks and a smaller U₁.
Tied values receive average ranks. The variance is adjusted with a tie correction. Exact p-values are only used here for small samples without ties.
It is an effect size derived from the U statistic. Positive values suggest Group A tends higher, negative values suggest Group A tends lower.
U₁ describes Group A against Group B. U₂ describes the reverse comparison. Their sum always equals n₁ × n₂.
No. This page limits exact calculation to smaller untied inputs for speed and browser stability. Larger or tied samples use the asymptotic estimate.
No. Paired observations need a paired nonparametric method, such as the Wilcoxon signed-rank test, not the Mann-Whitney U test.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.