Mann-Whitney U Test
Computes the Mann-Whitney U test, the non-parametric alternative to the t-test for comparing two independent groups. Instead of comparing means, it compares the ranks of the combined data, which makes it valid even when the data don't follow a normal distribution or are ordinal. The tool computes the U statistic and the normal approximation z, with a tie correction. Enter the two groups of observations, separated by commas.
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Mann-Whitney U Test
Computes the Mann-Whitney U test, the non-parametric alternative to the t-test for comparing two independent groups. Instead of comparing means, it compares the ranks of the combined data, which makes it valid even when the data don't follow a normal distribution or are ordinal. The tool computes the U statistic and the normal approximation z, with a tie correction. Enter the two groups of observations, separated by commas.
Comparing two groups without assuming normality
The t-test presumes the data roughly follow a normal distribution. When they don't, or when they're merely ordinal, like grades from 1 to 5, the t-test slips. The Mann-Whitney U test is the robust alternative: it doesn't look at the values themselves, but at their positions when all the data from both groups are ranked together.
The logic is simple and powerful. If one group tends to have larger values, its observations will occupy the higher positions in the combined ranking, and the U statistic will capture that imbalance. By working with positions, the test is immune to extreme values and odd distributions. For larger samples, the distribution of U approaches a normal, which allows computing a z.
Enter the two groups of observations, separated by commas. The tool computes the U statistic and the normal approximation z, already with the tie correction, which matters when there are repeated values across groups. With the z you obtain the p-value and decide whether the two groups differ significantly.
Related Tools
Kruskal-Wallis H Test
Computes the Kruskal-Wallis H test, the non-parametric version of ANOVA for comparing three or more independent groups. Just as Mann-Whitney does for two groups, it works with the ranks of the data instead of the raw values, dispensing with the normality assumption. The H statistic approximately follows a chi-square distribution. It's the choice when the data are ordinal or clearly non-normal. Enter the groups: values by comma, groups by semicolon.
Cliff's Delta (Effect Size)
Computes Cliff's delta, a non-parametric effect-size measure between two groups. It answers a direct question: if I draw a value at random from each group, how much more likely is one to be larger than the other? It ranges from −1 to +1; zero means complete overlap. Because it works only with order comparisons, it requires no assumptions about the distribution and is robust to outliers. It's the ideal companion to the Mann-Whitney test. Enter the two groups of values.
Wilcoxon Signed-Rank Test
Computes the Wilcoxon signed-rank test, the non-parametric alternative to the paired t-test. When you measure the same subjects twice — before and after a treatment — and the data don't follow a normal distribution, this is the test to use. It works with the differences between pairs: it ranks the magnitudes of those differences, assigns ranks and separately sums the ranks of the positive and negative differences. The tool computes W+, W− and the normal approximation z, with a tie correction. Enter the two paired series.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.