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.
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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.
The ANOVA for when the data won't cooperate
Classic ANOVA is powerful, but it asks that the data be roughly normal and have similar variances. When those conditions don't hold, or when the data are ordinal, the Kruskal-Wallis test takes over. It does for three or more groups what Mann-Whitney does for two: it compares positions instead of values.
The procedure ranks all the observations from the groups together, assigns positions and sums those positions within each group. If the groups are similar, the rank sums will be proportional to their sizes; if one group stands out, its sum will deviate from what's expected, and the H statistic will grow. For reasonable samples, H approximately follows a chi-square distribution.
Enter the groups, with values separated by commas and groups by semicolons. The tool returns the H statistic and the degrees of freedom. As in ANOVA, a significant result indicates at least one group differs, without saying which; non-parametric multiple comparisons, like Dunn's, are the next step.
Related Tools
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.
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.
Kolmogorov-Smirnov Test (Two-Sample)
Computes the two-sample Kolmogorov-Smirnov test, which checks whether two samples come from the same distribution — without assuming what that distribution is. It compares the empirical cumulative distribution functions of the two samples and takes the largest vertical distance between them, the D statistic. Unlike the t-test, which only compares means, the KS test is sensitive to any difference in shape, spread or location. Enter the two samples of values.
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