scipy.stats.kruskal(*args, **kwargs)[source]

Compute the Kruskal-Wallis H-test for independent samples

The Kruskal-Wallis H-test tests the null hypothesis that the population median of all of the groups are equal. It is a non-parametric version of ANOVA. The test works on 2 or more independent samples, which may have different sizes. Note that rejecting the null hypothesis does not indicate which of the groups differs. Post-hoc comparisons between groups are required to determine which groups are different.

sample1, sample2, … : array_like

Two or more arrays with the sample measurements can be given as arguments.

nan_policy : {‘propagate’, ‘raise’, ‘omit’}, optional

Defines how to handle when input contains nan. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default is ‘propagate’.

statistic : float

The Kruskal-Wallis H statistic, corrected for ties

pvalue : float

The p-value for the test using the assumption that H has a chi square distribution

See also

1-way ANOVA
Mann-Whitney rank test on two samples.
Friedman test for repeated measurements


Due to the assumption that H has a chi square distribution, the number of samples in each group must not be too small. A typical rule is that each sample must have at least 5 measurements.


[1]W. H. Kruskal & W. W. Wallis, “Use of Ranks in One-Criterion Variance Analysis”, Journal of the American Statistical Association, Vol. 47, Issue 260, pp. 583-621, 1952.


>>> from scipy import stats
>>> x = [1, 3, 5, 7, 9]
>>> y = [2, 4, 6, 8, 10]
>>> stats.kruskal(x, y)
KruskalResult(statistic=0.2727272727272734, pvalue=0.6015081344405895)
>>> x = [1, 1, 1]
>>> y = [2, 2, 2]
>>> z = [2, 2]
>>> stats.kruskal(x, y, z)
KruskalResult(statistic=7.0, pvalue=0.0301973834223185)