scipy.stats.kruskal(*args, nan_policy='propagate')[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. Samples must be one-dimensional.

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

Defines how to handle when input contains nan. The following options are available (default is ‘propagate’):

  • ‘propagate’: returns nan

  • ‘raise’: throws an error

  • ‘omit’: performs the calculations ignoring nan values


The Kruskal-Wallis H statistic, corrected for ties.


The p-value for the test using the assumption that H has a chi square distribution. The p-value returned is the survival function of the chi square distribution evaluated at H.

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.



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)