scipy.stats.ranksums¶

scipy.stats.ranksums(x, y, alternative='two-sided')[source]¶

Compute the Wilcoxon rank-sum statistic for two samples.

The Wilcoxon rank-sum test tests the null hypothesis that two sets of measurements are drawn from the same distribution. The alternative hypothesis is that values in one sample are more likely to be larger than the values in the other sample.

This test should be used to compare two samples from continuous distributions. It does not handle ties between measurements in x and y. For tie-handling and an optional continuity correction see scipy.stats.mannwhitneyu.

Parameters

x,yarray_like

The data from the two samples.

alternative{‘two-sided’, ‘less’, ‘greater’}, optional

Defines the alternative hypothesis. Default is ‘two-sided’. The following options are available:

‘two-sided’: one of the distributions (underlying x or y) is stochastically greater than the other.
‘less’: the distribution underlying x is stochastically less than the distribution underlying y.
‘greater’: the distribution underlying x is stochastically greater than the distribution underlying y.

New in version 1.7.0.

Returns

statisticfloat: The test statistic under the large-sample approximation that the rank sum statistic is normally distributed.
pvaluefloat: The p-value of the test.

References

1: https://en.wikipedia.org/wiki/Wilcoxon_rank-sum_test

Examples

We can test the hypothesis that two independent unequal-sized samples are drawn from the same distribution with computing the Wilcoxon rank-sum statistic.

>>> from scipy.stats import ranksums
>>> rng = np.random.default_rng()
>>> sample1 = rng.uniform(-1, 1, 200)
>>> sample2 = rng.uniform(-0.5, 1.5, 300) # a shifted distribution
>>> ranksums(sample1, sample2)
RanksumsResult(statistic=-7.887059, pvalue=3.09390448e-15)  # may vary
>>> ranksums(sample1, sample2, alternative='less')
RanksumsResult(statistic=-7.750585297581713, pvalue=4.573497606342543e-15) # may vary
>>> ranksums(sample1, sample2, alternative='greater')
RanksumsResult(statistic=-7.750585297581713, pvalue=0.9999999999999954) # may vary

The p-value of less than 0.05 indicates that this test rejects the hypothesis at the 5% significance level.

scipy.stats.rankdata scipy.stats.wilcoxon