scipy.stats.ranksums#

scipy.stats.ranksums(x, y, alternative='two-sided', *, axis=0, nan_policy='propagate')[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.

axisint or None, default: 0

If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If None, the input will be raveled before computing the statistic.

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

Defines how to handle input NaNs.

propagate: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.
omit: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output will be NaN.
raise: if a NaN is present, a ValueError will be raised.

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