Skip to main content
`Ctrl`+`K`
scipy.stats.

# ranksums

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

  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,y array_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.

      Added in version 1.7.0.

    axis int 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.

    keepdims bool, default: False

      If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.

  Returns:
    statistic float

      The test statistic under the large-sample approximation that the rank sum statistic is normally distributed.

    pvalue float

      The p-value of the test.

  Notes

  Beginning in SciPy 1.9, `np.matrix` inputs (not recommended for new code) are converted to `np.ndarray` before the calculation is performed. In this case, the output will be a scalar or `np.ndarray` of appropriate shape rather than a 2D `np.matrix`. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or `np.ndarray` rather than a masked array with `mask=False`.

  Array API Standard Support

  `ranksums` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ⛔
  PyTorch | ⛔ | ⛔
  JAX | ⛔ | ⛔
  Dask | ⛔ | n/a

  > See Support for the array API standard for more information.

  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.

      >>> import numpy as np
      >>> 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.