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scipy.stats.

# median_test

scipy.stats.median_test(*samples, ties='below', correction=True, lambda_=1, nan_policy='propagate')

  Perform a Mood’s median test.

  Test that two or more samples come from populations with the same median.

  Let `n = len(samples)` be the number of samples. The “grand median” of all the data is computed, and a contingency table is formed by classifying the values in each sample as being above or below the grand median. The contingency table, along with correction and lambda_, are passed to `scipy.stats.chi2_contingency` to compute the test statistic and p-value.

  Parameters:
    *samples array_like

      The set of samples. There must be at least two samples. Each sample must be a one-dimensional sequence containing at least one value. The samples are not required to have the same length.

    ties str, optional

      Determines how values equal to the grand median are classified in the contingency table. The string must be one of:

          "below":
              Values equal to the grand median are counted as "below".
          "above":
              Values equal to the grand median are counted as "above".
          "ignore":
              Values equal to the grand median are not counted.

      The default is “below”.

    correction bool, optional

      If True, and there are just two samples, apply Yates’ correction for continuity when computing the test statistic associated with the contingency table. Default is True.

    lambda_float or str, optional

      By default, the statistic computed in this test is Pearson’s chi-squared statistic. lambda_ allows a statistic from the Cressie-Read power divergence family to be used instead. See `power_divergence` for details. Default is 1 (Pearson’s chi-squared statistic).

    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’.

  Returns:
    res MedianTestResult

      An object containing attributes:

      statisticfloat

        The test statistic. The statistic that is returned is determined by lambda_. The default is Pearson’s chi-squared statistic.

      pvaluefloat

        The p-value of the test.

      medianfloat

        The grand median.

      tablendarray

        The contingency table. The shape of the table is (2, n), where n is the number of samples. The first row holds the counts of the values above the grand median, and the second row holds the counts of the values below the grand median. The table allows further analysis with, for example, `scipy.stats.chi2_contingency`, or with `scipy.stats.fisher_exact` if there are two samples, without having to recompute the table. If `nan_policy` is “propagate” and there are nans in the input, the return value for `table` is `None`.

  See also

  `kruskal`

    Compute the Kruskal-Wallis H-test for independent samples.

  `mannwhitneyu`

    Computes the Mann-Whitney rank test on samples x and y.

  Notes

  Added in version 0.15.0.

  References

  [1]

  Mood, A. M., Introduction to the Theory of Statistics. McGraw-Hill (1950), pp. 394-399.

  [2]

  Zar, J. H., Biostatistical Analysis, 5th ed. Prentice Hall (2010). See Sections 8.12 and 10.15.

  Examples

  A biologist runs an experiment in which there are three groups of plants. Group 1 has 16 plants, group 2 has 15 plants, and group 3 has 17 plants. Each plant produces a number of seeds. The seed counts for each group are:

      Group 1: 10 14 14 18 20 22 24 25 31 31 32 39 43 43 48 49
      Group 2: 28 30 31 33 34 35 36 40 44 55 57 61 91 92 99
      Group 3:  0  3  9 22 23 25 25 33 34 34 40 45 46 48 62 67 84

  The following code applies Mood’s median test to these samples.

      >>> g1 = [10, 14, 14, 18, 20, 22, 24, 25, 31, 31, 32, 39, 43, 43, 48, 49]
      >>> g2 = [28, 30, 31, 33, 34, 35, 36, 40, 44, 55, 57, 61, 91, 92, 99]
      >>> g3 = [0, 3, 9, 22, 23, 25, 25, 33, 34, 34, 40, 45, 46, 48, 62, 67, 84]
      >>> from scipy.stats import median_test
      >>> res = median_test(g1, g2, g3)

  The median is

      >>> res.median
      34.0

  and the contingency table is

      >>> res.table
      array([[ 5, 10,  7],
             [11,  5, 10]])

  p is too large to conclude that the medians are not the same:

      >>> res.pvalue
      0.12609082774093244

  The “G-test” can be performed by passing `lambda_="log-likelihood"` to `median_test`.

      >>> res = median_test(g1, g2, g3, lambda_="log-likelihood")
      >>> res.pvalue
      0.12224779737117837

  The median occurs several times in the data, so we’ll get a different result if, for example, `ties="above"` is used:

      >>> res = median_test(g1, g2, g3, ties="above")
      >>> res.pvalue
      0.063873276069553273

      >>> res.table
      array([[ 5, 11,  9],
             [11,  4,  8]])

  This example demonstrates that if the data set is not large and there are values equal to the median, the p-value can be sensitive to the choice of ties.