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

# friedmanchisquare

scipy.stats.friedmanchisquare(*samples, axis=0, nan_policy='propagate', keepdims=False)

  Compute the Friedman test for repeated samples.

  The Friedman test tests the null hypothesis that repeated samples of the same individuals have the same distribution. It is often used to test for consistency among samples obtained in different ways. For example, if two sampling techniques are used on the same set of individuals, the Friedman test can be used to determine if the two sampling techniques are consistent.

  Parameters:
    *samples array_like

      Arrays of observations. All of the arrays must have the same number of elements. At least three samples must be given.

    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, correcting for ties.

    pvalue float

      The associated p-value assuming that the test statistic has a chi squared distribution.

  See also

  Friedman test for repeated samples

    Extended example

  Notes

  Due to the assumption that the test statistic has a chi squared distribution, the p-value is only reliable for n > 10 and more than 6 repeated samples.

  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

  `friedmanchisquare` 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

  `friedmanchisquare` also accepts MArrays backed by the backends indicated above; masked values will be treated as though they were not present.

  See Support for the array API standard for more information.

  References

  [1]

  https://en.wikipedia.org/wiki/Friedman_test

  [2]

  Demsar, J. (2006). Statistical comparisons of classifiers over multiple data sets. Journal of Machine Learning Research, 7, 1-30.

  Examples

      >>> import numpy as np
      >>> rng = np.random.default_rng(seed=18)
      >>> x = rng.random((6, 10))
      >>> from scipy.stats import friedmanchisquare
      >>> res = friedmanchisquare(x[0], x[1], x[2], x[3], x[4], x[5])
      >>> res.statistic, res.pvalue
      (11.428571428571416, 0.043514520866727614)

  The p-value is less than 0.05; however, as noted above, the results may not be reliable since we have a small number of repeated samples.

  For a more detailed example, see Friedman test for repeated samples.