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scipy.stats.

# levene

scipy.stats.levene(*samples, center='median', proportiontocut=0.05, axis=0, nan_policy='propagate', keepdims=False)

  Perform Levene test for equal variances.

  The Levene test tests the null hypothesis that all input samples are from populations with equal variances. Levene’s test is an alternative to Bartlett’s test `bartlett` in the case where there are significant deviations from normality.

  Parameters:
    sample1, sample2, …array_like

      The sample data, possibly with different lengths.

    center{‘mean’, ‘median’, ‘trimmed’}, optional

      Which statistics to use to center data points within each sample. Default is ‘median’.

    proportiontocut float, optional

      When center is ‘trimmed’, this gives the proportion of data points to cut from each end. (See `scipy.stats.trim_mean`.) Default is 0.05.

    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.

    pvalue float

      The p-value for the test.

  See also

  `fligner`

    A non-parametric test for the equality of k variances

  `bartlett`

    A parametric test for equality of k variances in normal samples

  Levene test for equal variances

    Extended example

  Notes

  Three variations of Levene’s test are possible. The possibilities and their recommended usages are:

  - ‘median’ : Recommended for skewed (non-normal) distributions>

  - ‘mean’ : Recommended for symmetric, moderate-tailed distributions.

  - ‘trimmed’ : Recommended for heavy-tailed distributions.

  The test version using the mean was proposed in the original article of Levene ([2]) while the median and trimmed mean have been studied by Brown and Forsythe ([3]), sometimes also referred to as Brown-Forsythe test.

  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

  `levene` 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://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm

  [2]

  Levene, H. (1960). In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, I. Olkin et al. eds., Stanford University Press, pp. 278-292.

  [3]

  Brown, M. B. and Forsythe, A. B. (1974), Journal of the American Statistical Association, 69, 364-367

  Examples

  Test whether the lists a, b and c come from populations with equal variances.

      >>> import numpy as np
      >>> from scipy import stats
      >>> a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]
      >>> b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]
      >>> c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]
      >>> stat, p = stats.levene(a, b, c)
      >>> p
      0.002431505967249681

  The small p-value suggests that the populations do not have equal variances.

  This is not surprising, given that the sample variance of b is much larger than that of a and c:

      >>> [np.var(x, ddof=1) for x in [a, b, c]]
      [0.007054444444444413, 0.13073888888888888, 0.008890000000000002]

  For a more detailed example, see Levene test for equal variances.