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scipy.stats.

# fligner

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

  Perform Fligner-Killeen test for equality of variance.

  Fligner’s test tests the null hypothesis that all input samples are from populations with equal variances. Fligner-Killeen’s test is distribution free when populations are identical [2].

  Parameters:
    sample1, sample2, …array_like

      Arrays of sample data. Need not be the same length.

    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 hypothesis test.

  See also

  `bartlett`

    A parametric test for equality of k variances in normal samples

  `levene`

    A robust parametric test for equality of k variances

  Fligner-Killeen test for equality of variance

    Extended example

  Notes

  As with Levene’s test there are three variants of Fligner’s test that differ by the measure of central tendency used in the test. See `levene` for more information.

  Conover et al. (1981) examine many of the existing parametric and nonparametric tests by extensive simulations and they conclude that the tests proposed by Fligner and Killeen (1976) and Levene (1960) appear to be superior in terms of robustness of departures from normality and power [3].

  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

  `fligner` 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 | ⚠️ no JIT | ⚠️ no JIT
  Dask | ⛔ | n/a

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

  References

  [1]

  Qu, A., Lindsay, B. G., and Li, B. (2000). Improving generalized estimating equations using quadratic inference functions. Biometrika, 87(4), 823-836. DOI:10.1093/biomet/87.4.823

  [2]

  Fligner, M.A. and Killeen, T.J. (1976). Distribution-free two-sample tests for scale. Journal of the American Statistical Association. 71(353), 210-213.

  [3]

  Conover, W. J., Johnson, M. E. and Johnson M. M. (1981). A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics, 23(4), 351-361.

  Examples

      >>> import numpy as np
      >>> from scipy import stats

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

      >>> 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.fligner(a, b, c)
      >>> p
      0.00450826080004775

  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 Fligner-Killeen test for equality of variance.