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scipy.stats.

# skewtest

scipy.stats.skewtest(a, axis=0, nan_policy='propagate', alternative='two-sided', *, keepdims=False)

  Test whether the skew is different from the normal distribution.

  This function tests the null hypothesis that the skewness of the population that the sample was drawn from is the same as that of a corresponding normal distribution.

  Parameters:
    a array

      The data to be tested. Must contain at least eight observations.

    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.

    alternative{‘two-sided’, ‘less’, ‘greater’}, optional

      Defines the alternative hypothesis. Default is ‘two-sided’. The following options are available:

      - ‘two-sided’: the skewness of the distribution underlying the sample is different from that of the normal distribution (i.e. 0)

      - ‘less’: the skewness of the distribution underlying the sample is less than that of the normal distribution

      - ‘greater’: the skewness of the distribution underlying the sample is greater than that of the normal distribution

      Added in version 1.7.0.

    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 computed z-score for this test.

    pvalue float

      The p-value for the hypothesis test.

  See also

  Skewness test

    Extended example

  Notes

  The sample size must be at least 8.

  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`.

  `skewtest` 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 | ⚠️ computes graph | n/a

  See Support for the array API standard for more information.

  References

  [1]

  R. B. D’Agostino, A. J. Belanger and R. B. D’Agostino Jr., “A suggestion for using powerful and informative tests of normality”, American Statistician 44, pp. 316-321, 1990.

  Examples

      >>> from scipy.stats import skewtest
      >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8])
      SkewtestResult(statistic=1.0108048609177787, pvalue=0.3121098361421897)
      >>> skewtest([2, 8, 0, 4, 1, 9, 9, 0])
      SkewtestResult(statistic=0.44626385374196975, pvalue=0.6554066631275459)
      >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8000])
      SkewtestResult(statistic=3.571773510360407, pvalue=0.0003545719905823133)
      >>> skewtest([100, 100, 100, 100, 100, 100, 100, 101])
      SkewtestResult(statistic=3.5717766638478072, pvalue=0.000354567720281634)
      >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8], alternative='less')
      SkewtestResult(statistic=1.0108048609177787, pvalue=0.8439450819289052)
      >>> skewtest([1, 2, 3, 4, 5, 6, 7, 8], alternative='greater')
      SkewtestResult(statistic=1.0108048609177787, pvalue=0.15605491807109484)

  For a more detailed example, see Skewness test.