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scipy.stats.

# shapiro

scipy.stats.shapiro(x, *, axis=None, nan_policy='propagate', keepdims=False)

  Perform the Shapiro-Wilk test for normality.

  The Shapiro-Wilk test tests the null hypothesis that the data was drawn from a normal distribution.

  Parameters:
    x array_like

      Array of sample data. Must contain at least three observations.

    axis int or None, default: None

      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.

    p-value float

      The p-value for the hypothesis test.

  See also

  `anderson`

    The Anderson-Darling test for normality

  `kstest`

    The Kolmogorov-Smirnov test for goodness of fit.

  Shapiro-Wilk test for normality

    Extended example

  Notes

  The algorithm used is described in [4], but censoring parameters as described are not implemented. For N > 5000 the W test statistic is accurate, but the p-value may not be.

  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

  `shapiro` 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/prc/section2/prc213.htm DOI:10.18434/M32189

  [2]

  Shapiro, S. S. & Wilk, M.B, “An analysis of variance test for normality (complete samples)”, Biometrika, 1965, Vol. 52, pp. 591-611, DOI:10.2307/2333709

  [3]

  Razali, N. M. & Wah, Y. B., “Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests”, Journal of Statistical Modeling and Analytics, 2011, Vol. 2, pp. 21-33.

  [4]

  Royston, P. “A toolkit for testing for non-normality in complete and censored samples.” Journal of the Royal Statistical Society: Series D (The Statistician) 42.1 (1993): 37-43.

  Examples

      >>> import numpy as np
      >>> from scipy import stats
      >>> rng = np.random.default_rng()
      >>> x = stats.norm.rvs(loc=5, scale=3, size=100, random_state=rng)
      >>> shapiro_test = stats.shapiro(x)
      >>> shapiro_test
      ShapiroResult(statistic=0.9813305735588074, pvalue=0.16855233907699585)
      >>> shapiro_test.statistic
      0.9813305735588074
      >>> shapiro_test.pvalue
      0.16855233907699585

  For a more detailed example, see Shapiro-Wilk test for normality.