# scipy.stats.normaltest

scipy.stats.normaltest(a, axis=0, nan_policy='propagate')

  Test whether a sample differs from a normal distribution.

  This function tests the null hypothesis that a sample comes from a normal distribution. It is based on D’Agostino and Pearson’s [1], [2] test that combines skew and kurtosis to produce an omnibus test of normality.

  Parameters
    a array_like

      The array containing the sample to be tested.

    axis int or None, optional

      Axis along which to compute test. Default is 0. If None, compute over the whole array a.

    nan_policy{‘propagate’, ‘raise’, ‘omit’}, optional

      Defines how to handle when input contains nan. The following options are available (default is ‘propagate’):

      > - ‘propagate’: returns nan

      > - ‘raise’: throws an error

      > - ‘omit’: performs the calculations ignoring nan values

  Returns
    statistic float or array

      `s^2 + k^2`, where `s` is the z-score returned by `skewtest` and `k` is the z-score returned by `kurtosistest`.

    pvalue float or array

      A 2-sided chi squared probability for the hypothesis test.

  References

  1

    D’Agostino, R. B. (1971), “An omnibus test of normality for moderate and large sample size”, Biometrika, 58, 341-348

  2

    D’Agostino, R. and Pearson, E. S. (1973), “Tests for departure from normality”, Biometrika, 60, 613-622

  Examples

      >>> from scipy import stats
      >>> rng = np.random.default_rng()
      >>> pts = 1000
      >>> a = rng.normal(0, 1, size=pts)
      >>> b = rng.normal(2, 1, size=pts)
      >>> x = np.concatenate((a, b))
      >>> k2, p = stats.normaltest(x)
      >>> alpha = 1e-3
      >>> print("p = {:g}".format(p))
      p = 8.4713e-19
      >>> if p < alpha:  # null hypothesis: x comes from a normal distribution
      ...     print("The null hypothesis can be rejected")
      ... else:
      ...     print("The null hypothesis cannot be rejected")
      The null hypothesis can be rejected

scipy.stats.kurtosistest Quasi-Monte Carlo submodule (`scipy.stats.qmc`)