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. 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. :ref:`hypothesis_shapiro` : 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. 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., "Remark AS R94: A Remark on Algorithm AS 181: The W-test for Normality", 1995, Applied Statistics, Vol. 44, :doi:`10.2307/2986146` 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 :ref:`hypothesis_shapiro`. r‹