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A comparison of various tests of normality. (English) Zbl 1112.62039

Summary: This article studies twelve different normality tests that are used for assessing the assumption that a sample was drawn from a normally distributed population and compares their powers. The tests in question are chi-square, Kolmogorov–Smirnov, Anderson–Darling, Kuiper, Shapiro–Wilk, Ajne, modified Ajne, modified Kuiper, D’Agostino, modified Kolmogorov–Smirnov, Vasicek, and Jarque–Bera. Each test is described and power comparisons are also obtained by using Monte Carlo computations. To do this, first normally distributed populations with different standard deviations are taken and then simulation is conducted for nonnormal populations. The results are discussed and interpreted separately.

MSC:

62G10 Nonparametric hypothesis testing
65C05 Monte Carlo methods

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References:

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