A test of the null hypothesis that a sample has been drawn from a normal distribution. An attractively simple test is that proposed by Geary in 1935. The Geary test compares the ratio of the mean deviation divided by the standard deviation with the theoretical ratio for a normal distribution, which is . An alternative is the D'Agostino test suggested by D'Agostino in 1971. With ordered observations x(1)≤x(2)≤…≤x(n), the test statistic is D, given by where x¯ is the sample mean (see mean data). Special tables are required.
Several more general tests of specified distributions have special cases for testing for normality. Examples include the Anderson–Darling test and the Shapiro–Wilk test. See also Cramér–von Mises test; Kolmogorov–Smirnov test.
Subjects: Probability and Statistics.