Testing Normality of Transformed Data

Kristian Linnet

Journal of the Royal Statistical Society Series C, 1988, vol. 37, issue 2, 180-186

Abstract: Applications of the Anderson–Darling, Cramér–von Mises and Kolmogorov‐Smirnov tests of normality to transformed data are considered. It is assumed that the transformation involves an unknown parameter that has to be estimated from the data. Unless allowance is taken for the estimation of a transformation parameter, these tests become conservative. For example, the nominal 0.05 significance level for the Anderson–Darling test corresponds to a real level of 0.014 (N = 50). Simulation studies show that the null distributions of the test statistics are independent of parameter values. Thus, using critical values that are appropriate when the mean, standard deviation and transformation parameter are unknown, which are tabulated here, these goodness‐of‐fit tests can be applied to transformed variables.

Date: 1988
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