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Biometrika 1973 60(3):613-622; doi:10.1093/biomet/60.3.613
© 1973 by Biometrika Trust
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Tests for departure from normality. Empirical results for the distributions of b2 and {surd}b1

RALPH D'AGOSTINO and E. S. PEARSON

Boston University
University College London

This paper is a preliminary to a detailed survey of the relative powers of a number of omnibus and directional tests of nonnormality. The probability integrals of {surd}b1 and b2, the standardized third and fourth moment statistics, are found for random samples from a normal distribution. Main attention is given to b2. Extensive computer simulation and curve fitting have been used to provide charts of probability levels out to the 0.1% point, for 20 ≤ n ≤ 200. For {surd}b1, the parameters of Johnson's symmetrical SU approximation are tabled for values of n between 8 and 1000. An illustration is given of two ‘omnibus’ tests applying the charts and table, involving the joint use of {surd}b1 and b2.

Key Words: Testing for departure from normality • Omnibus tests • Directional tests • Skewness and kurtosis • Third and fourth moment statistics • Simulation


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