Tests for departure from normality. Empirical results for the distributions of b2 and √b1
- 1 December 1973
- journal article
- research article
- Published by Oxford University Press (OUP) in Biometrika
- Vol. 60 (3) , 613-622
- https://doi.org/10.1093/biomet/60.3.613
Abstract
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 √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 √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 √b1 and b2.Keywords
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