Citation

Lewis T, Saunders IW, Westcott M. Biometrika 1984; 71(3): 515-522.

Copyright

(Copyright © 1984, Biometrika Trust, Publisher Oxford University Press)

DOI

10.1093/biomet/71.3.515

PMID

unavailable

Abstract

Explicit expressions for the first three moments of Pearson's X2 statistic for a two-way contingency table are used to investigate the accuracy of the χ2 approximation to its distribution. The usual 'minimum expected value' criterion is shown to give a global bound on the accuracy of the moments, but to be too conservative. This is illustrated by examples. It is shown that the adequacy of the approximation depends on the significance level that is to be used as well as the accuracy of the moments. When the χ22 approximation is inadequate, corrections based on the moments can be used. Numerical studies of the usefulness of these corrections are presented.