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Biometrika 1980 67(2):447-453; doi:10.1093/biomet/67.2.447
© 1980 by Biometrika Trust
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An approximation to the distribution of the X2 goodness-of-fit statistic for use with small expectations

H. BAYO LAWAL and GRAHAM J. G. UPTON

Department of Mathematics, Ahmadu Bello University Nigeria
Department of Mathematics, University of Essex

This paper is concerned with the X2 goodness-of-fit test when the observed frequencies are supposed to be distributed according to a specified multinomial distribution. We propose a log normal approximation to the distribution of X2. Our results suggest that the approximation is valid providing that the smallest expectation is greater than r/d{oslash}, where r is the number of expectations less than 5, and d is the number of degrees of freedom.

Key Words: Chi-squared distribution • Chi-squared goodness-of-fit test • Log normal distribution • Small expectation.


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