An approximation to the distribution of the X 2 goodness-of-fit statistic for use with small expectations

Abstract

This paper is concerned with the X 2 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 X 2 . Our results suggest that the approximation is valid providing that the smallest expectation is greater than r/d ⊘ , where r is the number of expectations less than 5, and d is the number of degrees of freedom.