Asymptotic Expansions of the Null Distribution of Bartlett's Statistic

Abstract

In this paper, the asymptotic expansions of the null distribution of the Bartlett's statistic for testing the homogeneity of variance in independent normal samples with unequal sizes are obtained. Series representations of the density of the Bartlett's statistic are given in terms of incomplete gamma as well as incomplete beta functions. The forms of the resulting cumulative distributions seem quite tractable for computation of critical values. Some indication of the relation of earlier work to our expansions is also given.