Comparisons of the X2, Y2, Freeman-Tukey and Williams's improved G2 test statistics in small samples of one-way multinomials

Abstract

SUMMARY This paper is concerned with comparison of the null hypothesis distributions of four goodness-of-fit test statistics in multinomial samples. Most previous such work has been concerned only with Pearson's chi-squared and the likelihood ratio statistic. Here four statistics are examined. Several null hypotheses ranging from the equiprobable to the extremely skew were employed for moderate samples sizes with moderate numbers of cells. Results suggest that in comparison to other test criteria, Pearson' X 2 has, in one-way layouts, a distribution closest to χ 2 .