Exact and approximate distributions of the chi-square statistic for equiprobability

Abstract

The distribution of the chi-square goodness-of-fit statistic is studied in the equiprobable case. Tables of exact critical values are given for a = .1, .05, .01, .005; k = 2(1)4, N = 26(1)50; k = 5, N = 26(1)40; k = 6(1)10, N = 26(1)30, where a is the desired significance level, k is the number of cells and N is the sample size. Methods of fitting the true distribution are compared. If k> 3, it is found that a simple additive adjustment to the asymptotic chi-square fit leads to high accuracy even for N between 10 and 20. For k = 2, the Yates corrected chi-square statistic is very accurately fitted by the usual chi-square distribution.

Keywords:

• continuity correction
• exact critical values
• variance test
• index of dispersion
• goodness of fit test
• beta fit
• Yates correction