Tests of Chi-Squared Type

Abstract

This chapter considers two classes of chi-squared procedures: one, called classical because it contains such familiar statistics as the log likelihood ratio, Neyman modified chi-squared, and Freeman-Tukey; and the second, consisting of nonnegative definite quadratic forms in the standardized cell frequencies. A different approach that may aid the choosing of a statistic is to examine the type of lack of fit measured by each statistic. The use of data-dependent cells increases the flexibility of chi-squared tests, fortunately without increasing their complexity in practice. Chi-squared tests are generally less powerful than empirical distribution function tests and special-purpose tests of fit. An objection to the use of chi-squared tests has been the arbitrariness introduced by the necessity to choose cells. Some of the most useful recent work on chi-squared tests involves the study of quadratic forms in the standardized cell frequencies other than the sum of squares used by Pearson.