The Use of Chi-Squared Statistics for Categorical Data Problems

Summary The use of χ2 statistics for categorical data problems was initiated by Karl Pearson, but it took several years before the asymptotic distribution of these statistics was well understood. The general structure of asymptotic results for χ2 statistics is reviewed and the applicability of the general structure to a variety of problems of practical interest is discussed. These problems include the use of χ2 statistics in small-sample situations and in large sparse tables, in cluster sampling, and in cases where they do not have asymptotic χ2 distributions.