Multisample Homogeneity Tests

Abstract

Homogeneity techniques are needed to identify differences between two or more data sets. As with goodness-of-fit techniques, major differences occur between discrete and continuous data. Unlike symmetric techniques such as Fisher’s (1934) exact test, Pearson’s (1900) x ² test, and Zelterman’s (1987) test, all of which are used to test homogeneity for discrete data, MRPP asymmetric techniques such as the Goodman and Kruskal (1954) test distinguish between the response categories and the possible differences among the data sets. For continuous data, the homogeneity techniques include the generalized runs test, the Kolmogorov-Smirnov test, and tests based on empirical coverages. Specific examples are given for both discrete and continuous data to show definitive differences among the operating characteristics of these techniques.