Multinomial goodness-of-fit: Large-sample tests with survey design correction and exact tests for small samples

Abstract

I introduce the new mgof command to compute distributional tests for discrete (categorical, multinomial) variables. The command supports large-sample tests for complex survey designs and exact tests for small samples as well as classic large-sample χ2-approximation tests based on Pearson's X2, the likelihood ratio, or any other statistic from the power-divergence family (Cressie and Read, 1984, Journal of the Royal Statistical Society, Series B (Methodological) 46: 440-464). The complex survey correction is based on the approach by Rao and Scott (1981, Journal of the American Statistical Association 76: 221-230) and parallels the survey design correction used for independence tests in svy: tabulate. mgof computes the exact tests by using Monte Carlo methods or exhaustive enumeration, mgof also provides an exact one-sample Kolmogorov-Smirnov test for discrete data. © 2008 StataCorp LP.