Multinomial Goodness-of-Fit: Large-Sample Tests with Survey Design Correction and Exact Tests for Small Samples

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 X 2 -approximation tests based on Pearson's X 2 , 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.