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
largesample tests for complex survey designs and exact tests for small
samples as well as classic large-sample x2-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.
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Ben Jann
View all articles with these keywords:
mgof, mgofi, multinomial, goodness-of-fit, chi-squared, categorical data, exact tests, Monte Carlo, exhaustive enumeration, combinatorial algorithms, complex survey correction, power-divergence statistic, Kolmogorov–Smirnov, Benford's law
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