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

Ben Jann

No 2, ETH Zurich Sociology Working Papers from ETH Zurich, Chair of Sociology

Abstract: A new Stata command called -mgof- is introduced. The command is used to compute distributional tests for discrete (categorical, multinomial) variables. Apart from classic large sample $\chi^2$-approximation tests based on Pearson's $X^2$, the likelihood ratio, or any other statistic from the power-divergence family (Cressie and Read 1984), large sample tests for complex survey designs and exact tests for small samples are supported. The complex survey correction is based on the approach by Rao and Scott (1981) and parallels the survey design correction used for independence tests in -svy:tabulate-. The exact tests are computed using Monte Carlo methods or exhaustive enumeration. An exact Kolmogorov-Smirnov test for discrete data is also provided.

Keywords: 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 (search for similar items in EconPapers)
JEL-codes: C12 C16 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2008-01
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Citations: View citations in EconPapers (7)

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Related works:
Software Item: MGOF: Stata module to perform goodness-of-fit tests for multinomial data (2021)
Journal Article: Multinomial goodness-of-fit: Large-sample tests with survey design correction and exact tests for small samples (2008)
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