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

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  • Ben Jann

    () (ETH Zurich)

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 Chi^2-approximation tests based on Pearson’s Chi^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 par- allels the survey design correction used for independence tests in svy: tabulate. mgof computes the exact tests by using Monte Carlo methods or exhaustive enu- meration. mgof also provides an exact one-sample Kolmogorov-Smirnov test for discrete data. Copyright 2008 by StataCorp LP.

Suggested Citation

  • Ben Jann, 2008. "Multinomial goodness-of-fit: Large-sample tests with survey design correction and exact tests for small samples," Stata Journal, StataCorp LP, vol. 8(2), pages 147-169, June.
  • Handle: RePEc:tsj:stataj:v:8:y:2008:i:2:p:147-169
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    1. repec:eee:jbrese:v:80:y:2017:i:c:p:73-81 is not listed on IDEAS

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    Keywords

    mgof; mgofi; multinomial; goodness-of-fit; chi-squared; cat- egorical data; exact tests; Monte Carlo; exhaustive enumeration; combinatorial algorithms; complex survey correction; power-divergence statistic; Kolmogorov-Smirnov; Benford's law;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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