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

Author

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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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    Cited by:

    1. Scott A. Brave & Kevin A. Roberts, 2019. "The Competitive Effects of Performance-Enhancing Drugs: MLB in the Posttesting Era," Journal of Sports Economics, , vol. 20(6), pages 747-781, August.
    2. Bašić, Zvonimir & Quercia, Simone, 2022. "The influence of self and social image concerns on lying," Games and Economic Behavior, Elsevier, vol. 133(C), pages 162-169.
    3. John Micklewright & Sylke V. Schnepf, 2010. "How reliable are income data collected with a single question?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(2), pages 409-429, April.
    4. Ioana Sorina Deleanu, 2017. "Do Countries Consistently Engage in Misinforming the International Community about Their Efforts to Combat Money Laundering? Evidence Using Benford’s Law," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-19, January.
    5. Hopp, Christian & Hoover, Gary A., 2017. "How prevalent is academic misconduct in management research?," Journal of Business Research, Elsevier, vol. 80(C), pages 73-81.
    6. Toke Reinholt Fosgaard, 2020. "Students Cheat More: Comparing the Dishonesty of a Student Sample and a Representative Sample in the Laboratory," Scandinavian Journal of Economics, Wiley Blackwell, vol. 122(1), pages 257-279, January.

    More about this item

    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;
    All these keywords.

    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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