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


  • Ben Jann


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.

Suggested Citation

  • Ben Jann, 2008. "Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples," ETH Zurich Sociology Working Papers 2, ETH Zurich, Chair of Sociology.
  • Handle: RePEc:ets:wpaper:2

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    3. 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.
    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


    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;
    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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