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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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    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;

    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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