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

Listed:
• Ben Jann

## 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.

## 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
as

File URL: http://repec.ethz.ch/ets/papers/jann_mgof.pdf
File Function: First version, 2008
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## Citations

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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. 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.
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.

### 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;
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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