Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples
AbstractA 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.
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Bibliographic InfoPaper provided by ETH Zurich, Chair of Sociology in its series ETH Zurich Sociology Working Papers with number 2.
Length: 23 pages
Date of creation: Jan 2008
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Web page: http://www.socio.ethz.ch/
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;
Other versions of this item:
- 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.
- Ben Jann, 2007. "MGOF: Stata module to perform goodness-of-fit tests for multinomial data," Statistical Software Components S456854, Boston College Department of Economics, revised 14 Jul 2008.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-01-19 (All new papers)
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