• Journal of the Korean Data and Information Science Society
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• v.11 no.1
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• pp.83-90
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• 2000

The chi-squared test statistic is usually employed for testing independence of two categorical variables in a two-way contingency table. It is well known that, under independence, the test statistic has an asymptotic chi-squared distribution under multinomial or product-multinomial models. For the case where both margins fixed, the sampling model of the contingency table is a multiple hypergeometric distribution and the chi-squared test statistic follows the same limiting distribution. In this paper, we study the difference between the small sample and large sample distributions of the chi-squared test statistic for the case with fixed margins. For a few small sample cases, the exact small sample distribution of the test statistic is directly computed. For a few large sample sizes, the small sample distribution of the statistic is generated via a Monte Carlo algorithm, and then is compared with the large sample distribution via chi-squared probability plots and Kolmogorov-Smirnov tests.