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Abstract Exact small sample behavior in two-way contingency tables is investigated for Pearson's chi-square statistic (X 2), Light and Margolin's C statistic and its related R 2 measure of association, Kullback's minimum discrimination information statistic (2Î), and Goodman and Kruskal's Lambda. R 2 is shown to be identical to Goodman and Kruskal's tb , leading to a test for independence based on tb. In small samples from a product of multinomials model, the null distribution of C is better approximated by a χ2 distribution than is the null distribution of X 2; both are considerably better approximated by a χ2 distribution than is the null distribution of 2Î. It is proved for tables with two columns and any number of rows that if the column totals are equal, then X 2 ≤ 2Î; thus, X 2 is more conservative than 2Î. Hence, use of 2Î should be avoided in testing independence in tables with small samples.
Margolin et al. (Sun,) studied this question.