An Analysis of Variance for Categorical Data, II: Small Sample Comparisons with Chi Square and other Competitors

摘要: 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 its related R 2 measure of association, Kullback's minimum discrimination information (2I), Goodman Kruskal's Lambda. shown to be identical tb , leading a test independence based on tb. In samples from product multinomials model, the null distribution better approximated by χ2 than X 2; both are considerably 2I. It proved with two columns any number rows that if column totals equal, then ≤ 2I; thus, more conservative Hence, use 2I should avoided testing samples.