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分类数据的方差分析（二）：与卡方等方法的小样本比较AI 解读

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…

分类数据的方差分析AI 解读

A measure of variation for categorical data is discussed. We develop an analysis of variance for a one-way table, where the response variable is categorical. The data can be viewed alternatively as falling in a two-dimensional contingency table with one margin fixed. Components of variation are derived, and their properties are investigated under a common multinomial model. Using these components, we propose a measure of the variation in the response variable explained by…