1. An Analysis of Variance for Categorical Data, II: Small Sample Comparisons with Chi Square and Other Competitors.
- Author
-
Margolin, Barry H. and Light, Richard J.
- Subjects
MATHEMATICAL statistics ,ANALYSIS of variance ,DISTRIBUTION (Probability theory) ,STATISTICAL hypothesis testing ,ASSOCIATIONS, institutions, etc. ,STATISTICAL correlation - Abstract
Exact small sample behavior in two-way contingency tables is investigated for Pearson's chi-square statistic (X²), Light and Margolin's C statistic and its related R² measure of association, Kuliback's minimum discrimination information statistic (2&lcirc;), and Goodman and Kruskal's Lambda. R² is shown to be identical to Goodman and Kruskal's t
b , leading to a test for independence based on 4. In small samples from a product of multinomials model, the null distribution of C is better approximated by a x² distribution than is the null distribution of X²; both are considerably better approximated by a x² distribution than is the null distribution of 2&lcirc;. It is proved for tables with two columns and any number of rows that if the column totals are equal, then X² ≤ 2&lcirc;; thus, X² is more conservative than 2&lcirc;. Hence, use of 2&lcirc; should be avoided in testing independence in tables with small samples. [ABSTRACT FROM AUTHOR]- Published
- 1974
- Full Text
- View/download PDF