Comparison of Statistical Tests of Independence for Sparse I x J Contingency Tables.

ABSTRACT Contingency tables, and their associated statistical tests, are frequently used in educational and social research. Popular statistical tests used in contingency table analyses include the Pearson chi-square test and the likelihood ratio chi-square test. These two t=,sts are chi-square distributed under large sample conditions. However, when a given contingency table includes small cell frequencies the obtained chi-square statistic may not be asymptotically valid, and the associated probability values will be inappropriate. An alternative statistic which has been recommended for small samples or sparse conditions is the power-divergence statistic (Read & Cressie, 1988). This study was an investigation of the performance of three tests of independence for I x J contingency tables under small sample conditions. Specifically, the objectives of the research were to investigate the power and Type I error rates under small sample or sparse conditions of the Pearson chi-square test, the likelihood ratio chi-square test, and the Read and Cressie power-divergence statistic with lambda = 2/3 (Read & Cressie, 1988). The power and Type I error rates were estimated for a variety of table dimensions, marginal distributions, sample sizes, and effect sizes. (Contains 16 references, 4 figures, and 4 tables.) (Author)