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

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 rate