Current Methodologies for the Analysis of Contingency Tables: Robustness with Respect to Small Expected Values

摘要

The primary purpose of this study is to investigate the robustness characteristics of some of the current methodologies for the analysis of contingency tables as the size of the table increases. A Monte Carlo simulation provides estimates of exact significance levels for comparison with nominal levels. An extensive array of tables, probability designs, and sample sizes are used. Three asymptotic chi-squared statistics are evaluated: the Pearson statistic, the Kullback minimum discrimination information statistics, and the Grizzle, Starmer, and Koch (GSK) Wald statistic. A 95% confidence interval criterion about the nominal levels is defined, and certain minimum sample sizes (Nm) are determined. These Nm provide the parameters for calculation of critical expected value (CEV) distributions. The CEV distributions are extensively analyzed. The GSK statistic is shown to be highly conservative, significantly biased by the presence of zero cells, and less robust as the size of the table increases. The Kullback statistic is shown to be generally liberal with best performance at the lower nominal levels, and little change in robustness characteristics is noted. The Pearson statistic is shown to be somewhat conservative and clearly superior to the other statistics, and the robustness with respect to small expected values is significantly improved as the size of the table increases. (Author)