What sample sizes are needed to get correct significance levels for log-linear models? - A Monte Carlo Study using the SPSS-procedure "Hiloglinear"

Pearson's 2 ! and the Likelihood-ratio statistic 2 G are the most common and widely used test statistics for log-linear models. They are both asymptotically distributed as chi-squared variables. The present article reports the results of a Monte-Carlo study which compares the two test statistics for two-, threeand four-dimensional contingency tables, employing conditions which may be judged reasonable for psychological research and using one of the most prominent computer programs (SPSS "Hiloglinear"). Our results are consistent with previous research in that, on the whole, Pearson's 2 ! behaves better than 2 G . As a rule of thumb one may state that Pearson's 2 ! will not result in severely inflated alpha values (empirical values of .075 or larger for a nominal level of .05) if the total sample size equals five times the number of cells and the smallest expected cell frequency is larger than 0.50. On contrast, the Likelihood-ratio statistic 2 G yields in some cases severely inflated empirical alpha values for the higher interactions even if the total sample size equals ten times the number of cells and the smallest expected cell frequency is larger than one. In those cases where sample size is large enough to use Pearson's 2 ! , Pearson's 2 ! is preferable to 2 G , as it is generally closer to the nominal alpha. For cases not covered by this rule parametric bootstrapping is recommended.