Asymptotic log-linear analysis: some cautions concerning sparse frequency tables.
Traditional asymptotic probability values resulting from log-linear analyses of sparse frequency tables are often much too large. Asymptotic probability values for chi-squared and likelihood-ratio statistics are compared to nonasymptotic and exact probability values for selected log-linear models. The asymptotic probability values are all too often substantially larger than the exact probability values for the analysis of sparse frequency tables. An exact nondirectional permutation method is presented to analyze combined independent multinomial distributions. Exact nondirectional permutation methods to analyze hypergeometric distributions associated with r-way frequency tables are confined to r = 2.
Mielke
Paul W
PW
Department of Statistics, Colorado State University, Fort Collins, CO 80523-1877, USA. mielke@lamar.colostate.edu
Berry
Kenneth J
KJ
Johnston
Janis E
JE
D016009:Chi-Square Distribution; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D008432:Mathematical Computing; D011336:Probability; D011589:Psychology, Experimental / Q000706:statistics & numerical data*; D015203:Reproducibility of Results