F-type statistics and the analysis of binomial data with overdispersion

The analysis of binomial data that exhibit overdispersion in a randomized complete block design is investigated. More specifically, the asymptotic distribution of the test statistic for the treatment effects in the presence of overdispersion and random effects is considered. A Monte Carlo simulation attempts to quantify the error in the approximation by the F-distribution to the distribution of the test statistic given by many popular statistics packages including SAS. The influence of different parameter values (i.e., number of treatments, number of observations per cell, degree of overdispersion, etc.) on the goodness of the approximations is evaluated. General recommendations are given for practical analysis of binomial data.