Bootstrap goodness-of-fit test for the beta-binomial model

A common question in the analysis of binary data is how to deal with overdispersion. One widely advocated sampling distribution for overdispersed binary data is the beta-binomial model. For example, this distribution is often used to model litter effects in toxicological experiments. Testing the null hypothesis of a beta-binomial distribution against all other distributions is difficult, however, when the litter sizes vary greatly. Herein, we propose a test statistic based on combining Pearson statistics from individual litter sizes, and estimate the p-value using bootstrap techniques. A Monte Carlo study confirms the accuracy and power of the test against a beta-binomial distribution contaminated with a few outliers. The method is applied to data from environmental toxicity studies.