The distribution of a sample of binary responses, such asSCORE = the number of positive responses ofm trials, can be modeled by the betabinomial compound density. The heritability ofSCORE is estimated following the method detailed by W. G. Hill [(1972). Biometrics27:293–311], but the formula for the standard error is changed. The beta mixing density forp(response) allows for a variety of shapes for the distribution of individualp(response) values about the population mean. An example is provided in whichSCORE has a low heritability but the response to divergent selection can be seen clearly in the change in the shape of the distribution of individualp(response) values. These changes in shape can be diagnosed from sample estimates of the beta shape parameters, since these determine the mean, mode, and variance.