Inference concerning a common dispersion of several treatment groups in the analysis of over/underdispersed count data

Over/underdispersed count data arise in many biostatistical practices in which a number of different treatment groups are compared in an experiment. In the analysis of several treatment groups of such count data, a very common statistical inference problem is to test whether these data come from the same population. The usual practice for testing homogeneity of several treatment groups in terms of means and dispersions is first to test the equality of dispersions and then to test the equality of the means based on the result of the test for equality of dispersions. Previous studies reported test procedures for testing the homogeneity of the means of several treatment groups with an assumption of equal or unequal dispersions. This article develops test procedures for testing the validity of the equal or unequal dispersions assumption of several treatment groups in the analysis of over/underdispersed count data. We consider the C(α) test based on the maximum likelihood (ML) method using the negative binomial model as well as the three other C(α) tests based on the method of moments, extended quasi-likelihood, and double extended quasi-likelihood using the models specified by the first two moments of counts. Monte Carlo simulations are then used to study the comparative behavior of these C(α) tests along with the likelihood ratio test in terms of size and power. The simulation results demonstrate that all four statistics hold the nominal level reasonably well in most of the data situations studied here, and the C(α) test based on ML shows some edge in power over the other three C(α) tests. Finally, applications to biostatistical practices are analyzed.