Procedures for testing homogeneity of proportions, in the presence of over-dispersion or under-dispersion, occurring in several groups in toxicology (teratology or mutagenicity) or other similar fields, are developed. We consider C(α) (Neyman, 1959, in Probability and Statistics: The Harold Cramer Volume, pp. 213-234, New York: Wiley) or score type tests (Rao, 1947, Proceedings of the Cambridge Philosophical Society 44, 50-57) based on a parametric model, namely, the extended beta-binomial model (Prentice, 1986, Journal of the American Statistical Association 81, 321-327) and two semi-parametric models using quasi-likelihood (Wedderburn, 1974, Biometrika 61, 439-447) and extended quasi-likelihood (Nelder and Pregibon, 1987, Biometrika 74, 221-232). These procedures and a recent procedure by Rao and Scott (1992, Biometrics 48, 577-585), based on the concept of design effect and effective sample size, are compared, through simulation, in terms of size, power, and robustness for departures from data distribution and dispersion homogeneity. To study robustness in terms of departure from data distribution, we simulate data from the beta-binomial distribution, the probit normal binomial distribution, and the logit normal binomial distribution. Simulation shows evidence that, for litter sizes and number of litters that may arise in practice, a score test, based on the quasi-likelihood, performs best in that it holds nominal level well in all data distribution situations considered here, it shows some edge in power over some other statistics in some situations, and also shows robustness in presence of moderate dispersion heterogeneity. This statistic has a very simple form, and it requires estimates of the parameters only under the null hypotheses.