Analysis of Variance (ANOVA) is the easiest and most widely used model nowadays in statistics. ANOVA however requires a set of assumptions for the model to be a valid choice and for the inferences to be accurate. Among many, ANOVA assumes the data in question is normally distributed and homogenous. However, data from most disciplines does not meet the assumption of normality and/or equal variance. Regrettably, researchers do not always check whether the assumptions are met, and if these assumptions are violated, inferences might well be wrong. We conducted a simulation study to compare the performance of standard ANOVA to Poisson and Negative Binomial models when applied to counts data. We considered different combination of sample sizes and underlying distributions. In this simulation study, we first assed Type I error for each model involved. We then compared power as well as the quality of the estimated parameters across the models.