Count data are commonly assumed to have a Poisson distribution, especially when there is no diagnostic procedure for checking this assumption. However, count data rarely fit the restrictive assumptions of the Poisson distribution. The violation of much of such assumptions commonly results in overdispersion, which invalidates the Poisson distribution. Undetected overdispersion may entail important misleading inferences, so its detection is essential. In this study, different overdispersion diagnostic tests are evaluated through two simulation studies. In Exp. 1, the nominal error rate is compared under different sample sizes and λ conditions. Analysis shows a remarkable performance of the χdf2 test. In Exp. 2 and 3, statistical power is compared under different sample sizes, λ, and overdispersion conditions, χ2 and LR tests provide the highest statistical power.