Clinical trial count data may be skewed and heteroscedastic. The discrete degree of skewness and of kurtosis are generally not accounted for in hypothesis testing. Parametric methods comparing the first moment, such as t-test and Welch U-test might be invalid if obvious difference in higher moments exist. Non-parametric methods, e.g., Wilcoxon RS test, Brunner-Munzel test, ranked Welch U-test, have been proposed to deal with generalized/non-parametric Behrens-Fisher problem. The performance comparison of these methods has been conducted in the literature. However, none of these tests is robust under all scenarios. In this research, we perform simulation studies to compare the test performance among parametric, semi-parametric and non-parametric approaches with count data that can be highly skewed. We consider a combined test, a two-stage approach and a weighted-test framework for further comparison. This research work finding may provide some guidance in identifying appropriate statistical tests for count data that are potentially highly skewed seen in medical imaging clinical trial applications.