Mediation analysis is prominent in psychology, biology and sociology. A mediator is middle causal relationship between independent variable and dependent variable. A simulation study was conducted to compare 3 methods to test the statistical significance of the mediated effect. Three Tests based on the difference in coefficients, Freedman & Schatzkin, Clogg et al. and McGuigan & Langholtz are used in this study. The simulations consisted of 2000 replications of skew-normal distribution for a variety of sample sizes. This study proposes to compare statistical power to detect mediation effect and Type I error rate between three statistical tests when the mediator and dependent variable are skew-normal distribution. The simulation results show that Clogg et al. test has more accurate Type I error rate than Freedman & Schatzkin test and Type I error rate of McGuigan & Langholtz test has the farthest from significant level. The power to detect mediation effect of Freedman & Schatzkin test is no different from Clogg et al. test. The power of McGuigan & Langholtz test has lower than two tests, but the power of McGuigan & Langholtz test are similar to two tests when sample sizes are large.