Power analysis for t-test with non-normal data and unequal variances

A Monte Carlo based power analysis is proposed for t-test to deal with non-normality and heterogeneity in real data. The step-by-step procedure of the proposed method is introduced in the paper. For comparing the performance of the Monte Carlo based power analysis to that of conventional pooled-variance t-test, a simulation study was conducted. The results indicate the Monte Carlo based power analysis provided well-controlled empirical Type I error rate, whereas the conventional pooled-variance t-test failed to yield nominal-level Type I error rate. Both an R package and its corresponding online interface are provided to implement the proposed method.