Two independent samples t test is a parametric statistical method that have several assumptions underlying this method. The assumption applied in the use of two independent samples t test is normal population and equal variance. These assumptions will affect accuracy of the result if the underlying assumptions satisfied or not. Many people use the t statistic to compare two samples even when the underlying assumptions are in doubt. This paper is intended as an introductory article that gives brief overview about the robustness or sensitivity of this popular test statistic with respect to changes in the assumptions. One way to investigate the robustness or sensitivity of two independent samples t test using Monte Carlo simulation with R.