The Two-Sample t-test and the Influence of Outliers : - A simulation study on how the type I error rate is impacted by outliers of different magnitude.

Abstract: This study investigates how outliers of different magnitude impact the robustness of the twosample t-test. A simulation study approach is used to analyze the behavior of type I error rates when outliers are added to generated data. Outliers may distort parameter estimates such as the mean and variance and cause misleading test results. Previous research has shown that Welch’s ttest performs better than the traditional Student’s t-test when group variances are unequal. Therefore these two alternative statistics are compared in terms of type I error rates when outliers are added to the samples. The results show that control of type I error rates can be maintained in the presence of a single outlier. Depending on the magnitude of the outlier and the sample size, there are scenarios where the t-test is robust. However, the sensitivity of the t-test is illustrated by deteriorating type I error rates when more than one outlier are included. The comparison between Welch’s t-test and Student’s t-test shows that the former is marginally more robust against outlier influence.