Empirical Distributions of the Robustified t-test Statistics

Abstract

One sample t-test is commonly used for the statistical analysis of experimental data in comparing the mean difference between matched pairs such as the pretreatment and posttreatment assessments. It is well known that the t-test is sensitive to data contamination that occurs frequently in practical applications. To overcome the non-robustness of the t-test, Park (2018) developed two robustified analogues of this test based on robust statistics and provided the asymptotic distributions for the statistics, assuming that the sample size is large enough. These asymptotic results may not be adequate for making statistical inference including hypothesis testing and confidence interval when the sample size is small or even moderate. The purpose of this paper is to conduct Monte Carlo simulations to obtain the empirical distributions of these test statistics and their quantiles to conduct accurate statistical inference. Useful tables are also constructed for a quick finding of their empirical quantiles with different sample sizes.