Robust tests for the Behrens-Fisher problem when the underlying distribution is short-tailed symmetric: An application to dopamine and schizophrenia data

Abstract

In this study, the robust versions of the well-known Welch (W) and generalized p-value (GP) tests, i.e., robust Welch (RW) and robust generalized p-value (RGP) tests, are proposed for testing the equality of two means when the underlying distribution is short-tailed symmetric (STS) and variances are unknown and arbitrary. They are based on modified maximum likelihood (MML) estimators which have closed forms and are approximately equivalent to the maximum likelihood (ML) estimators. Under various scenarios, the proposed and existing tests are compared in terms of Type I error rates and powers via a Monte Carlo simulation study in R software program. Also, robustness of the proposed tests is investigated. Simulation results indicate that proposed tests perform as well as or better than the W and GP tests, while they satisfactorily control the Type I error rates. Moreover, RW and RGP tests are generally more robust to departures from the assumed model than their normal-theory counterparts. Finally, a real data set taken from psychology literature is used for illustrative purposes.