What question did this study set out to answer?

To propose robust tests for equality of two means in short-tailed symmetric distributions and compare their performance with existing methods.

May 15, 2026Open Access

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

Key Points

To propose robust tests for equality of two means in short-tailed symmetric distributions and compare their performance with existing methods.
Developed robust Welch and generalized p-value tests based on modified maximum likelihood estimators.
Conducted a Monte Carlo simulation study comparing Type I error rates and powers of the proposed and existing tests using R software.
Illustrated the application of the robust tests on real data from psychology literature.
Proposed tests showed equal or better performance than traditional Welch and generalized p-value tests regarding Type I error rates.
RW and RGP tests demonstrated greater robustness to deviations from model assumptions compared to normal-theory tests.
Simulation results confirmed satisfactory control of Type I error rates for the robust tests.

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.

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