Hypothesis testing for two population means: parametric or non-parametric test?

Tsagris, Michail; Alenazi, Abdulaziz; Verrou, Kleio-Maria; Pandis, Nikolaos (2019). Hypothesis testing for two population means: parametric or non-parametric test? Journal of statistical computation and simulation, 90(2), pp. 252-270. Taylor & Francis 10.1080/00949655.2019.1677659

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The parametric Welch t-test and the non-parametric Wilcoxon–Mann–Whitney, empirical and exponential empirical likelihood tests are commonly used for hypothesis testing of two population means. In order to circumvent the inflated type I error problem of the nonparametric likelihood testing procedures, a simple calibration using the t distribution and bootstrapping is proposed. Those testing procedures are then being compared via extensive Monte Carlo simulations on the grounds of type I error and power. Evidence is provided supporting that (a) the t calibration and bootstrap improve the type I error of the non-parametric likelihoods, (b) the Welch ttest attains the type I error and produces high levels of power, and (c) the Wilcoxon–Mann–Whitney test produces inflated type I error
while computation of the exact p-value is not feasible in the presence of ties. An application to real gene expression data illustrates the computational superiority of the Welch t-test.

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