Robustness and power of the parametric t test and the nonparametric Wilcoxon test under non-independence of observations

A large part of previous work dealt with the robustness of parametric significance tests against non-normality, heteroscedasticity, or a combination of both. The behavior of tests under violations of the independence assumption received comparatively less attention. Therefore, in applications, researches may overlook that robustness and power properties of tests can vary with the sign and the magnitude of the correlation between samples. The common paired t test is known to be less powerful in cases of negative between-group correlations. In this case, Bortz and Schuster (2010) recommend the application of the nonparametric Wilcoxon test. Using Monte-Carlo simulations, we analyzed the behavior of the t- and the Wilcoxon tests for the one- and two-sample problem under various degrees of positive and negative correlations, population distributions, sample sizes, and true differences in location. It is shown that already minimal departures from independence heavily affect Type I error rates of the two-sample tests. In addition, results for the one-sample tests clearly suggest that the sign of the underlying correlation cannot be used as a basis to decide whether to use the t test or the Wilcoxon test. Both tests show a dramatic power loss when samples are negatively correlated. Finally, in these cases, the well-known power advantage of the Wilcoxon test diminishes when distributions are skewed and samples are small.