Robust nonparametric tests for the two-sample location problem

Abstract

We construct and investigate robust nonparametric tests for the twosample location problem. A test based on a suitable scaling of the median of the set of differences between the two samples, which is the Hodges-Lehmann shift estimator corresponding to the Wilcoxon two-sample rank test, leads to higher robustness against outliers than the Wilcoxon test itself, while preserving its efficiency under a broad range of distributions. The good performance of the constructed test is investigated under different distributions and outlier configurations and compared to alternatives like the two-sample t-, the Wilcoxon and the median test, as well as to tests based on the difference of the sample medians or the one-sample HodgesLehmann estimators.

Control charts for the mean based on robust two-sample tests

“…However, the t-test is not robust against outliers since a few can cause a substantial loss in power or an exceedance of the significance level [17]. It is possible to construct robust tests by replacing the sample means and the pooled standard deviation by robust alternatives [14]. An obvious choice to estimate the location difference robustly is the difference of the sample medians,…”

“…In [14] two scale estimators, which estimate the variability within the subwindows, are suggested. The estimator…”

“…For the MD-and the HL-tests the distribution under the null hypothesis is unknown in finite samples. In [14] it is proposed to use the permutation principle to construct distribution-free tests. In that case, all B = n k splits of the complete window in two subwindows can be determined.…”

“…We examine control charts based on the two-sample t-test, the Wilcoxon rank-sum test and the median test. Furthermore, we consider tests based on the difference of the sample medians and the one-sample HodgesLehmann estimators as well as the two-sample Hodges-Lehmann estimator [13,14]. They serve as robust alternatives to the t-test.…”

“…They serve as robust alternatives to the t-test. In [14], only classical test properties, i.e. the size and power of the aforementioned tests, are investigated in different scenarios.…”