Modified Wilcoxon-Mann-Whitney Test and Power against Strong Null.

Area of Science:

• Statistics
• Statistical hypothesis testing

Background:

• The Wilcoxon-Mann-Whitney (WMW) test is a widely used rank-based procedure for testing the strong null hypothesis that two independent samples originate from the same distribution.
• The Fligner-Policello (FP) test, a modification of the WMW test, is primarily known for comparing population medians but can also test the strong null hypothesis.

Purpose of the Study:

• To compare the statistical power of the WMW and FP tests when applied to the strong null hypothesis.
• To introduce and evaluate a new modified WMW test that integrates aspects of both the WMW and FP tests.

Main Methods:

• Comparative analysis of the power of the WMW and FP tests under the strong null hypothesis.
• Development and Monte Carlo simulation of a novel combined WMW-FP test.

Main Results:

• Neither the WMW nor the FP test demonstrates uniformly superior power; significant power differences exist between the two tests.
• The proposed combined WMW-FP test exhibits good power performance, outperforming both the individual WMW and FP tests in simulations.

Conclusions:

• The choice between WMW and FP tests for the strong null hypothesis depends on specific data characteristics, as neither is universally more powerful.
• The newly developed combined WMW-FP test offers a robust and powerful alternative for testing the strong null hypothesis, with an efficient open-source implementation available.