Evaluating the Performance of Some Statistical Location Difference Tests

Abstract

This article shows the results of a simulation experiment evaluating the comparative effectiveness of the application of classical and new shift tests in the context of errors of the second kind using the example of the normal, lognormal, exponential, gamma and Weibull distributions. The experiment procedure is described in detail, based on the results of 100 simulations for each type of distribution; a "binary tree" algorithm is used to solve the classification problem. The result of its application made it possible to detect "areas of effectiveness" of tests depending on the parameters of the scenario. At the same time, the Wilcoxon test showed the best comparative effectiveness, the second - the modified Yuen-Dixon t-test. It is noted that in many cases, with insignificant values ​of the shift parameter, all tests gave an erroneous conclusion. The conclusion presents further prospects and directions for the development of this topic.