STATISTICAL SIMULATIONS METHOD IN APPLIED STATISTICS
Alexander Ivanovich Orlov · Industrial laboratory Diagnostics of materials · 2019
The new paradigm of mathematical research methods is based on the effective application of information and communication technologies both in calculating the characteristics of the methods of data analysis and in simulation modeling. Pseudo-random number generators underlie many modern data analysis technologies. To solve specific applied problems, researchers permanently develop the new methods for processing statistical data, i.e., measurement results (observations, tests, analyzes, experiments) and expert estimations. The properties of each newly proposed method must be studied. The intellectual tools are limit theorems and method of statistical simulations (Monte-Carlo method). In 2016, our journal opened a discussion on the current state and prospects for the development of statistical modeling, i.e., the theory and practice of applicating the method of the statistical simulations (Monte-Carlo method), and various variants of the simulation. The previous discussion about the properties of such generators was conducted in our journal in 1985 - 1993. This article is devoted to application of the statistical simulations method to the study of the properties of statistical criteria for testing the homogeneity of two independent samples. We consider: the Kramer - Welch criterion, which coincides with Student's criterion when sample sizes are equal; the criteria of Lord, Wilcoxon (Mann - Whitney), Wolfowitz, Van der Waerden, Smirnov, со 2 (Lehmann - Rosenblatt). It is necessary to set the distribution functions of the elements of two samples. We use the normal and Weibull - Gnedenko distributions. It is shown advisable to use the Lehmann - Rosenblatt со 2 test when testing the hypothesis of coincidence of the distribution functions of two samples. If there is a reason to assume that the distributions differ mainly in the shift, then the Wilcoxon and Van der Waerden criteria can be used. However, even in this case, the со 2 test may be more powerful. In the general case, apart from the Lehmann - Rosenblatt criterion, the use of the Smirnov criterion is permissible, taking into account the difference between the real level of significance and the nominal one. The frequency of the discrepancies of statistical findings based on different criteria is studied.