Application of parametric criteria for homogeneity of variances under conditions of standard assumption violation

When analyzing measurement series in various applications, it becomes necessary to ensure that the scattering characteristics of the measured quantities have not changed over time, or that the accuracy of measurements carried out by different laboratories in similar tests meets the necessary requirements. For these purposes, it is advisable to use various k-sample parametric criteria for testing hypotheses about the homogeneity of variances (about the equality of variances). The prerequisite for the possibility of using parametric criteria is that the analyzed samples belong to normal distribution laws, which is not always the case. When the assumption of normal distribution of statistics is violated, parametric criteria usually change significantly, which excludes the possibility of using classical results when testing hypotheses. The best parametric tests have a significant advantage in power over nonparametric tests. This advantage is usually retained when the standard assumption of normality is violated. The paper shows how the distributions of parametric test statistics change under conditions of violation of the standard assumption. It is shown that using simulation modeling based on the Monte Carlo method and with appropriate software support, it is possible to find the distributions of the statistics of the applied criteria under non-standard conditions corresponding to specific applications. The use of the results of such modeling makes it possible to make correct statistical conclusions based on the criteria used. The methodology of applying parametric criteria of homogeneity of variances under conditions of violation of the standard assumption is considered. The method involves, at the first stage, testing the hypothesis about the belonging of the analyzed samples to normal laws using a set of special criteria. In case of a negative result, at the second stage a law is selected that describes the combined sample. At the third stage, using the results of the modeling under this law, a conclusion is formed based on the applied criteria. Examples of the implementation of the methodology within the framework of the developed software system are given.