Criteria of test against absence of trend in dispersion characteristics

Distributions of various parametric and nonparametric tests are studied using methods of statistical modeling. Such tests are designed to test hypotheses for randomness or absence of a trend in dispersion characteristics. Respective studies are carried out for different sample sizes with the tested hypothesis being true. Procedure of interactive simulation of distributions of the test statistics is proposed and implemented. Such procedure allows valid usage of corresponding tests in case of violation of standard assumptions. The results of comparative analysis of the power of the tests against competing hypotheses with different models of linear, periodic, and mixed trend in the distribution characteristics are shown. Preferences for using different criteria are given.