КОМП'ЮТЕРНА МОДЕЛЬ ДОСЛІДЖЕННЯ ІНФОРМАТИВНОСТІ КРИТЕРІЮ СТЬЮДЕНТА

Abstract

The state of technical objects can be checked by comparing the average values ​​of samples of measurements of their parameters. Non-parametric statistics allow you to draw statistical conclusions, in particular, to evaluate distribution characteristics and test statistical hypotheses, without, as a rule, weakly justified assumptions that the distribution function of the sample elements belongs to one or another parametric family. For example, it is widely believed that statistical data often follow a normal distribution. Meanwhile, the analysis of practical results, in particular, measurement errors, always leads to the same conclusion - in the vast majority of cases, real distributions differ significantly from normal ones. In the tasks of non-destructive testing, technical diagnostics and monitoring of the state of objects, non-parametric statistics are the basis for research and decision-making about suitability or quality. Despite the large number of publications dedicated to research on specific issues of the use of non-parametric statistics methods, the internal structure of this scientific direction remains an actual problem even at the present time. Most often, in practice, the problem of belonging of samples to one general population is solved. One of the main verification criteria is the Student criterion. But, in order to use them, it is necessary to check samples for "normality". Uncritical use of the normality hypothesis often leads to significant errors, for example, when rejecting the results of observations (outliers), during statistical quality control, and in other cases. If the samples are short (n⩽20), and the measurements are normal random variables, then classical mathematical statistics suggests solving this problem with a modified Student's test [1]. The power of this criterion is no worse than the classic Student's criterion. This is especially evident with short samples (n≤20). In this article, by conducting computational experiments, the informativeness of the modified and classic Student's criterion was compared. The study was conducted for samples of random variables with three distribution laws - logistic, exponential and Rayleigh. The result showed that the modified Student's test has more power than the classical test. But, as expected, both criteria are sensitive to the symmetry of the distribution law - the greater its asymmetry, the greater the error of accepting the null hypothesis.