Algorithm for automation of the method of testing statistical hypotheses according to the Pearson criterion by the means of MATLAB

Abstract

The purpose of the work is to develop and improve the methods of computer modeling and digitalization of procedures for testing statistical hypotheses according to consent criteria for use in high-tech software and measuring complexes of automated control systems. In most cases that are important for practice, the analysis of the statistical properties of distributions requires multiple checks performed using numerical methods, which require the tools of powerful software and computing environments. Examples of such cases are the procedures for finding information subsets of features in regression and statistical analysis, as well as identifying parameter deviations in automated control systems. It is noted that the tasks of processing experimental data do not always fit into the framework of the theory of normal processes and have exclusively such hypotheses. To test such hypotheses, modern mathematical statistics has developed criteria based on specially developed probabilistic rules that distinguish between zero and alternative hypotheses. Moreover, if for the testable (zero) hypothesis the distribution of statistics is known exactly or approximately, then for the alternative it has a greater degree of uncertainty and it (the alternative) itself is not a complete negation of the null hypothesis. As the zero and alternative hypotheses move away from each other, the statistics of the consent criterion begins to take a larger absolute value than with the null hypothesis, which allows us to build a critical area on the basis of estimating the set of this statistics values. However, the use of analytical methods for statistical analysis to determine the discrepancy between empirical and hypothetical statistics in practice is associated with the use, as a rule, of complex computational calculation algorithms and the implementation of high requirements for the assessment accuracy, which they cannot provide. To solve this problem, it is proposed to use numerical methods of computer modeling and integration of probability density of distribution according to the Simpson algorithm using the tools of built-in functions of the Statistics Toolbox of the MATLAB environment. The proposed method for automation of statistical analysis of zero and alternative hypotheses is implemented on the example of applying the Pearson criterion to verify compliance with the normal distribution of two random data samples, one of which meets the normal distribution law. The obtained graphic and numerical results of computer modeling confirm the correspondence of one of the testable distributions to a given normal distribution according to the null hypothesis.