Model of the reliability of the test, alternative models inside class correlation

Abstract

The aim was to create a model of the reliability of the test, the application of which would in the practical work with the tests to receive the value of the coefficient of reliability in the theoretical framework from zero to one, as is customary in classical theory of reliability tests. The basic idea of solving this problem was in determining the true variance of the test results, the value of which is equal to the arithmetical average of the results of the repeated measurements. Methodology of the research was based on provisions of the classical theory of sports tests, mathematical theory of reliability of motor tests, on the model of intraclass correlation, ANOVA, using the method of Shapiro-Wilk. Calculations were carried out using Excel and Mathematica computer programs. It was shown that the intraclass correlation model is incomplete with the line of the classical theory of reliability tests. The proposed model of retest reliability does not have this shortage, and the corresponding coefficient is defined in terms of the classical theory of reliability (0 ÷ 1). In the range of almost important quantities of the proposed model and the intraclass model correlations lead to different estimates of the reliability of the test not only quantitatively (≈ 20%), but also qualitatively, i.e., with significant excess width of the ranges of test estimation of reliability coefficient of the corresponding size.