Методика застосування критеріїв Вілкоксона і Манна-Уітні в педагогічному експерименті

Abstract

Сформульовано алгоритм застосування критеріїв Вілкоксона і Манна-Уітні для перевірки гіпотези Н0: F1(x) = F2(x) про однорідність вибірок. Розглянуто приклади застосування критеріїв у педагогічному експерименті. Зокрема, обчислено статистичні значення критерію Вілкоксона і критерію Манна-Уітні, показано їх звʼязок з областю прийняття гіпотези Н0 при різних альтернативних гіпотезах Н1. In [1], we considered the problems of identifying and calculating the criteria for testing the hypothesis of homogeneity of two independent samples. In particular, we drew attention to the ambiguous names of the hypothesis test criterion. We also noted the difference between the assumptions and formulations of the hypothesis. In this case, different formulas for calculations require proof of their equivalence. Our analysis of research and publications has shown that examples of the application of the criteria of homogeneity of Wilcoxon and Mann-Whitney samples are largely technical in nature. That is, these examples usually contain tools for calculating statistics and do not cover all the possibilities of applying the criteria. Therefore, the method of using criteria requires an optimal combination of theoretical principles with the formation of practical skills of hypothesis testing. When conducting a pedagogical experiment, the researcher should be able to consider theoretically sound calculation examples. These examples of the application of criteria should be available primarily to researchers who are not mathematicians. Our experience has confirmed the need for the researcher to acquire stable skills in the practical application of the criteria of sample homogeneity in scientific and pedagogical research. We considered the concept of sample homogeneity in conducting a pedagogical experiment on the examples of statistical information of control and experimental groups. It was noted that the homogeneity of the samples can not always be determined by direct observation of their elements. We formulated an algorithm for applying the Wilcoxon and Mann-Whitney criteria to test the hypothesis Н0: F1(x) = F2(x) about the homogeneity of the samples. We have considered examples of the application of criteria in a pedagogical experiment. In particular, the statistical values of the Wilcoxon test and the Mann-Whitney criteria were calculated. Also, we show their connection with the area of acceptance of hypothesis Н0 under different alternative hypotheses Н1. The prospect of our further research is the formation of methods for applying the criteria most commonly used in scientific and pedagogical research of distributions of random variables.