Parametric Test Efficiency One-Way Repeated Measures Analysis of Variance and its Nonparametric Alternative Friedman Test

Abstract

The study aimed to study the efficiency of the one-way repeated measures analysis of variance, and the Friedman test, which is used if the data do not meet the assumptions of the (F) test. the simulation was used to generate random samples that follow the standard normal distribution, the Mediator distribution of skewness and kurtosis, and the highly skewness and kurtosis distribution. For the purpose of comparing the efficiency of the two tests. So that the generated samples consist of 3 treatments for the three different distributions. Three different sizes of the generated samples were used, so that they were 8 for the small sample size, 20 for the medium-sized sample size, and 50 for the large-sized sample size. The effect size and statistical power were relied upon as comparative criteria. The results of the study showed that in the case of the sample following the standard normal distribution, it turned out that the ANOVA test was more powerful and effective than the Friedman test for all sample sizes. In the case of the sample, which follows the Mediator distribution of skewness and kurtosis, it is clear that the effect size values and the statistical power of the Friedman test are higher than those calculated for the analysis of variance test in most cases. Also, in the case of the sample following a highly skewness and kurtuous distribution, it is clear that the Friedman test is more powerful and influential than the analysis of variance test in all cases.