Stochastic process computational modeling for learning research

Abstract

The goal of our research was to compare and systematize several approaches to non-parametric null hypothesis significance testing using computer-based statistical modeling. For teaching purposes, a statistical model for simulation of null hypothesis significance testing was created. The results were analyzed using Fisher's angular transformation, Chi-square, Mann-Whitney, and Fisher's exact tests. Appropriate software was created, allowing us to recommend new illustrative materials for expressing the limitations of the tests that were examined. Learning investigations as a technique of comprehending inductive statistics has been proposed, based on the fact that modern personal computers can run simulations in a reasonable amount of time with great precision. The collected results revealed that the most often used non-parametric tests for small samples have low power. Traditional null hypothesis significance testing does not allow students to analyze test power because the true differences between samples are unknown. As a result, in Ukrainian statistical education, including PhD studies, the emphasis must shift away from null hypothesis significance testing and toward statistical modeling as a modern and practical approach of establishing scientific hypotheses. This finding is supported by scientific papers and the American Statistical Association's recommendation.