Computational modelling of stochastic processes for learning research

Abstract

The objectives of our work were to use computer-based statistical modelling for comparison and systematisation of various approaches to non-parametric null hypothesis significance testing. Statistical model for simulation of null hypothesis significance testing has been built for educational purpose. Fisher’s angular transformation, Chi-square, Mann-Whitney and Fisher’s exact tests were analysed. Appropriate software has been developed and gave us possibility to suggest new illustrative materials for describing the limitations of analysed tests. Learning researches as the method of understanding inductive statistics have been suggested, taking into account that modern personal computers provide acceptable time of the simulations with high precision. The obtained results showed low power of the most popular non-parametric tests for small samples. Students can’t analyse the test power at traditional null hypothesis significance testing, because the real differences between samples are unknown. Therefore, it is necessary to change the accents in Ukrainian statistical education, including PhD studies, from using null hypothesis significance testing to statistical modelling as a modern and effective method of proving the scientific hypothesises. This conclusions correlate with observed scientific publications and the recommendation of the American Statistical Association.