Development of an Informal Test for the Fit of a Probability Distribution Model for Teaching

Abstract

Informally testing the fit of a probability distribution model is educationally a desirable precursor to formal methods for senior secondary school students. Limited research on how to teach such an informal approach, lack of statistically sound criteria to enable drawing of conclusions, as well as New Zealand assessment requirements led to this study. Focusing on the Poisson distribution, the criteria used by ten Grade 12 teachers for informally testing the fit of a probability distribution model was investigated using an online task-based interview procedure. It was found that criteria currently used by the teachers were unreliable as they could not correctly assess model fit, in particular, sample size was not taken into account. The teachers then used an interactive goodness of fit simulation-based visual inference tool (GFVIT) developed by the first author to determine if the teachers developed any new understandings about goodness of fit. After using GFVIT teachers reported a deeper understanding of model fit and that the tool had allowed them to take into account sample size when testing the fit of the probability distribution model through the visualization of expected distributional shape variation. Hence, a new informal test for the fit of a probability distribution is proposed.