Measuring the basics of probabilistic reasoning: the irt-based construction of the probabilistic reasoning questionnaire

Some of the difficulties students have in learning basic data analysis stem from a lack of basic understanding of probabilities. The aim of the present study was to develop a scale to measure basic probabilistic reasoning skills, which are deemed necessary to successfully complete introductory statistics courses. Specifically, our aim was to accurately measure low levels of ability in order to identify students with difficulties in this domain. Item Response Theory was applied to construct a scale. The validity of the scale was studied with reference to math skills and self-efficacy, attitude towards statistics, and numeracy. Finally, the equivalence of the scale across genders was assessed by analyzing Differential Item Functioning. The scale has advantages in introductory statistics teaching. Indeed, once students who are more likely to encounter difficulties are identified, ad-hoc training courses can be developed, focusing on probability knowledge that is required at the exam, in order to improve students' performance.