Measuring Probabilistic Reasoning: The Construction of a New Scale Applying Item Response Theory

Probabilistic reasoning skills are important in various contexts. The aim of the present study was to develop a new instrument (the Probabilistic Reasoning Scale – PRS) to accurately measure low levels of probabilistic reasoning ability in order to identify people with difficulties in this domain. Item response theory was applied to construct the scale, and to investigate differential item functioning (i.e., whether the items were invariant) across genders, educational levels, and languages. Additionally, we tested the validity of the scale by investigating the relationships between the PRS and several other measures. The results revealed that the items had a low level of difficulty. Nonetheless, the discriminative measures showed that the items can discriminate between individuals with different trait levels, and the test information function showed that the scale accurately assesses low levels of probabilistic reasoning ability. Additionally, through investigating differential item functioning, the measurement equivalence of the scale at the item level was confirmed for gender, educational status, and language (i.e., Italian and English). Concerning validity, the results showed the expected correlations with numerical skills, math-related attitudes, statistics achievement, IQ, reasoning skills, and risky choices both in the Italian and British samples. In conclusion, the PRS is an ideal instrument for identifying individuals who struggle with basic probabilistic reasoning, and who could be targeted by specific interventions.