Effect of 2-PL and 3-PL Models on the Ability Estimate in Mathematics Binary Items

Abstract

The investigation delves into examining the influence of 2-parameter logistic (PL) and 3-parameter logistic models on the ability estimates of students in mathematical binary items. It ascertained the parameters of the items in the 2-PL and 3-PL models. We employed Item Response Theory (IRT) in the design of this research survey, with a sample comprising 1015 senior secondary (SS) students in SS III classes who were analyzed using both models in the investigation. The Mathematics Achievement Test instrument was adapted from the General Mathematics Paper 1 of the Senior School Certificate Examination administered by the West Africa Examinations Council (WAEC). Results indicated that the 2-PL model shows lower difficulty levels but higher discriminatory indices. Statistical analysis revealed a significant (F = 19.52, p < 0.05 and F = 18.52, p < 0.05) effect of both models, respectively, on ability estimates in mathematics binary items among Nigerian secondary school students. We established that item parameters in the 2-PL and 3-PL models significantly affected the ability estimate of Nigeria secondary school students in binary mathematics items, while the 3-PL model provided a better ability estimate than the 2-PL model.