Abstract

This is a quantitative empirical research study validating the invariance of item difficulty parameters estimates based on the two competing measurement frameworks, the classical test theory (CTT) and the item response theory (IRT). In order to achieve the set goal, one fifty five (155) different independent samples were drawn from the population of students (35,262) who sat for the 2004 Paper 1 Botswana Junior Secondary School Certificate in Mathematics. These samples were selected based on gender, gender by educational regions, ability groups, and educational regions). The item difficulty parameter estimates from CTT and IRT were tested for invariance using repeated measure ANOVA at 0.05 significant levels. The study focussed on two research questions which were: (i) which of the two test theories CTT or IRT item difficulty parameter estimates vary across different samples of persons? and (ii) which of the two test theories CTT or IRT item difficulty parameter estimates vary across sample sizes? These research questions were answered through testing of hypothesis derived from each research questions. The research findings were that the item difficulty parameter estimates based on CTT theoretical framework were variant across the different independent samples. The item difficulty parameter estimates based on IRT theoretical framework were invariant across the different independent groups and also the item difficulty parameter estimates for IRT were invariant across groups with varying sample sizes. Overall, the findings from this study discredited the CTT theoretical framework for its inability to produce item difficulty invariant parameter estimates.

 Key words: CTT, IRT Invariance Item and person parameters