Assessing the comparability between classical test theory (CTT) and item response theory (IRT) models in estimating test item parameters

This study assessed the comparability of test items parameter estimates between Classical test theory (CTT) and Item response theory (IRT) models using 2010 Botswana Junior Certificate (JC) mathematics paper 1 test items. A simple random sample of ten thousand (10,000) students was selected from the population of thirty six thousand, nine hundred and forty (36,940) students who sat for the JC mathematics examination paper 1 in 2010,using SPSS computer software. To estimate for the test items parameters in terms of item difficulty, item discrimination and the students’ responses to the test items were analysed using both the CTT and IRT (3PLM) models. Pearson correlation coefficients were used to determine if the IRT and CTT test items parameter estimates were comparable and dependent t-test was used to find out whether the relationship between IRT and CTT test items parameter estimates were statistically significant. From the result of the analysis, it was found that the CTT and IRT item difficulty and item discrimination values were positively linearly correlated and there was no statistical significant difference between the item difficulty and item discrimination parameter estimates by CTT and IRT.

Keywords: IRT (Item response theory), CTT (Classical test theory), Item difficulty, Item discrimination.