Comparative Analysis of Classical Test Theory and Item Response Theory Based Item Parameter Estimates of Senior School Certificate Mathematics Examination

Abstract

The study compared Classical Test Theory (CTT) and Item Response Theory (IRT)-estimated item difficulty and item discrimination indices in relation to the ability of examinees in Senior School Certificate Examination (SSCE) in Mathematics with a view to providing empirical basis for informed decisions on the appropriateness of statistical and psychometric tests. The study adopted ex-post-facto design. A sample of 6,000 students was selected from the population of 35,262 students who sat for the NECO SSCE Mathematics Paper 1 in 2008 in Osun State, Nigeria. An instrument consisting of 60-multiple-choice items, May/June 2008 NECO SSCE Mathematics Paper 1 was used. Three sampling plans: random, gender and ability sampling plans were employed to study the behaviours of the examinees scores under the CTT and IRT measurement frameworks. BILOG-MG 3 was used to estimate the indices of item parameters and SPSS 20 was used to compare CTT- and IRT-based item parameters. The results showed that CTT-based item difficulty estimates and oneparameter IRT item difficulty estimates were comparable (the correlations were generally in the -0.702 to -0.988 range in large sample and -0.622 to - 0.989 range in small sample). Results also indicated that CTT-based and two-parameter IRT-based item discrimination estimates were comparable (the correlations were in the 0.430 to 0.880 ranges in large sample and 0.531 to 0.950 range in small sample). The study concluded that CTT and IRT were comparable in estimating item characteristics of statistical and psychometric tests and thus could be used as complementary procedures in the development of national examinations