Investigate into Invariance Properties of Item Response Theory (irt) by Two and Three Parameter Models

Despite the well-known theoretical differences between item response theory (IRT) and classical test theory (CTT), research examining their empirical properties has failed to reveal consistent, demonstrable differences due to usage of samples with errors, incorrect assumptions & incorrect calculations. Dr. Natarajan (India, 1984) had proved the item invariance with his classic 20 X 76 test data and group invariance with 25 X 1000 test data. However, this research will investigate the invariance property of IRT using real live data and also find out how far is this IRT theory an enabler of accurate estimation of parameters over and above the classical test theory (CTT) properties? The objectives of the present research will be: a) to demonstrate through an illustration, the classical test theory (CTT) is a group dependent statistical analysis and bring out its limitations b) to ascertain group invariance of item parameters and item invariance of ability parameters in IRT c) to hypothesize that IRT based item parameter/ability parameters are invariant and more accurate than CTT characteristics. A large scale country wise computer based test (CBT) examinations assessment data is used for this research. The current findings indicate that in CTT, the facility value and index of difficulty are group dependent. Studies are being carried out on invariance property, the core and critical characteristic of IRT for which results are expected in next one year.