Investigate into invariance properties of item response theory irt by two and three parameter models in terms of item parameters ability parameter of a group of online test takers and establish such invariance properties of irt as opposed to variance of index of difficulty in classical test theory ctt of the same groups

Abstract

In the theory of measurements, Classical Test Theory (CTT) and Item Response Theory (IRT) are the two widely used competing measurement theories. The present research with usage of real live data had empirically tested the invariance property of IRT and lack of invariance in CTT w.r.t item parameters and person parameters. This research mainly focused on investigating into Invariance Properties of Item Response Theory by two and three parameter logistic models in terms of Item Parameters/Ability Parameter of a Group of Online test takers and establish such Invariance Properties of IRT as opposed to variance of Index of difficulty in classical test theory of the same groups. newlineChapter 3 deals with the Objective 1 of this research To prove that item parameters (Facility value -P and Index of Difficulty-Q) in CTT are group dependent and Person Parameter (Number Right Score) is test dependent newlineChapter 4 covers objective 2 of this research To hypothesize that IRT based item parameters are invariant and more accurate than CTT characteristics (i,e) group invariance of item parameters newlineChapter 5 covers the objective 3 of this research To hypothesize that IRT based ability parameters are invariant no matter which group of items like odd numbered items in a test or even numbered items in a test are used and that ability parameters are more accurate than CTT characteristics newlineThe data used for this research pertains to Sikkim Manipal University semester end computer based examinations in the subject area of Research Methodology held February 2012. The test consisted of 75 multiple choice items out of which 40 were of one mark. The present research used the dichotomously scored response data of these 40 items. The final sample after sanitization and cleaning of data consisted of 6544 student s response data. newlineFor testing the group invariance of item parameters three sampling plans each progressively dissimilar from other were employed (Top Half- Bottom Half, Delhi-Uttar Pradesh and HAG-LAG) and for testing the invariance property of ability parameter, two different test subsets comprising of 19 Odd and 19 even items were used, drawn from the main data after discarding two items which were not fitting in IRT models. XXII newline newlineThe major findings of this research were newline1. The facility value (P) and the index of difficulty (Q) in CTT could not exhibit the invariance property and found to vary across the different sample groups. We can deduce that the item parameters in CTT are group dependent and will depend on the group of examinees who are administered the test (i,e) they are group dependent. newline newline2. The item parameters in IRT exhibited the invariance property across the different sample groups. They were invariant of the group of examinees and not dependent on the group of examinees to whom test was administered. (i,e) they are group invariant(Unique as well). newline newline newline