Comparison of test equating methods based on item response theory: PISA 2012 science test sample

The objective of this study is to compare test equating methods based on item response theory over real data and to detect the method that gives the least error. For this purpose, two booklets selected from PISA 2012 science literacy test (booklet-1 and booklet-8) were equated using scale linking (mean-mean, mean-sigma, Stocking- Lord, Haebara) and test equating methods (IRT true-score equating, IRT observedscore equating), and error rates obtained from various methods were analysed. The research study group consisted of a total of 701 students including 350 students answering booklet-1 and 351 students answering booklet-8. In the study that was carried out in common-item nonequivalent groups design, there were a total of 33 dichotomous scored items including 17 common items in each booklet. For the data analysis, firstly item response theory assumptions were tested. At the second stage, item and ability parameters were estimated using two-parameter logistic model (2PLM) via BLOG-MG software. In parameter estimation, EAP (Expected A Posteriori) method was used. Then, scale linking process was carried out for four different methods via STUIRT software. In the final stage, scores obtained from two booklets were equated with POLYEQUATE software and WMSE (weighted mean square error) index was calculated for error rates that were obtained from different methods. According to the results obtained from the research, it was observed that the least error rate was obtained with mean-sigma method. This method was followed by mean-mean, Stocking-Lord and Haebara methods respectively. When the results obtained from the test equating methods were analyzed, it was found that, while both methods yielded similar results, IRT observed-score equating method gave less rate compared to IRT true-score equating method. Keywords: Test Equating, Item Response Theory, Equating Methods, Equating Error.