Abstract:

In this study, the objective was to compare different scale linking methods over the PISA 2012 mathematics literacy data. For this purpose, scores obtained from two selected booklets were equated using scale linking (mean-mean, mean-sigma, Stocking-Lord, Haebara) and test equating methods (IRT true-score equating, IRT observed-score equating) based on the item response theory, and results obtained from different methods were analyzed. The study was conducted using answers given to mathematics tests in booklet-4 and booklet-11. Therefore, the sample consists of 716 students in Turkey; 348 of these participants are the takers of booklet-4, 368 of them are the takers of booklet-11. In order to equate test forms “the common-item nonequivalent groups” design was used in this research. In the first stage of data analysis, unidimensionality assumption of the item response theory was analysed. Then PARSCALE 4.1 was used to estimate item and ability parameters. Generalized partial credit and two-parameter logistic model were used to estimate parameters. Afterwards STUIRT program was used for scale linking for four different methods. In the last step test scores obtained from different forms were equated by using POLYEQUATE program. Equating error obtained from different methods calculated with weighted mean squares error (WMSE) index. Results showed that Stocking-Lord method had the smallest equating error in true-score equating and Haebara method had the smallest equating error in observed-score equating. The amount of maximum error has been established that of the mean-sigma method.

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