Parametrik Ve Parametrik Olmayan Madde Tepki Kuramında Farklı Örneklem Büyüklüklerine Ve Boyutluluklarına Göre Parametre Değişmezliğinin İncelenmesi

Abstract

The aim of this study is to determine the invariance of the estimated parameters in regard to Item Response Theory (IRT) applications within different dimensionality and sample characteristics. To realize this aim, students' answers in 'A' test booklet of the first stage of TEOG applied in 2015 were used as the data of the study. The universe size of the study was determined as 63.871. The groups of 50, 100, 200, 500, 1000 and 5000 people who were randomly selected from the universe comprised the sample of the study.. mathematics subtest, which gives the assumptions that are necessary for one-dimensional applications of IRT, was used in one dimensional model analyses. Since all subtests are one-dimensional, a multidimensional construct was formed by the researcher to be used in multidimensional IRT analyses. Thus, for multidimensional IRT analyses, the results of a two-dimensional test, which was artificially formed by combining certain items from Science and Religion Culture and Moral Knowledge tests, were used. Two-parameter logistic model for one-dimensional parametric IRT (PIRT), Monotone Homogeneity Model for one-dimensional non-parametric IRT (NIRT) and multidimensional extension of the two-parameter Logistic Model for multidimensional IRT (MIRT) were used. As a result of the study in which one dimensional test was analyzed in regard to NIRT, it was found that item parameter means did not show significant changes based on the sample size. However, item parameter invariance was found when the sample size was 200 and larger. When it was analyzed in regard to PIRT, it was found that at least a sample size of 1000 have to be used for item parameter estimations nearly as high as the universe value (parameter). It was found that invariance for item parameters was not obtained by analyzing the two-parameter test in regard to parametric and nonparametric IRT and MIRT. Regardless of the correlation type, there was a high correlation between the parametric and nonparametric IRT and the ability parameters obtained from the one-dimensional test. Similar results were obtained when the assumption of unidimensionality was violated. Similarly, the ability parameters of the multidimensional test obtained from PIRT and MIRT were found to be statistically significant and have a correlation level close to perfect regardless of the sample size and correlation type. Finally, the parametric and nonparametric IRT of one-dimensional and multidimensional tests and the reliability coefficients obtained from MIRT were found to be nearly as high as the universe value (parameter).