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The aim of this study is to analyze 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 test booklet 'A' of the first stage of TEOG, Secondary Education Placement Test applied by the Ministry of Education in Turkey, in 2015 were used as the data. The population 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 population comprised the sample of the study. One-dimensional mathematics subtest and artificially formed two-dimensional test results were used within IRT applications. As a result of the findings obtained from the study within the analysis of the one-dimensional test in regard to one-dimensional nonparametric IRT (ODNPIRT), item parameter invariance was obtained from the sample size 200. When it was analyzed in regard to one-dimensional parametric IRT (ODPIRT), it was found that at least a sample size of 1000 has to be used for item parameter estimations nearly as high as the population value (parameter). It was found that invariance for item parameters was not obtained by analyzing the two-parameter test in regard to ODPIRT, ODNPIRT and Multidimensional IRT (MDIRT).

An Analysis of Parameter Invariance according to Different Sample Sizes and Dimensions in Parametric and Nonparametric Item Response Theory