This study aimed to compare the item and ability parameters estimated from two different approaches of Item Response Theory, which are parametric and non-parametric, according to the factors of test length, sample size and the item psychometric qualities. The study was prepared in a basic research method and the data of the study is obtained from the Trends of International Mathematics and Science (TIMSS) 2011 application. From the main data set, 16 different data sets were formed according to the research questions and the conditions of the factors. The results showed that all of the item parameters estimated according to the parametric and non-parametric models from the data sets which are composed of different number of items and sample sizes were correlated significantly and highly. Among of the abilities estimated by non-parametric models in all sample size and test length factors, it was concluded that ability parameters are significantly and highly correlated. To sum up, it was found that both approaches had resulted in so highly and significantly correlated item and ability parameters. This finding showed that if the assumptions of parametric item response theory models are not met as a required level, the non-parametric alternative models can be used in the conditions that studied in this research.
Key words: Parametric item response theory, non-parametric item response theory, Mokken scaling, sample size, test length
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