A study on determining differential item function in different scale types and comparison of methods

The first measurement in history was made based on the lengths of human limbs such as span, fathom, step. This need for measurement has brought to the agenda the measurement of concepts such as intelligence, success, behavior, learning that cannot be directly observed as civilizations develop. The question of how accurately the various measurement tools developed to measure implicit properties are the primary question that needs to be answered for all scales. It is unacceptable for the developed scales to provide advantage or disadvantage to the people who take the scale due to their specific characteristics. In this thesis presented, firstly, Introduction to Statistics Literacy Test was developed to measure learning latent feature. The applicability of the developed test has been demonstrated. In addition, in this thesis, the data of 2019 Karadeniz Technical University Foreign Student Exam (KTUYOS-2019) were used. For both scales, the assumptions of the Item Response Theory were provided and the most suitable model in the theory was determined. Item and person parameters were estimated for both available scales. Then, a Differential Item Function analysis to find out whether there are items that may cause bias in the scale, if any, which items are; Breslow-Day was investigated for gender, school and sociocultural status with Logistic Regression, Lord's Statistics of χ^2, Likelihood Ratio and Raju's Field Measurements. With the help of these analyzes, both the items containing the current Differential Item Function were determined and the methods were compared. It has been observed that even in cases where sufficient sample size and appropriate test length are provided, methods based on Classical Test Theory give distant and inconsistent results. In addition, it was concluded that the Likelihood Ratio, which is one of the methods based on the Item Response Theory, coincides exactly when the necessary conditions are met.