A comparative study on the methods of making a raw to theta score conversion table using item response theory

The main purpose of this study is to compare and evaluate the performance of alternative methods to convert from raw total scores to theta scores. There are various practical needs for which providing a raw-to-theta conversion table is requested. This paper, first, introduced various specific situations that required preparing such conversion table. Then, along with the test characteristic curve method which is commonly used for making the conversion table, two alternative methods based on expected a posteriori were explained. A real data analysis and a simulation study were conducted to systematically compare their performances. The main factors considered in the simulation study were the levels of test difficulty and the 1 parameter-, 2 parameter-, and 3 parameter- logistic models. The study results have shown that the use of expected a posteriori method by summed score could provide the most accurate raw-to-theta conversions. Besides, more accurate conversions could be obtained when the level of test difficulty coincided with the examinees average ability. Also, when there was no problem in model fitting, 2 parameter model could lead to the best conversion results.