Effects of Item Parameter Distributions on Test Information Function

Abstract

Test information function (TIF) plays an important role in designing a test. The TIF does not only depend on the logistic model such as the 1PL, 2PL and 3PL logistic models, but it also on the parameter distributions of the model. In this study we conducted simulations using the R statistical software on different examinee sizes and different exam length, and we compare the results when using uniform parameter distribution and normal parameter distribution. The findings of this study illustrate the following: First, when using item parameters that are all uniformly distributed the obtained test information function is significantly small compared to the test information function obtained when we use item parameters that all follow a normal distribution. Second, the test information function increases as the length of the exam increases when we use item parameters that are all normally distributed. Third, this study also suggest great flexibility in writing an exam as we can choose the item parameter distribution depending on the goals of the test.