Estimating Item Parameters and Student Abilities: An IRT 2PL Analysis of Mathematics Examination

Abstract

This research aims to describe the characteristics of math test instruments are tested on 373 of 10th-grade vocational high school students and to describe student abilities. The analysis was conducted using the Item Response Theory (IRT) approach with the 2 Parameter Logistic (2PL) model. The whole analysis process was conducted with the help of the R Program, SPSS and Excel. This finding shows that 2 items did not fit the 2 PL model. Of the 28 items that fit the 2PL model, 3 do not have a good discriminating index because they have negative values. Of 30 items that were tested, 3 items were very easy, 21 items were moderate, one item was difficult, and five items were very difficult. Student abilities ranged between -4.69 logit and 4.09 logit with an average of 0.05 logit. Based on the category, the proportion of students with moderate ability reached 63.54%, high ability 15.28%, very high ability 1.34%, while students with low ability were 19.57%, and very low ability was only 0.27%. The maximum information function of this test was 29,37 (has good category) on the ability (θ) of -0,8 logit and SEM of 0.18 logit. Overall, the test was suitable for students with abilities between -2,6 and 2,4 logit. Based on these results, 25 items can be included in the question bank with suggestions for improvement in the proportion of difficulty level to reach a normal curve balance.

Keywords

• item response theory, mathematics examination, two parameter logistic