Abstract
When grade point averages (GPAs) are used for admission into tertiary education, there is an implicit assumption that the GPA of any two students relate to the same level of academic competency. However, this assumption does not hold when students are free to choose electives, and there are differences in their difficulty. Assessing the degree to which difficulty differs is complicated by two factors. Firstly, the sense in which we can compare subjects relies on the degree to which they measure the same construct. Secondly, if students’ choice of elective is related to their academic competency, selection bias could distort difficulty estimates. In this study, we utilized Item Response Theory (IRT) to examine dimensionality and difficulty of 11 electives in Norwegian high school with a sample of 21,832 third year students. Dimensionality was assessed by comparing models with different factor structures, and selection bias was accounted for when estimating difficulty by incorporating student choice via a selection model. Our results found that natural science and math (STEM) subjects measure something distinct from other subjects. Furthermore, we found that ignoring student choice of electives when estimating difficulty introduced considerable bias in difficulty estimation. When correcting for selection bias, the mean grade of STEM and non-STEM electives was 3.25, and 4.38 respectively. Hence, the GPA of Norwegian high school students does not only reflect their academic competencies, but also the decisions they make when choosing elective subjects.