Peak Shift Estimation: A Novel Method to Estimate Ranking of Selectively Omitted Examination Data

This paper focuses on examination results when examinees selectively skip examinations to compare the difficulty levels of these examinations, e.g., university entrance examinations, certification examinations, and outcomes of students' job-hunting activities. The resultant data is referred to as “selectively omitted examination data.” For instance, high school students select and apply to universities in consideration of the difficulty levels of the entrance examinations and their academic abilities. Based on their academic abilities, students skip university entrance examinations that are too challenging or too easy. In that case, the results include selectively omitted data. Existing methods, such as IRT and CTT, cannot estimate the difficulty levels of such examinations because of the omitted data. Understanding the difficulty level of these examinations can facilitate the formulation of a new index to assess organizational ability, number of students who pass, and difficulty of the examinations. This index would reflect the outcomes of the organizations' education, corresponding with perspectives on examinations. Therefore, we propose a novel method, Peak Shift Estimation, to estimate an examination's difficulty level based on selectively omitted examination data. We apply Peak Shift Estimation to the simulation data and demonstrate that it estimates the rank order of the difficulty level of examinations.