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In this paper, we focus on examination results when examinees selectivelyskip examinations, to compare the difficulty levels of these examinations. Wecall the resultant data 'selectively omitted examination data' Examples of thistype of examination are university entrance examinations, certificationexaminations, and the outcome of students' job-hunting activities. We can learnthe number of students accepted for each examination and organization but notthe examinees' identity. No research has focused on this type of data. When weknow the difficulty level of these examinations, we can obtain a new index toassess organization ability, how many students pass, and the difficulty of theexaminations. This index would reflect the outcomes of their educationcorresponding to perspectives on examinations. Therefore, we propose a novelmethod, Peak Shift Estimation, to estimate the difficulty level of anexamination based on selectively omitted examination data. First, we apply PeakShift Estimation to the simulation data and demonstrate that Peak ShiftEstimation estimates the rank order of the difficulty level of universityentrance examinations very robustly. Peak Shift Estimation is also suitable forestimating a multi-level scale for universities, that is, A, B, C, and D rankuniversity entrance examinations. We apply Peak Shift Estimation to real dataof the Tokyo metropolitan area and demonstrate that the rank correlationcoefficient between difficulty level ranking and true ranking is 0.844 and thatthe difference between 80 percent of universities is within 25 ranks. Theaccuracy of Peak Shift Estimation is thus low and must be improved; however,this is the first study to focus on ranking selectively omitted examinationdata, and therefore, one of our contributions is to shed light on this method.

PEAK SHIFT ESTIMATION A novel method to estimate ranking of selectively omitted examination data