In this paper, we focus on examination results when examinees selectively skip examinations, to compare the difficulty levels of these examinations. We call the resultant data 'selectively omitted examination data' Examples of this type of examination are university entrance examinations, certification examinations, and the outcome of students' job-hunting activities. We can learn the number of students accepted for each examination and organization but not the examinees' identity. No research has focused on this type of data. When we know the difficulty level of these examinations, we can obtain a new index to assess organization ability, how many students pass, and the difficulty of the examinations. This index would reflect the outcomes of their education corresponding to perspectives on examinations. Therefore, we propose a novel method, Peak Shift Estimation, to estimate the difficulty level of an examination based on selectively omitted examination data. First, we apply Peak Shift Estimation to the simulation data and demonstrate that Peak Shift Estimation estimates the rank order of the difficulty level of university entrance examinations very robustly. Peak Shift Estimation is also suitable for estimating a multi-level scale for universities, that is, A, B, C, and D rank university entrance examinations. We apply Peak Shift Estimation to real data of the Tokyo metropolitan area and demonstrate that the rank correlation coefficient between difficulty level ranking and true ranking is 0.844 and that the difference between 80 percent of universities is within 25 ranks. The accuracy of Peak Shift Estimation is thus low and must be improved; however, this is the first study to focus on ranking selectively omitted examination data, and therefore, one of our contributions is to shed light on this method.

翻译：在本文中,我们在有选择地跳过考试时注重考试结果,以比较考试的困难程度。我们称由此得出的数据为“选择性省略考试数据 ” 。这类考试的例子包括大学入学考试、认证考试和学生求职活动的结果。我们可以了解每次考试和组织接受的学生人数,但不包括考试者的身份。没有研究侧重于这类数据。当我们了解这些考试的困难程度时,我们可以获得新的指数来评估组织能力、学生通过人数和考试的困难程度。这个指数将反映他们与考试观点相对应的教育结果。因此,我们建议一种新颖的方法,即峰值变动估计考试的难度程度,以有选择地省略漏考试数据为基础。首先,我们对模拟数据采用峰值变动估计,但表明峰值变动估计率估计是大学入学考试难度的级别。因此,峰值调整率和大学排名排名的比值也适合估算大学的多级比例,也就是说,A、B、C和D级的比值是真实的比值等级。