Statistical methods for detecting anomalies in examination results at the institutional level

Shlipakov E.V., Uteshev I.A., Arkushin M.M., Gryanchenko V.A., Shcherbakov D.E., Yashchenko I.V.
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This study proposes a methodology for anomaly detection in educational assessment data, demonstrated on the case of the 2023–2024 Basic State Exam (BSE) in mathematics in Russia. The relevance of the study is related to the absence of mandatory video surveillance during the examination period, which creates a risk of potential rule violations both by individual students and by entire educational institutions. By analyzing the distribution of primary scores, we identify a big spike in the area between grades 2 and 3 as a specific pattern in results that may indicate cases of cheating during the exam. To determine the most suspicious results, two anomaly criteria were constructed. The first criterion relies on comparing the magnitude of the spike in empirical distribution function in school’s results with the corresponding regional average level. This criterion made it possible to identify 47 educational institutions with abnormally high values of the spike. The second (general) criterion was derived from comparing students’ scores on the examination with their performance on a diagnostic mathematics test conducted in grade 8 under video surveillance. This comparison is appropriate because almost the same group of students took part in both assessments. This approach helps reduce the number of detected anomalies by distinguishing those more likely to reflect actual protocol violations from those arising due to the specific characteristics of a particular student population and their exam preparation within a given educational institution. The application of the oneclass support vector machine method enabled the identification of 12 schools with atypical anomalous results. The proposed methodology could be useful for the detection of potential cases of cheating during exams and the development of methods for preventing such behavior. In particular, it can be used to support targeted preventive work with specific schools in order to reduce the risk of exam rule violations.

Keywords: anomaly detection, statistical analysis, empirical distribution function, one-class support vector machine, Basic State Examination, detection of cheating
Citation in English: Shlipakov E.V., Uteshev I.A., Arkushin M.M., Gryanchenko V.A., Shcherbakov D.E., Yashchenko I.V. Statistical methods for detecting anomalies in examination results at the institutional level // Computer Research and Modeling, 2026, vol. 18, no. 2, pp. 537-552
Citation in English: Shlipakov E.V., Uteshev I.A., Arkushin M.M., Gryanchenko V.A., Shcherbakov D.E., Yashchenko I.V. Statistical methods for detecting anomalies in examination results at the institutional level // Computer Research and Modeling, 2026, vol. 18, no. 2, pp. 537-552
DOI: 10.20537/2076-7633-2026-18-2-537-552
URL: http://crm-en.ics.org.ru/journal/article/3722/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2026 Shlipakov E.V., Uteshev I.A., Arkushin M.M., Gryanchenko V.A., Shcherbakov D.E., Yashchenko I.V.

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