The advantage of having a wide range of assessment and scoring forms based on multiple assessment systems is unanimously recognized. Online systems offer a number of advantages: immediate response, instant storage of results, the ability to easily make comparisons between different groups and different points in time. The use of questionnaires formalizes the response, facilitating the evaluation. Multiple-choice questions significantly reduce the chance of a random answer. However, such an online system can be much more.

A multiple-choice assessment system was created and was used from 2006 to 2024 to evaluate over 3,000 students in topics of chemistry. The system was used in multiple assessments - each student had the opportunity to test themselves several times. When determining the grade, for each set of assessments associated with a student, one assessment was eliminated - the weakest one, in the case of multiple assessments - and the average was calculated with the remaining evaluations. Each test contained 30 multiple-choice questions, and each correct answer was awarded 3 points. In a previous study, attention was paid to the distribution of students by the number of assessments, which, once identified, allows estimating the number of students which dropped out before the evaluation. One of the challenges of the education system is school dropout, and estimating the extent of this phenomenon helps in the development of policies and strategies to reduce it. School dropout is indeed a significant challenge for education systems around the world, and accurate measurement of this phenomenon is crucial for effective intervention. However, measurement itself presents challenges. Different metrics can paint indifferent pictures of the same situation. An accurate example of this is class disparity: dropout rates generally increase in poorly developed areas, even in the case of bright students. Furthermore, accurately tracking students across schools, regions, and years requires sophisticated data systems, which many educational jurisdictions lack. The issue here is addressed from an indirect perspective.

In the present study, the sample of the number of student evaluations was analyzed under 3 distribution hypotheses: the classical Poisson and two of its generalizations: Conway–Maxwell–Poisson and Consul-Jain-Poisson. Minimum points from the Chi-Squared statistic measuring the agreement between observed frequencies of students by the number of assessments and the expected frequencies obtained from the theoretical models as a function of unknown parameters has been obtained. However, the Chi-Squared test has rejected the null hypothesis for all three distributions at a risk of being in error of 5%. The study provided a negative result: all these distributions were rejected. Further investigation is required in order to fit the data to a theoretical model of distribution. When it comes to the educational system, the possibility to accurately estimate the student dropouts serves to plan and deploy countermeasures, and to provide more counseling.

Keywords: Rare event modeling, Discrete count data, Student attrition, Student engagement metrics, Goodness-of-fit testing, Overdispersion analysis.