Similarities and Dissimilarities in Student Grades Distributions, Over Time and by Gender

The focus of this article is to analyze the distribution patterns of student grades over time for different subjects and by gender. Specifically, we examined the final term grades of upper secondary students in Portuguese public schools across four subjects (Mathematics, Portuguese Language, Philosophy, and Physical Education) from the academic years 2013-2014 to 2017-2018. These grades reflect the teachers' perceptions of the students' knowledge gained throughout the academic year. We expected to see some regularity in the grade distributions over time for a particular subject. However, we found that the similarity of grades across subjects and time was so striking that differences were barely noticeable by visual inspection. Due to the very large sample sizes (in the order of tens of thousands), the quantification of similarities and dissimilarities was done through distribution’s proximity statistics and not by classic statistical methods, like Chi-Square or comparison of means tests. Additionally, we applied a methodology of multiple equivalence tests to globally compare the relative frequencies of each of the grades in pairs of independent samples. Our analysis showed that there was a high level of similarity in grades for the same subject over time, but we also found differences between subjects and between genders.