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Eurasian Society of Educational Research
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Eurasian Society of Educational Research
7321 Parkway Drive South, Hanover, MD 21076, USA
distributions proximity statistics equivalence testing gender disparity student grades

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

Pedro Ferreira , Luísa Canto e Castro , Carina Silva

The focus of this article is to analyze the distribution patterns of student grades over time for different subjects and by gender. Specifically, we e.


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.

Keywords: Distribution’s proximity statistics, equivalence testing, gender disparity, student grades.

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Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B, 57(1), 289–300. https://doi.org/10.1111/j.2517-6161.1995.tb02031.x   

Brookhart, S. M., Guskey, T. R., Bowers, A. J., McMillan, J. H., Smith, J. K., Smith, L. F., Stevens, M. T., & Welsh, M. E. (2016). A century of grading research: Meaning and value in the most common educational measure. Review of Educational Research, 86(4), 803–848. https://doi.org/10.3102/0034654316672069

Cieslak, D. A., Hoens, T. R., Chawla, N. V., & Kegelmeyer, W. P. (2012). Hellinger distance decision trees are robust and skew-insensitive. Data Mining and Knowledge Discovery, 24, 136-158. https://doi.org/10.1007/s10618-011-0222-1

Faraggi, D., & Reiser, B. (2002). Estimation of the area under the ROC curve. Statistics in Medicine, 21(20), 3093–3106. https://doi.org/10.1002/sim.1228

Griffin, R., & Townsley, M. (2021). Points, points, and more points: High school grade inflation and deflation when homework and employability scores are incorporated. Journal of School Administration Research and Development, 6(1), 1-11. https://doi.org/10.32674/jsard.v6i1.3460

Hellinger, E. (1909). Neue begründung der theorie quadratischer formen von unendlichvielen veränderlichen. [New foundation of the theory of quadratic forms of infinitely many variables]. Journal für die Reine und Angewandte Mathematik, 136, 210–271. https://doi.org/10.1515/crll.1909.136.210

Jensen, K., Müller, H.-H., & Schäfer, H. (2000). Regional confidence bands for ROC curves. Statistics in Medicine, 19(4), 493–509. https://doi.org/btw9pf

Lakens, D., Scheel, A. M., & Isager, P. M. (2018). Equivalence testing for psychological research: A tutorial. Advances in Methods and Practices in Psychological Science, 1(2), 259–269. https://doi.org/10.1177/2515245918770963

Lewin, D. R. (2021). What can we learn from exam grade distributions? International Journal for the Scholarship of Teaching and Learning, 15(2), Article 7. https://doi.org/10.20429/ijsotl.2021.150207

Ma, X. (2001). Stability of school academic performance across subject areas. Journal of Educational Measurement, 38(1), 1–18. https://doi.org/10.1111/j.1745-3984.2001.tb01114.x

Meinck, S., & Brese, F. (2019). Trends in gender gaps: Using 20 years of evidence from TIMSS. Large-scale Assessments in Education, 7, Article 8. https://doi.org/10.1186/s40536-019-0076-3 

O’Dea, R. E., Lagisz, M., Jennions, M. D., & Nakagawa, S. (2018). Gender differences in individual variation in academic grades fail to fit expected patterns for STEM. Nature Communications, 9, Article 3777. https://doi.org/10.1038/s41467-018-06292-0

Pastore, M., & Calcagni, A. (2019). Measuring distribution similarities between samples: A distribution-free overlapping index. Frontiers in Psychology, 10, Article 1089. https://doi.org/10.3389/fpsyg.2019.01089 

Prøitz, T. S. (2013). Variations in grading practice – subjects matter. Education Inquiry, 4(3), Article 22629. https://doi.org/10.3402/edui.v4i3.22629

Resh, N. (2009). Justice in grades allocation: Teachers’ perspective. Social Psychology of Education, 12, 315–325. https://doi.org/10.1007/s11218-008-9073-z

Schuirmann, D. J. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. Journal of Pharmacokinetics and Biopharmaceutics, 15, 657–680. https://doi.org/10.1007/BF01068419 

Silva, C., Turkman, M. A. A., & Sousa, L. (2020). Impact of OVL variation on AUC bias estimated by non-parametric methods. In O. Gervasi, B. Murgante, S. Misra, C. Garau, I. Blečić, D. Taniar, B. O. Apduhan, A. M. A. C. Rocha, E. Tarantino, C. M. Torre & Y. Karaca (Eds.), Computational Science and Its Applications–ICCSA 2020 (vol 12251, pp. 173-184). Springer. https://doi.org/10.1007/978-3-030-58808-3_14

Svennberg, L., & Högberg, H. (2018). Who gains? Sociological parameters for obtaining high grades in physical education. Nordic Journal of Studies in Educational Policy, 4(1), 48-60. https://doi.org/10.1080/20020317.2018.1440112

Weitzman, M. S. (1970). Measure of the overlap of income distribution of white and negro families in the United States (Technical paper 22). U.S. Department of Commerce. https://searchworks.stanford.edu/view/7507794

Workman, J., & Heyder, A. (2020). Gender achievement gaps: The role of social costs to trying hard in high school. Social Psychology of Education, 23, 1407–1427. https://doi.org/10.1007/s11218-020-09588-6