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Estimating a missing examination score

Authors: Michael Loui and Athena Lin
Journal / Conference: Journal of College Science Teaching
In science and engineering courses, instructors administer multiple examinations as major assessments of students’ learning. When a student is unable to take an exam, the instructor might estimate the missing exam score to calculate the student’s course grade.
Using exam score data from multiple offerings of two large courses at a public university, we compared the accuracy of four methods to estimate an exam score, including linear regression methods. To measure accuracy, we calculated the normalized root mean square error (NRMSE). We found that the NRMSE values for linear models with equal weights were close to the NRMSE values for ordinary least squares (OLS) regression models. For both the OLS and equal weight models, using normalized exam scores generally yielded more accurate estimates than using raw exam scores. The results indicate that instructors should use the equal weight model with normalized scores to estimate a missing exam score.