A quantitative analysis of the uncertainty in grading of written exams in mathematics and physics

Abstract

The most common way to grade students in courses at university and university college level is to use final written exams. The aim of final exams is generally to provide a reliable and a valid measurement of the extent to which a student has achieved the learning outcomes for the course. A source of uncertainty in grading students based on an exam is that such exams only consist of a limited number of exercises. We investigate the extent of this uncertainty by means of a statistical analysis of the results of 23 different examinations taken by 2788 students. The amount of uncertainty is substantial and typically ranges over three grades. Increasing the duration of the examination decreases the uncertainty, however.