A continuous scoring function for confidence-based marking using multiple choice questions

In most multiple-choice tests using confidence based marking (CBM), a discrete certainty scale is applied, often with three or four probability intervals of equal length. In this paper we derive a continuous certainty scale for CBM which we think circumvents the alleged complexity that would be inherent in a continuous scale. In our approach, the examinee, given a correct answer, is awarded the same number of points as her reported degree of confidence that her chosen alternative is the correct answer, i.e., the examinee's uncertainty is directly reflected in terms of the number of points achieved if the answer is correct. We test our continuous scoring scheme in an examination in basic statistics at our university. The results indicate that most students are quite good at assessing their confidence levels, but students tend on average to overrate their confidence for high levels of stated confidence and underrate their confidence for low levels of stated confidence.