Assessing multiple choice question (MCQ) tests - a mathematical perspective

Abstract

The reasoning behind popular methods for analysing the raw data generated by multiple choice question (MCQ) tests is not always appreciated, occasionally with disastrous results.This article discusses and analyses three options for processing the raw data produced by MCQ tests. The article shows that one extreme option is not to penalize a student for wrong answers or for missing out questions, and the other extreme option is actually to penalize both aspects.The intermediate option of focusing on the number of questions actually attempted while penalizing wrong answers can be regarded as the fairest. In this case blind guessing will on average not help the student, although partial knowledge will lessen the negative impact on the final overall score. There are still many interesting challenges in designing techniques for MCQ tests.