The effect of the number of distractors and the "None of the above" - "All of the above" options in multiple choice questions

Multiple choice questions (MCQs) are commonly used for assessment in higher education. With increased use of on-line examination it is likely that the usage of MCQs will be even more in years to come. It is therefore of interest to examine some characteristics of these type of questions such as the effect of the number of distractors used and the "None of the above" (NOTA) or "All of the above" (AOTA) options. The tutor-web is an open-source, on-line drilling system that is freely available to anyone having access to the Internet. The system was designed to be used for teaching mathematics and statistics but can in principle be used for other subjects as well. The system offers thousands of multiple choice questions at high school and university level. In addition to be a tool used by students for learning it has also been used as a testbed for research on web-assisted education. The tutor-web system was used both as a learning tool and as a testing tool in a university course on mathematical statistics in the spring of 2020. Around 300 students were enrolled in the course providing tens of thousands of answers to MCQs designed to investigate the effect of the number of distractors and the use of NOTA and AOTA options in questions. The main findings of the study were that the probability of answering a question correctly was highest when a AOTA option was used as a distractor and when NOTA and AOTA were not used in questions. The probability of answering a question correctly decreased with the number of distractors.