A subset selection technique for scoring items on a multiple choice test

On a multiple-choice test in which each item hask alternative responses, the test taker is permitted to choose any subset which he believes contains the one correct answer. A scoring system is devised that depends on the size of the subset and on whether or not the correct answer is eliminated. The mean and variance of the score per item are obtained. Methods are derived for determining the total number of items that should be included on the test so that the average score on all items can be regarded as a good measure of the subject's knowledge. Efficiency comparisons between conventional and the subset selection scoring procedures are made. The analogous problem ofr > 1 correct answers for each item (withr fixed and known) is also considered.The authors are grateful to M. Aitkin, C. Coombs, F. Lord, and the reviewers for their comments and suggestions.