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Journal of Probability and Statistics
Volume 2014 (2014), Article ID 240263, 8 pages
Research Article

New Indices for Refining Multiple Choice Questions

1Department of Mathematics, Institute of Applied Mathematics in Science and Engineering, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
2Department of Medical Sciences, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
3Medical Education Unit, University of Castilla-La Mancha, 13071 Ciudad Real, Spain

Received 8 September 2014; Accepted 7 December 2014; Published 23 December 2014

Academic Editor: Chin-Shang Li

Copyright © 2014 Mariano Amo-Salas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Multiple choice questions (MCQs) are one of the most popular tools to evaluate learning and knowledge in higher education. Nowadays, there are a few indices to measure reliability and validity of these questions, for instance, to check the difficulty of a particular question (item) or the ability to discriminate from less to more knowledge. In this work two new indices have been constructed: (i) the no answer index measures the relationship between the number of errors and the number of no answers; (ii) the homogeneity index measures homogeneity of the wrong responses (distractors). The indices are based on the lack-of-fit statistic, whose distribution is approximated by a chi-square distribution for a large number of errors. An algorithm combining several traditional and new indices has been developed to refine continuously a database of MCQs. The final objective of this work is the classification of MCQs from a large database of items in order to produce an automated-supervised system of generating tests with specific characteristics, such as more or less difficulty or capacity of discriminating knowledge of the topic.