Multiple-choice test items with "none of the above" as an alternative

We analyze idealized multiple-choice tests and examine the effects when some or all of the items are modified so as to include “none of the above” as an answer option. As regards this modification, we study item difficulty, discrimination, and reliability, both for scoring rules that suppress guessing and those that encourage it. We also briefly consider the influence of test-taker misinformation. In agreement with virtually all published empirical findings, we show that the variant formats are more difficult than the content-equivalent regular items, albeit for the variant format where “none of the above” is the correct alternative, a predicted, apparent selection effect mitigates this increase through guessing. As regards item discrimination, it is greater for the regular item format for tests with mixed formats, save for those tests where the regular item format is in minority. This explains the confusion in the empirical literature in this regard.