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Penalties in multiple-choice and true-false questions
Abstract
In multiple-choice and true-false (T-F) questions a student expresses his ignorance by leaving questions unanswered, guessing randomly, answering according to some predetermined formula or, in T-F tests, by marking all those which are unknown as 'true' or all as 'false'. Each of these no-knowledge strategies should, on average, yield the same score. It is shown that partial knowledge is awarded partmarks in multiple-choice. question and T-F tests, since the chance of guessing correctly is greater when students possess some knowledge than when they guess randomly. There is a constant relationship between the score obtained by the informed guesser and the minimum, maximum and randomguessing scores, this relationship being independent of the scoring system. Modifications of the scoring system (i.e. of the magnitude of the penalty for incorrect responses) affect only the reward for unanswered questions: in the absence of a penalty the reward for unanswered questions equals the minimum score - a score. which is unattainable by random guessing; with a large penalty the reward for unanswered questions approaches the maximum score obtainable.
