A Note on Correcting for Chance Success in Objective Tests

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Abstract
The conventional scoring formula to “correct for guessing” is derived and is compared with a regression method for scoring which has been recently proposed by Hamilton. It is shown that the usual formula, S = R – W/(n−1), yields a close approximation (correct within one point) to the maximum-likelihood estimate of an individual's “true score” on the test, if we assume that the individual “knows” or “does not know” the answer to each item, that guessing at unknown items is random, and that success at guessing is governed by the binomial law. It is also shown that the usual scoring formula yields an unbiased estimate of the individual's “true score,” when the true score is defined as the mean score over an indefinitely large number of independent attempts at the test or at equivalent (parallel) tests.

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