Test-Retest Reliability of a Formula-Scored Multiple-Choice Test
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In an ideal multiple-choice test, defined as a multiple-choice test containing only items with options that are all equally guessworthy, the probability of guessing the correct answer to an item is equal to the reciprocal of the number of the item's options. This article presents an asymptotically exact estimator of the test-retest reliability of an ideal multiple-choice test. When all test items have the same number of options, computation of the estimator requires, in addition to the number of options per item, the same information as computation of the Kuder-Richardson Formula 21: the total number of items answered correctly on a single testing occasion by each person tested. Both for ideal multiple-choice tests and for nonideal multiple-choice tests for which the average probability of guessing the correct answer to an item is equal to the reciprocal of the number of options per item, Monte Carlo data show that the estimator is considerably more accurate than the Kuder-Richardson Formula 21 and, in fact, is very nearly exact in populations of the order of 1000 persons.
The article of record as published may be found at http://dx.doi.org/10.2466/pr0.19220.127.116.119
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