An Approximation of the K out N Reliability of a Test, and a Scoring Procedure for Determining which Items an Examinee Knows

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Abstract
Consider any scoring procedure for determining whether an examinee knows the answer to a test item. Let xi = 1 if a correct decision is made about whether the examinee knows the i th item; otherwise xi = 0. The k out of n reliability of a test is ρk = Pr (Σxi ≥k). That is, ρk is the probability of making at least k correct decisions for a typical (randomly sampled) examinee. This paper proposes an approximation of ρk that can be estimated with an answer-until-correct test. The paper also suggests a scoring procedure that might be used when ρk is judged to be too small under a conventional scoring rule where it is decided an examinee knows if and only if the correct response is given.

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