A closed sequential procedure for comparing the binomial distribution to a standard

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Abstract
Fhanér (1974) proposed an approach to measuring achievement where the binomial error model is assumed, and where the goal is to determine whether an examinee's per cent correct true score is above or below a known constant. Wilcox (19806), as well as van den Brink & Koele (1980), point out that a substantially larger number of items might be required when guessing is incorporated into Fhanér's solution. The purpose of this brief note is to derive the exact sampling distribution of a closed sequential procedure that solves the problem considered by Fhanér. We then show that the probability of a correct decision under the new procedure is exactly the same as it is when Fhanér's procedure is applied. In addition, the number of observations under the closed sequential procedure is always less than or equal to the number required under the fixed sample size approach. In some cases, the number of observations is considerably less.

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