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Optimum Item Difficulty for a Multiple Choice Test

Sorum, Marilyn
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Difficulty Level, Item Analysis, Multiple Choice Tests, Test Items


A method to compute the optimum item difficulties for a multiple choice test is presented. It is assumed that: (1) the ability being measured is normally distributed; (2) the proportion of examinees at any given ability level who know the answer to an item is pa, which is assumed to be a normal ogive function of ability; (3) the proportion who answer the item correctly, if all examinees attempt it, is pa + 1/k (1-pa), where 1/k involves the probability of guessing the correct answer. The simplest procedure and the one followed in this paper, is to take k equal to the number of choices for the item. when these assumptions are made, and all test items include five choices, the optimum item difficulty to be used when a particular proportion of examinees is to be selected as successful can be determined by the presented procedure. The item-test biserial correlation, corrected for guessing and based on an average group, is involved in the computation. Procedures for computing item difficulties are described for the case when there are groups for whom the test is not of approximately middle difficulty.

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