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Optimum Level of Item Difficulty

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Difficulty Level, Test Construction, Test Items


If a test is to be used only to separate examinees into passing and failing groups by means of a single cutting score, it is generally agreed that the best free-response test will consist of items that are of 50-percent difficulty for examinees who are just on the dividing line between passing and failing. This fact is frequently misinterpreted to the effect that in the stated situation the best free-response test for selecting x percent of the applicants is a test composed of items of x percent difficulty (i.e., x percent correct answers). It is demonstrated here that if the first of the foregoing prescriptions is true, the second cannot be true in general. A table is given showing the values of delta that would be obtained if the second prescription were (ill-advisedly) followed. A practical procedure for "peaking" a test where there is not single cutting score is also presented.

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