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A Simulation-Monte Carlo Study of Item Difficulty Measures Delta and D.6

Tucker, Ledyard R
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Item Analysis, Item Response Theory, Monte Carlo Methods, Psychometrics, Test Reliability


An investigation was conducted by simulation-Monte Carlo techniques of item deltas and a possible new item difficulty measure, D.6, derived from the relation of proportion correct on an item to observed score on a test. Measure D.6 was the standardized test score for which the probability of a correct response was .6, half way between a chance level of .2 and a probability of unity. A major problem involves replacement of a trait score in IRT with the less than perfectly reliable test score. A second problem concerns the unidimensional assumption. Results indicate for item deltas that differing discriminating powers of items should be taken into account in converting deltas from an experimental sample to a reference population. With respect to the D.6 measure, in addition to some computational problems which were encountered effects of control test reliability and homogeneity were observed. (29pp.)

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