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Educational and Psychological Measurement
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The Standardized Mean Difference within the Framework of Item Response Theory

Wen-Chung Wang

National Chung Cheng University

Hsueh-Chu Chen

Wu Fen Institute of Technology

As item response theory (IRT) becomes popular in educational and psychological testing, there is a need of reporting IRT-based effect size measures. In this study, we show how the standardized mean difference can be generalized into such a measure. A disattenuation procedure based on the IRT test reliability is proposed to correct the attenuation on the sampling variance due to measurement error. Simulations were conducted to investigate whether the direct generalization and the disattenuation procedure were appropriate. The independent variables were (a) item response model, (b) test length, (c) sample size, (d) effect size, and (e) test-person match. The dependent variable was the empirical effect size measure. The results indicated that the direct generalization of the standardized mean difference into the IRT context is applicable and the disattenuation procedure is appropriate. An empirical example about English assents for Taiwan students is given.

Key Words: effect size • classical test theory • item response theory • Rasch model • rating scale model • measurement error • attenuation

Educational and Psychological Measurement, Vol. 64, No. 2, 201-223 (2004)
DOI: 10.1177/0013164403261049
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