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Toward a Coherent View of Reliability in Test Theory

Li, Heng; Wainer, Howard
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Statistical Analysis, Test Reliability, Variance Component Analysis


Reliability of test scores, as estimated through measures of internal consistency, has been characterized mathematically in many ways that appear, on the surface at least, to be very dissimilar to one another. In this essay we provide a general mathematical framework that specializes to four different reliability coefficients. Through consideration of this general framework it becomes easier to convey to students both the individual character of the different formulations of reliability and the extent of their underlying similarity. In addition to providing a coherent view of reliability, the unified formula is also found to be a convenient vehicle for introducing more specialized topics, such as the Kaiser-Guttman rule.

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