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Some Perspectives on "The Attenuation Paradox in Test Theory"

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Attenuation Paradox, Loevinger, Jane, Test Theory, Test Validity, Testing Problems


Four points relating to Dr. Loevinger's "attenuation paradox" are brought forward: The usual product-moment "validity" coefficient is inadequate for any discussion of the paradox. A curvilinear correlation coefficient must be used. The "region of paradox" is still found when the correct coefficient is used, although its size is reduced. A greatly magnified notion of the extent to which the "paradox" occurs in actual achievement and aptitude testing is frequently encountered. Some numerical values are tabled so as to clarify this point. It is pointed out that any over-all "validity" coefficient for a group of examinees can be no more than an average of heterogeneous information. It is not surprising if this inhomogeneity produces so-called paradoxes. Such a composite coefficient is not basic to psychometrics. The discriminating power of the test for a specified decision problem regarding a specified examinee is the truly basic concept. A very simple index for describing this discriminating power is defined. One instance where a consideration of the discriminating power of a test at a particular ability level leads to some practical conclusions (irrespective of the "region of paradox") is mentioned, and a common misconception is corrected. A table is given showing the optimum item-difficulty level for the peaked tests required when the examiner's purpose is merely to classify a group of examinees as successful or unsuccessful.

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