Reconsideration of the "Attenuation Paradox"--and Some New Paradoxes in Test Validity.
A number of mental-test theorists have called attention to the fact that increasing test reliability beyond an optimal point can actually lead to a decrement in the validity of that test with respect to a criterion. This non-monotonic relation between reliability and validity has been referred to by Loevinger as the “attentuation paradox,” because Spearman’s correction for attenuation leads one to expect that increasing reliability will always increase validity. In this paper a mathematical link between test reliability and test validity is derived which takes into account the correlation between error scores on a test and error scores on a criterion measure the test is designed to predict. It is proved that when the correlation between these two sets of error scores is positive, the non-monotonic relation between test reliability and test validity which has been viewed as a paradox occurs universally.