Abstract
Prior to discussing and challenging two criticisms on coefficient alpha , the well-known lower bound to test-score reliability, we discuss classical test theory and the theory of coefficient alpha . The first criticism expressed in the psychometrics literature is that coefficient alpha is only useful when the model of essential tau -equivalence is consistent with the item-score data. Because this model is highly restrictive, coefficient alpha is smaller than test-score reliability and one should not use it. We argue that lower bounds are useful when they assess product quality features, such as a test-score’s reliability. The second criticism expressed is that coefficient alpha incorrectly ignores correlated errors. If correlated errors would enter the computation of coefficient alpha , theoretical values of coefficient alpha could be greater than the test-score reliability. Because quality measures that are systematically too high are undesirable, critics dismiss coefficient alpha . We argue that introducing correlated errors is inconsistent with the derivation of the lower bound theorem and that the properties of coefficient alpha remain intact when data contain correlated errors.
Highlights
Prior to discussing and challenging two criticisms on coefficient α, the well-known lower bound to test-score reliability, we discuss classical test theory and the theory of coefficient α
First we discuss the basics of classical test theory (CTT), including relevant definitions and assumptions, reliability, coefficient α, and the theorem that states that alpha is a lower bound to the reliability
We critically discuss the claims regularly found in the literature that coefficient α is only useful if the items in the test satisfy essential τ -equivalence and that theoretically, coefficient α can be greater than the reliability
Summary
Until the 1950s, the dominant method for determining test-score reliability was the splithalf method. Given two test halves, several correction methods were available for determining the whole test’s reliability, but agreement about which method was optimal was absent Amidst this insecurity, Cronbach (1951) argued persuasively that an already existing method (e.g., Guttman, 1945; Hoyt, 1941; Kuder & Richardson, 1937) he renamed coefficient α could replace the split-half method and solve both problems of the split-half method in one stroke. Without reiterating his arguments, Cronbach’s suggestion that coefficient α solves all problems is a perfect example of a message that arrives at the right time when people are most perceptive (but see Cortina 1993; Green, Lissitz, & Mulaik, 1977; Schmitt, 1996, for early critical accounts). Coefficient α became one of the centerpieces of psychological reporting, and until the present day tens of thousands of articles in psychological science and other research areas report coefficient α for the scales they use
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