Part II: On the Use, the Misuse, and the Very Limited Usefulness of Cronbach’s Alpha: Discussing Lower Bounds and Correlated Errors

Prior to discussing and challenging two criticisms on coefficient $$\alpha $$ α , the well-known lower bound to test-score reliability, we discuss classical test theory and the theory of coefficient $$\alpha $$ α . The first criticism expressed in the psychometrics literature is that coefficient $$\alpha $$ α is only useful when the model of essential $$\tau $$ τ -equivalence is consistent with the item-score data. Because this model is highly restrictive, coefficient $$\alpha $$ α 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 $$\alpha $$ α incorrectly ignores correlated errors. If correlated errors would enter the computation of coefficient $$\alpha $$ α , theoretical values of coefficient $$\alpha $$ α could be greater than the test-score reliability. Because quality measures that are systematically too high are undesirable, critics dismiss coefficient $$\alpha $$ α . We argue that introducing correlated errors is inconsistent with the derivation of the lower bound theorem and that the properties of coefficient $$\alpha $$ α remain intact when data contain correlated errors.