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 α 12ptminimalamsmathwasysymamsfontsamssymbamsbsymathrsfsupgreek-69ptdocument document, the well-known lower bound to test-score reliability, we discuss classical test theory and the theory of coefficient α 12ptminimalamsmathwasysymamsfontsamssymbamsbsymathrsfsupgreek-69ptdocument document. The first criticism expressed in the psychometrics literature is that coefficient α 12ptminimalamsmathwasysymamsfontsamssymbamsbsymathrsfsupgreek-69ptdocument document is only useful when the model of essential τ 12ptminimalamsmathwasysymamsfontsamssymbamsbsymathrsfsupgreek-69ptdocument document -equivalence is consistent with the item-score data. Because this model is highly restrictive, coefficient α 12ptminimalamsmathwasysymamsfontsamssymbamsbsymathrsfsupgreek-69ptdocument document 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 α 12ptminimalamsmathwasysymamsfontsamssymbamsbsymathrsfsupgreek-69ptdocument document incorrectly ignores correlated errors. If correlated errors would enter the computation of coefficient α 12ptminimalamsmathwasysymamsfontsamssymbamsbsymathrsfsupgreek-69ptdocument document, theoretical values of coefficient α 12ptminimalamsmathwasysymamsfontsamssymbamsbsymathrsfsupgreek-69ptdocument document could be greater than the test-score reliability. Because quality measures that are systematically too high are undesirable, critics dismiss coefficient α</mml: mi