Cronbach's alpha will generally increase as the intercorrelations among test items increase, and is thus known as an internal consistency estimate of reliability of test scores. Because intercorrelations among test items are maximized when all items measure the same construct, Cronbach's alpha is widely believed to indirectly indicate the degree to which a set of items measures a single unidimensional latent construct. It is easy to show, however, that tests with the same test length and variance, but different underlying factorial structures can result in the same values of Cronbach's alpha. Indeed, several investigators have shown that alpha can take on quite high values even when the set of items measures several unrelated latent constructs.[1][9][10][11][12][13] As a result, alpha is most appropriately used when the items measure different substantive areas within a single construct. When the set of items measures more than one construct, coefficient omega_hierarchical is more appropriate.[14][15][16]
Alpha treats any covariance among items as true-score variance, even if items covary for spurious reasons. For example, alpha can be artificially inflated by making scales which consist of superficial changes to the wording within a set of items or by analyzing speeded tests.
A commonly accepted[citation needed] rule for describing internal consistency using Cronbach's alpha is as follows,[17][18][19] though a greater number of items in the test can artificially inflate the value of alpha[9] and a sample with a narrow range can deflate it, so this rule should be used with caution.
A commonly accepted rule of thumb for describing internal consistency is as follows:[17]