Correcting coefficient alpha for correlated errors: Is alpha(K) a lower bound to reliability?

When errors of measurement are positively correlated, coefficient alpha may overestimate the ``true'' reliability of a composite. To reduce this inflation bias, Komaroff (1997) has proposed an adjusted alpha coefficient, alpha(K). This article shows that alpha(K) is only guaranteed to be a lower bound to reliability if the latter does not include correlated error. If one's definition of reliability includes correlated error, then an alternative adjusted alpha, alpha(R), is suggested, which will always be a lower bound.