Controlling decremental and inflationary effects in reliability estimation resulting from violations of assumptions

Two assumptions in classical test theory, essential tau-equivalence and independence of measurement errors, when violated may produce attenuated or inflated estimates of reliability, respectively. Inflation stemming from correlated errors can be controlled by a procedure in which systematically created equivalent halves of a given measuring instrument are administered across two occasions. When poor approximations to equivalent halves are constructed for this purpose, however, distortion in the opposite direction may result, being sometimes quite large when measuring instruments are not essentially tau-equivalent (or, at the practical level, unidimensional). The nature of these decrements are discussed and illustrated, and a number of procedures for eliminating them introduced.