A zero-one programming approach to Gulliksen's matched random subtests method

Gulliksen’s matched random subtests method is a graphical method to split a test into parallel test halves. The method has practical relevance because it maximizes coefficient α as a lower bound to the classical test reliability coefficient. In this paper the same problem is formulated as a zero-one programming problem, the advantage being that it can be solved by computer algorithms that already exist. It is shown how the procedure can be generalized to split tests of any length. The paper concludes with an empirical example comparing Gulliksen’s original hand-method with the zero-one programming version. Index terms: Classical test theory, Gulliksen’s matched random subtests method, Item matching, Linear programming, Parallel tests, Test reliability, Zero-one programming.