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

In order to estimate the classical coefficient of test reliability, parallel measurements are needed. H. Gulliksen's matched random subtests method, which is a graphical method for splitting a test into parallel test halves, has practical relevance because it maximizes the alpha coefficient as a lower bound of the classical test reliability coefficient. This paper formulates this same problem as a zero-one programming problem, the advantage being that it can be solved by algorithms already existing in computer code. Focus is on giving Gulliksen's method a sound computational basis. How the procedure can be generalized to test splits into components of any length is shown. An empirical illustration of the procedure is provided, which involves the use of the algorithm developed by A. H. Land and A. Doig (1960), as implemented in the LANDO program. Item difficulties and item-test correlations were estimated from a sample of 5,418 subjects--a sample size that is large enough to prevent capitalizing on chance in the Gulliksen method. Two data tables and one graph are provided.