Estimation of reliability and true score variance from a split of a test into three arbitrary parts

This paper gives a method of estimating the reliability of a test which has been divided into three parts. The parts do not have to satisfy any statistical criteria like parallelism or-equivalence. If the parts are homogeneous in content (congeneric),i.e., if their true scores are linearly related and if sample size is large then the method described in this paper will give the precise value of the reliability parameter. If the homogeneity condition is violated then underestimation will typically result. However, the estimate will always be at least as accurate as coefficient and Guttman's lower bound ₃ when the same data are used. An application to real data is presented by way of illustration. Seven different splits of the same test are analyzed. The new method yields remarkably stable reliability estimates across splits as predicted by the theory. One deviating value can be accounted for by a certain unsuspected peculiarity of the test composition. Both coefficient and ₃ would not have led to the same discovery.Expanded version of a paper given at the Psychometric Society Meeting in Stanford, California, March 1974.