T au‐Equivalent and Congeneric Measurements

Abstract

To evaluate the reliability of a test, one needs a parallel test. When parallel tests are absent, one option is to rely on hypotheses such as that the test parts are essentially tau‐equivalent or congeneric, having only one factor in factor analysis. Such hypotheses are unrealistic, except that a test may be congeneric when there are only three test parts; in that case, however, it is impossible to decide what the number of factors really is. A preferable option is to use lower bounds to reliability, such as coefficient alpha. The Jackson & Agunwamba greatest lower bound (glb) is better than alpha but has a sampling bias problem. Bias correction methods are still under study. Nevertheless, when compared to reliability estimates derived from the hypothesis of congeneric tests, the glb is already to be preferred, because these estimates behave very similarly to glb, and display the same sampling bias but do not rely on the hypothesis of a congeneric test