Many well-known equations in classical test theory are mathematical identities in populations of individuals but not in random samples from those populations. First, test scores are subject to the same sampling error that is familiar in statistical estimation and hypothesis testing. Second, the assumptions made in derivation of formulas in test…

Equating a new standard test to an old reference test is considered when samples for equating are not randomly selected from the target population of test takers, identifying two problems from equating from biased samples. An empirical example with data from the Armed Services Vocational Aptitude Battery illustrates the approach. (SLD)