Eight different methods are reviewed for determining whether two or more tests are equivalent measures. These methods vary in restrictiveness from the Wilks-Votaw test of compound symmetry (which requires that all means, variances, and covariances are equal), to Joreskog's theory of congeneric tests (which requires only that the tests are measures of the same attribute except for errors of measurement). A formal statement of the problems is given, and the various definitions or criteria of equivalence are discussed. Notation conventions are presented. Then each of the eight statistical tests for evaluating the hypothesis of equivalence is described and compared with the others. These procedures are written in a common algebra and their Type I error rates and power are compared, as are the properties of their estimators and their sensitivity to violations of their assumptions. A numerical example is worked to illustrate the application of the techniques to an educational measurement problem. The eight tests are: Wilks-Votaw; McNemar's; Forsyth-Feldt-McNemar; Forsyth-Feldt-Normal Curve; Lord's; Lord-Villegas; Kristof's; and Joreskog's. (CTM)