This study compared the accuracies of nine previously proposed statistical significance tests for selecting identity, linear, and equipercentile equating functions in an equivalent groups equating design. The strategies included likelihood ratio tests for the loglinear models of tests' frequency distributions, regression tests, Kolmogorov-Smirnov tests, and equated score difference tests. Results showed that the most accurate strategies were the likelihood ratio tests and the equated score difference tests. The implications of these results are discussed in terms of applications to equating practice. (Contains 3 tables, 9 figures, and 2 notes.)