Correlational Equivalence Testing

Abstract

Equivalence testing confirms that two parameters are within an acceptable tolerance of each other by rejecting a statistical null hypothesis that the parameters are farther apart than that tolerance. Equivalence testing became popular in pharmaceutical research more than 30 years ago, but has only recently received serious attention in the social sciences. Suggestions for procedures testing the equivalence of two means abound, however, no equivalence test for the difference between two correlations has yet been suggested. This study compares three confidence intervals suggested for use in equivalence testing of means with respect to their coverage rate, bias, and width. The 1 - 2 alpha CI method is then applied to testing of two correlations for equivalence. Asymptotic methods for the construction of the 1 - 2 alpha CI, and formulas for approximating power and required N are provided. The properties of the CI are also investigated with Monte Carlo simulations.