On Detecting a Minimal Important Difference among Standardized Means

Abstract

As a generalization of the standardized mean difference between two independent populations, two different effect size measures have been proposed to represent the degree of disparity among several treatment groups. One index relies on the standard deviation of the standardized means and the second formula is the range of the standardized means. Despite the obvious usage of the two measures, the associated test procedures for detecting a minimal important difference among standardized means have not been well explicated. This article reviews and compares the two approaches to testing the hypothesis that treatments have negligible effects rather than that of no difference. The primary emphasis is to reveal the underlying properties of the two methods with regard to power behavior and sample size requirement across a variety of design configurations. To enhance the practical usefulness, a complete set of computer algorithms for calculating the critical values, p-values, power levels, and sample sizes is also developed.