The possible advantages of the mean absolute deviation 'effect' size

Abstract

A range of ‘effect’ sizes already exists, for presenting a relatively easy to interpret estimate of a difference or change between two sets of observations. All are based on use of the standard deviation of the observations, involving squaring and then square-rooting, which makes results hard to interpret, hard to teach and may distort extreme scores. An effect size based on the simpler mean absolute deviation overcomes these issues to some extent, while being at least as efficient and leading to the same substantive results in almost all cases. This paper proposes the use of an easy to comprehend effect size based on the mean difference between treatment groups, divided by their mean absolute deviation. Using a simulation of 1,656 trials each of 100 cases using a before and after design, the paper shows that the substantive findings from any such trial would be the same whether a traditional effect size like Cohen’s d or the mean absolute deviation effect size is used. The mean absolute deviation effect size works. Among the advantages of using the mean absolute deviation effect size are its relative simplicity, efficiency, everyday meaning, and the lack of distortion of extreme scores caused by the squaring involved in computing the standard deviation. Given that working with absolute values is no longer the barrier to computation that it apparently was before the advent of digital calculators, there is a clear place for the mean absolute deviation effect size.