Introducing the mean absolute deviation 'effect' size

Abstract

This paper revisits the use of effect sizes in the analysis of experimental and similar results, and reminds readers of the relative advantages of the mean absolute deviation as a measure of variation, as opposed to the more complex standard deviation. The mean absolute deviation is is easier to use and understand, and more tolerant of extreme values. The paper then proposes the use of an easy to comprehend effect size based on the mean difference between treatment groups, divided by the mean absolute deviation of all scores. Using a simulation based on 1,656 randomised controlled trials each with 100 cases, and a before and after design, the paper shows that the substantive findings from any such trial would be the same whether raw-score differences, a traditional effect size like Cohen’s d, or the mean absolute deviation effect size is used. The same would be true for any comparison, whether for a trial or a simpler cross-sectional design. It seems that there is a clear choice over which effect size to use. The main advantage in using raw scores as an outcome measure is that they are easy to comprehend. However, they might be misleading and so perhaps require more judgement to interpret than traditional ‘effect’ sizes. Among the advantages of using the mean absolute deviation effect size are its relative simplicity, 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 (termed ‘A’).