An Effect Size Primer: A Guide for Clinicians and ResearchersChristopher J. FergusonTexas A&M International UniversityIncreasing emphasis has been placed on the use of effect size reporting in the analysis of social science data.Nonetheless, the use of effect size reporting remains inconsistent, and interpretation of effect size estimatescontinues to be confused. Researchers are presented with numerous effect sizes estimate options, not allof which are appropriate for every research question. Clinicians also may have little guidance in theinterpretation of effect sizes relevant for clinical practice. The current article provides a primer of effectsize estimates for the social sciences. Common effect sizes estimates, their use, and interpretations arepresented as a guide for researchers.Keywords: effect size (statistical), null hypothesis testing, experimentation, statistical analysis, statisticalsignificance, practical significanceBy the 1990s, statisticians had been aware for some time thatnull-hypothesis significance testing (NHST) was, in many re-spects, insufficient for interpreting social science data (Berkson,1938; Cohen, 1994; Loftus, 1996; Lykken, 1968; Meehl, 1978;Snyder & Lawson, 1993). Subsequently the Wilkinson Task Force(Wilkinson & Task Force on Statistical Inference, 1999) recom-mended the reporting of effect sizes and effect size confidenceintervals (CIs). Nonetheless, the use of effect size measures re-mains inconsistent (Fidler et al., 2005; Osborne, 2008; Sink &Stroh, 2006). Researchers and clinicians may find themselves withlittle guidance as to how to select from among a multitude ofavailable effect sizes, interpret data from research, or gauge thepractical utility of reported effect sizes. The current article seeks toprovide a primer for clinicians and researchers in understandingeffect size reporting and interpretation.The Purpose of Effect Size ReportingNHST, has long been regarded as an imperfect tool for exam-ining data (e.g., Cohen, 1994; Loftus, 1996). Statistical signifi-cance of NHST is the product of several factors: the “true” effectsize in the population, the size of the sample used, and the alpha(p) level selected. Limitations of NHST include sensitivity tosample size, inability to accept the null hypothesis, and the failureof NHST to determine the practical significance of statisticalrelationships (Cohen, 1992, 1994; Loftus, 1996; Osborne, 2008).Kirk (1996) puts the limitations of NHST succinctly in noting thatthey fall under three main categories:First, NHST does not adequately answer research questions.Regarding falsify-ability, scientists need to know the probabilitythat a null hypothesis is true, given a data set. Unfortunately,NHST tells us the opposite, namely how likely a data set is to haveoccurred, given that the null hypothesis is true (Cohen, 1994; Kirk,1996).Second, no two sample means are ever identical (Tukey, 1991).The null hypothesis is, on a microscopic level at least, always false(Kirk, 1996). The result is the quixotic quest for power to dem-onstrate any difference as statistically significant without consid-ering whether small differences are meaningful. This is particu-larly an issue when sample selection is nonrandom as samplingerror is underestimated in NHST when sampling is nonrandom.NHST risks becoming something of a “trivial exercise” as a result(Kirk, 1996, p. 747).Third, the .05 p level is arbitrary, leading researchers to come todifferent conclusions from equal treatment effects (Kirk, 1996). Aresearcher who finds that a treatment effect is nonsignificant usinga sample of 100 participants, randomly assigned, may find thatsimply adding 100 more participants produces statistically signif-icant effects, even though the treatment effects remain identical.This criticism is put most eloquently in Rosnow and Rosenthal’s(1989) famous quote “Surely God loves the .06 nearly as much asthe .05” (p. 1277).At present, no clear replacement for NHST has emerged. How-ever, the Wilkinson Task Force (1999) recommends the use ofeffect size in addition to NHST.Effect sizes estimate the magnitude of effect or associationbetween two or more variables (Ferguson, in press; Snyder &Lawson, 1993). As with all statistical tools, effect size estimatesare just that, estimates. Mostly, effect sizes are resistant to samplesize influence, and thus provide a truer measure of the magnitudeof effect between variables.Effect sizes seen in the social sciences are oftentimes very small(Rosnow & Rosenthal, 2003). This has led to difficulties in theirinterpretation. There is no agreement on what magnitude of effectis necessary to establish practical significance. Cohen (1992) of-CHRISTOPHER J. FERGUSON received his PhD from the University of CentralFlorida. He is currently an assistant professor of clinical and forensicpsychology at Texas A&M International University. His primary researchinterests focus on violent behavior, youth violence as well as positive andnegative consequences of violent video game exposure. He is also inter-ested in measurement issues in psychology, and ways in which hypothesesare tested and evaluated.CORRESPONDENCE CONCERNING THIS ARTICLE should be addressed to Chris-topher J. Ferguson, Department of Behavioral, Applied Sciences andCriminal Justice, Texas A&M International University, 5201 UniversityBoulevard, Laredo, TX 78041. E-mail: [email protected] Psychology: Research and Practice © 2009 American Psychological Association2009, Vol. 40, No. 5, 532–538 0735-7028/09/$12.00 DOI: 10.1037/a0015808532fers the value of r ⫽ .1, as a cut-off for “small” effects (whichwould indicate only a 1% overlap in variance between two vari-ables). However, Cohen did not anchor his recommendationsacross effect sizes; as such, his recommendations for r and dultimately differ in magnitude when translated from one to an-other. For instance, Cohen suggests that r ⫽ .3 and d ⫽ .5 eachindicate a cut-off for moderate effects, yet r ⫽ .3 is not theequivalent of d ⫽ .5. Other scholars suggest a minimum of r ⫽ .2(Franzblau, 1958; Lipsey, 1998) or .3 (Hinkle, Weirsma, & Jurs,1988). In the current article, all effect size recommendations,where possible, are anchored to a minimum of r ⫽ .2, for practicalsignificance (Franzblau, 1958; Lipsey, 1998). These readily con-vert from r to d for instance, without altering the interpretation.Note that this is a suggested minimum not a guarantee that ob-served effect