```Date: Mon, 22 May 2006 19:02:52 -0400 Reply-To: Nick White Sender: "SPSSX(r) Discussion" From: Nick White Subject: Re: effect size - correlation Comments: To: "Zdaniuk, Bozena" In-Reply-To: <0741DA624F60AE43A659DD2264AA4A650159FAD4@ucsur-8.ucsur.nt.pitt.edu> Content-Type: text/plain; charset="us-ascii" J Cohen defined the effect size index for correlation analysis as f^2, where f^2 = R^2 / (1-R^2) (using partial R^2's in the multivariate case). He suggests the following for effect size interpretation based on correlation analysis: Small effect: f^2 = .02 Medium effect: f^2 = .15 Large effect: f^2 = .35 This is a general recommendation for multiple regression and correlation analysis and will be conservative for the bivariate case. The bivariate case should actually have effect size recommendations closer to Small effect: f^2 = .01 Medium effect: f^2 = .09 Large effect: f^2 = .25 In other words, since we use a value related to R^2 for the index, we also need to square the standard effect size criteria (.01 = .1^2, .09 = .3^2, and .25 = .5^2). Cohen then made adjustments to the criteria to reflect the fact that correlation analysis usually involves multiple variables. Cohen further comments that the criterion for large effect size is apt to be too high to be useful in psychological studies, but may actually be too low to be considered a "large effect" in sociology, economics and psychophysics. Source is the book, _Statistical Power Analysis for the Behavioral Sciences_, 2nd Edition (1988), by Jacob Cohen. Good luck! Nick White -----Original Message----- From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of Zdaniuk, Bozena Sent: Monday, May 22, 2006 5:14 PM To: SPSSX-L@LISTSERV.UGA.EDU Subject: effect size - correlation Hello, I assume that the squared coefficient of bivariate correlation can be used as a measure of effect size, right? If this is the case, could someone comment what would be considered a medium effect size for a bivariate correlation in the behavioral sciences? I realize that for tests based on means, the effect size of .5 is considered medium but for a correlation that would mean a coefficient of .7 which is very rarely found in beh. Science. Any comments, references would be greatly appreciated. Thanks a lot. Bozena ```

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