Abstract
Original article: Funder, D. C., & Ozer, D. J. (2019). Evaluating effect size in psychological research: Sense and nonsense. Advances in Methods and Practices in Psychological Science, 2, 156–168. doi:10.1177/2515245919847202
On page 158 of this article, the third paragraph in the section titled Squaring the Correlation included imprecise statements about the correlation coefficient (r). The original paragraph read as follows: The variance “explained” by the squared r refers to the squared deviations of the variable from its mean. Squaring the r changes the scale of the effect from the original units to squared units. One can search statistics textbook after textbook without finding any attempt to explain why (as opposed to assert that) these squared units are appropriate for evaluating effect size (i.e., why one would want to account for variance rather than standard deviation). The squared correlation may have some utility as a measure of model fit, but the original, unsquared r reflects the size of the effect on the metric of the original measured units.
For greater clarity, this paragraph has been revised to read as follows: The computation of variance involves squaring the deviations of a variable from its mean. However, squared deviations produce squared units that are less interpretable than raw units (e.g., squared conscientiousness units). As a consequence, r2 is also less interpretable than r because it reflects the proportion of variance in one variable accounted for by another. One can search statistics textbook after textbook without finding any attempt to explain why (as opposed to assert that) r2 is an appropriate effect-size measure. Although r2 has some utility as a measure for model fit and model comparison, the original, unsquared r is the equivalent of a regression slope when both variables are standardized, and this slope is like a z score, in standard-deviation units instead of squared units.