Squaring the correlation
As bad as these decontextualized criteria are, the other widely used way to evaluate effect size is arguably even worse. This method is to take the reported r and square it. For example, an r of .30, squared, yields the number .09 as the “proportion of variance explained,” and this conversion, when reported, often includes the word “only,” as in “the .30 correlation explained only 9% of the variance.”
We suggest that this calculation has become widespread for three reasons. First, it is easy arithmetic that gives the illusion of adding information to a statistic. Second, the common terminology of variance explained makes the number sound as if it does precisely what one would want to it do, the word explained evoking a particularly virtuous response. Third, the context in which this calculation is often deployed allows writers to disparage certain findings that they find incompatible with their own theoretical predilections. One prominent example is found in Mischel’s (1968) classic critique of personality psychology, in which he complained that the “personality coefficient” of .30, described by him as the highest correlation empirically found between trait measurements and behavior,3 “accounts for less than 10 percent of the relevant variance” (p. 38). As Abelson (1985) observed, “it is usually an effective criticism when one can highlight the explanatory weakness of an investigator’s pet variables in percentage terms” (p. 129).
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.
https://journals.sagepub.com/doi/full/10.1177/2515245919847202
