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We introduce the binomial effect size display (BESD), which is useful because it is (a) easily understood by researchers, students, and lay persons; (b) widely applicable; and (c) conveniently computed. The BESD displays the change in success rate (e.g., survival rate, improvement rate, etc.) attributable to a new treatment procedure. For example, an r of .32, the average size of the effect of psychotherapy, is said to account for "only 10% of the variance"; however, the BESD shows that this proportion of variance accounted for is equivalent to increasing the success rate from 34% to 66%, which would mean, for example, reducing an illness rate or a death rate from 66% to 34%.
Rosenthal et al. (Fri,) studied this question.