Five new nonparametric effect size estimators are proposed: the “probability of higher subgroup dominance based on Somers’ D” (PHD), and its variant PHG, based on Goodman-Kruskal gamma (G), and three new variants of traditional estimators, Grissom-Kim PS, Cliff’s d, and Vargha-Delaney A, called ordinal PS, ordinal d, and ordinal A. PHD and PHG are general estimators in three respects. First, they can be used strictly in polytomous ordinal settings, since the embedded estimators D and G are not restricted to binary settings. Second, it is shown that in the dichotomous cases, PS, d, and A, are special cases of D and hence of PHD. Third, because PHD and PHG are based on established correlation estimators, their calculation is straightforward, and they can be readily used in meta-analyses, provided that the embedded correlation estimators, D and G, are typically included in the report. The asymptotic standard errors for PHD and PHG and ordinal PS, d, and A are given, and their advantages are discussed in relation to those of Cohen’s d, f, and η2. PHD can be used as the basis for common language interpretation of the effect size r, Cohen d, Cohen f, and certain reliability estimators.