A Note on Cohen's Overlapping Proportions of Normal Distributions

Social scientists are often interested in computing the proportion of overlap and nonoverlap between two normal distributions that are separated by some magnitude. In his popular book, Statistical Power Analysis for the Behavioral Sciences (1988, 2nd ed.), Jacob Cohen provided a table (Table 2.2.1) for determining such proportions from common values of separation. Unfortunately, Cohen's proportions are inconsistent with his explication of the popular index of effect size, d; and his proportions are underestimates of distributional overlap and overestimates of nonoverlap. The authors explain how Cohen derived his values and then provide a revised, corrected table of proportions that also match values presented elsewhere.