Effect Size Explorer
An effect size like Cohen’s d is easy to report and hard to feel. This page turns a d into a tangible picture: two groups as overlapping bell curves, plus three plain-language readings — how much the distributions overlap, how often a random person from the higher group outscores a random person from the lower group, and Cohen’s U3.
With d = 0.20, the two distributions overlap by about 92%. A randomly chosen person from the higher group scores above a randomly chosen person from the lower group about 56% of the time (common-language effect size), and the higher group's average exceeds about 58% of the lower group (Cohen's U3).
How the figures are derived. Two equal-variance normal distributions are
separated by d standard deviations. Overlap is
2·Φ(−|d|/2) and Cohen’s U3 is Φ(d) (Cohen,
J., 1988, Statistical Power Analysis for the Behavioral Sciences, 2nd ed.). The
common-language effect size / probability of superiority is Φ(d/√2)
(McGraw, K. O., & Wong, S. P., 1992, Psychological Bulletin, 111(2), 361–365).
Φ is the standard-normal CDF. Every number above is computed from these
formulas — nothing is fabricated. This page uses a small, scoped client-side script to
add interactivity; it works fully without JavaScript (the chart re-renders server-side when you
submit a value).