Multiply by 37 (or Divide by 0.027): A Surprisingly Accurate Rule of Thumb for Converting Effect Sizes From Standard Deviations to Percentile Points

Abstract

Educational researchers often report effect sizes in standard deviation units (SD), but SD effects are hard to interpret. Effects are easier to interpret in percentile points, but converting SDs to percentile points involves a calculation that is not transparent to educational stakeholders. We show that if the outcome variable is normally distributed, we can approximate the percentile-point effect simply by multiplying the SD effect by 37 (or, equivalently, dividing the SD effect by 0.027). For students in the middle three-fifths of a normal distribution, this rule of thumb is always accurate to within 1.6 percentile points for effect sizes of up to 0.8 SD. Two examples show that the rule can be just as accurate for empirical effects from real studies. Applying the rule to empirical benchmarks, we find that the least effective third of educational interventions raise scores by 0 to 2 percentile points; the middle third raise scores by 2 to 7 percentile points; and the most effective third raise scores by more than 7 percentile points.