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Effect size. Ways to judge and report on differences between groups. Effect size. How large is the difference? (What is “the effect” of a new treatment? The significance test tells us: Is there any difference? (not zero) Can we reject H0? (H0: No difference between population means)
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Effect size Ways to judge and report on differences between groups
Effect size • How large is the difference? • (What is “the effect” of a new treatment? • The significance test tells us: • Is there any difference? (not zero) • Can we reject H0? (H0: No difference between population means) • But then we want to know • How big is the difference • The magnitude of the effect • Sometimes a statistically significant difference is small.
Effect size • There are several families of effect size • The correlation-base (r) • Standardized mean difference (d) • (This is like a z score) • Names to know • Glass (Glass’s delta) Delta = (M1 – M2)/S control • Cohen (Cohen’s d) • Hedges (Hedges g)
Effect size • The convention is reporting effect sizes is that M1- M2 is done so that the difference is positive if the treatment group is better. Cohen suggested that: 0 to .20 = small .5 (or so) = medium .8 = large But these are only very rough guides, and the standards for judging small, medium or large depend on the field of study and the concept or issue that is measured.
