1. Effect Size Joseph Stevens, Ph.D., University of Oregon (541) 346-2445, stevensj@uoregon.edustevensj@uoregon.edu © Stevens 2006

2. Two Kinds of Metric for Measuring the Magnitude of Effects Effect Size – Expresses the size of group difference in standard deviation units (e.g., Cohen’s d) Strength of Association Measures – Expresses magnitude of effect in a proportion or percentage (e.g., r 2, η 2, ω 2 )

3. Interpreting Effect Size Results Cohen’s “Rules-of-Thumb”  standardized mean difference effect size small = 0.20 medium = 0.50 large = 0.80  correlation coefficient small = 0.10 medium = 0.25 large = 0.40

4. The Standardized Mean Difference: Cohen’s d

5. Some Conversions to d

6. Other Conversions Many other formulae exist to convert NHST or other information to a common effect size metric Correlations must be converted using Fisher’s transformation (see handout)

7. The Inverse Variance Weight Standard error (SE) is a direct index of ES precision. Can be used to create confidence intervals. Hedges’ showed that the optimal weights for meta-analysis are:

8. Inverse Variance Weight Standardized Mean Difference: Fisher’s z transformed Correlation Coefficient:

9. The Weighted Mean Effect Size Start with the effect size (ES) and inverse variance weight (w) for 10 studies.

10. The Weighted Mean Effect Size Start with the effect size (ES) and inverse variance weight (w) Next, multiply w by ES Repeat for all effect sizes

11. The Weighted Mean Effect Size Sum the columns, w and ES Divide the sum of (w*ES) by the sum of (w)

12. The Standard Error of the Mean ES The standard error of the mean is the square root of 1 divided by the sum of the weights.

13. Mean, Standard Error, Z-test and Confidence Intervals Mean ES SE of the Mean ES Z-test for the Mean ES 95% Confidence Interval