Computing contrasts, effect sizes, and counternulls on other people's published data: General procedures for research consumers

We describe convenient statistical procedures that will enable research consumers (e.g., professional psychologists, graduate students, and researchers themselves) to reach beyond the published conclusions and make an independent assessment of the reported results. Appropriately conceived contrasts accompanied by effect size estimates often allow researchers to address precise predictions that the authors of the published report may have ignored or abandoned prematurely. We describe the use of t, F, and Z to compute contrasts with different raw ingredients, and we review 3 effect size indices (Cohen's d, Hedges's g, and the Pearson r) and a way of displaying the magnitude of any effect size r. We also describe how to construct confidence limits for the obtained effect as well as its null-counternull interval.