Moderation Effect Size and Power David A Kenny

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Moderation: Effect Size and Power David A. Kenny

Moderation: Effect Size and Power David A. Kenny

. Effect Size The standard effect size measure for interaction is Cohen’s f 2:

. Effect Size The standard effect size measure for interaction is Cohen’s f 2: where R 22 is the multiple correlation with X, M, and XM in the equation, and R 12 is the multiple correlation with X and M in the equation. Note f 2 = d 2/4 when the X and M are dichotomies.

Standards • Small: 0. 01 • Medium: 0. 25 • Large: 0. 40 •

Standards • Small: 0. 01 • Medium: 0. 25 • Large: 0. 40 • However, The average effect size in tests of moderation is only 0. 009 (Aguinis, Beaty, Boik, & Pierce, 2005), smaller than small.

Other Possibilities • X and M dichotomies • Compute d 1 (X = 1)

Other Possibilities • X and M dichotomies • Compute d 1 (X = 1) and d 2 (X = 2). • Effect size: d 2 - d 1 • Power in the case of two dichotomies is not so low.

Power Given f 2 = 0. 009 • Can use G*Power to determine power.

Power Given f 2 = 0. 009 • Can use G*Power to determine power. • Need 875 cases to have an 80% chance of rejecting the null hypothesis! • Thus, power in the typical test of moderation is very low.

Leverage • Some observations are more important in determining an effect. • Slope: How

Leverage • Some observations are more important in determining an effect. • Slope: How far the observation is from the mean. • Interaction: How far the product is from the mean; however, for the product most observations are very near the mean. • For tests of interaction, most observations have little or no leverage.

What to Do about Low Power? Lower alpha. Rely on replications. Report results.

What to Do about Low Power? Lower alpha. Rely on replications. Report results.

Additional Webinar • Mod. Text 8

Additional Webinar • Mod. Text 8

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