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Moderation: Effect Size and Power

Moderation: Effect Size and Power. David A. Kenny. Effect Size. The standard effect size measure for interaction is Cohen’s f 2 : where R 2 2 is the multiple correlation with X, M, and XM in the equation, and R 1 2 is the multiple correlation with X and M in the equation.

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Moderation: Effect Size and Power

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  1. Moderation: Effect Size and Power David A. Kenny

  2. Effect Size . The standard effect size measure for interaction is Cohen’s f2: where R22 is the multiple correlation with X, M, and XM in the equation, and R12is the multiple correlation with X and M in the equation. Note f2 = d2/4 when the X and M are dichotomies.

  3. 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.

  4. Other Possibilities • X and M dichotomies • Compute d1 (X = 1) and d2(X = 2) . • Effect size: d2- d1 • Power in the case of two dichotomies is not so low.

  5. Power Given f2 = 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.

  6. 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.

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

  8. Additional Webinar • ModText

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