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Power and Effect Size

Explore Type I and Type II errors, power, effect sizes, and common statistical terms with examples and formulas. Learn how to conduct power analysis and estimate effect sizes for accurate research in psychology and data analysis.

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Power and Effect Size

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  1. Power and Effect Size D. Wayne Mitchell, Ph.D. Kayla N. Jordan – StatisticalAnalyst Rstats Institute Psychology Department Missouri State University

  2. Review of Statistical Terms • I. Type I Error • Type II Error • Power • IV. Effect Size

  3. Four Common Effect Size Indices • (r-squared) r2 • (omega-squared) ω2 • (eta-squared) η2 • Cohen’s d

  4. Size! Small, Medium, Large? Cohen’s d = .20; r 2= .01 (small) Cohen’s d = .50; r 2= .06 (medium) Cohen’s d = .80; r 2= .14 (large)

  5. Given the correlation result: • (r (98) = .40, p < .05); r2 = .16 • Given the t-test result: • (t (22) = 4.16, p < .05) • ω2 = (t2-1)/ (t2 + df +1) = .40 r2 or η2 = t2/ (t2 + df ) = .44 Cohen’s d = 2t / = 1.77

  6. One-Way ANOVA Results: • See Pages 4 and 5 • Omega-Squared • Eta-Squared • Glasses Delta

  7. To do a Power Analysis • See Suggestions; Page 7 • Have to Estimate an Effect Size • Estimate the Smallest Effect that You Want to Detect • Realize the Complexity of the Design Requires Study to do Appropriate Power Analysis

  8. Some Rules of Thumb with Correlation – Regression • N > 50 + 8m (m = # IVs) • N > 50 + m (for individual predictions) • The effect one might expect… • rxy = est. rxy √ rxx ryy

  9. Some Needed Formulas f 2= eta2 / 1 - eta2 d = Mean1 – Mean2 √ s12+ s22 / 2

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