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POWER

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  1. POWER

  2. Overview • What is “power”? • How many people should you recruit for a particular study? • What is the historical context that makes power analysis important?

  3. Introduction • Sample size (n), effect sizes (such as r), and p-values are mutually related • Recall: The p-value depends on two things • Sample size (n) • Effect size, such as r • As the sample size gets bigger and the effect size gets bigger, p-values become more statisticallysignificant (smaller)

  4. Power • Power is the ability to detect an effect as statistically significant • Ability to be confident that an observed difference is real • Power Analysis (or Sample Size Analysis) • Process of determining the samplesize that would be needed todetermine that a particular effect size is statistically significant

  5. Power Analysis • To perform a power analysis, you need to make two decisions • What p-value do you care about? • Probably .05  • What is the smallest effect sizeyou would care about? • r = .20? r = .30? • Probably depends on thestudy

  6. Power Analysis • Power increases as the sample size increases, allowing you to detect smaller and smaller effects as statistically significant • If you only care about a large effect size (r = .50), you don’t need as large a sample • If you want to be able to detect small effect sizes (r = .10) as statistically significant, you’re going to need a large sample

  7. Online Calculators • Correlations (r) • http://vassarstats.net/tabs_r.html • Put in the n and r values, see what it takes to reach statistical significance • Cohen’s d (don’t need to know yet) • http://www.graphpad.com/quickcalcs/ttest1/?Format=SD • Put in “1” for each SD and “0” for the Group Two Mean • Put in the desired Cohen’s d for Group 1 Mean, see what it takes to reach statistical significance

  8. Summary Information With a bigger sample size, better able to detect smaller effect sizes as statistically significant

  9. Summary Information Small effect Medium effect Large effect

  10. Why Power Matters • Most studies in psychology and medicine have been underpowered (too small of samples to detect effects as statistically significant) • Waste of… • Tax dollars, charitable contributions, and tuition • Time of researchers, research assistants, staff • Time of research volunteers • Power analyses are relatively simple and produce better science

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