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POWER

Understand the concept of power analysis and how it relates to sample size determination for detecting statistically significant effects. Learn why power analysis is important in research and how it contributes to better science.

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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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