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Power

Power. Importance of Power. Assume that a theory is true. If we conduct experiments to test that theory, will the results always support the theory?. What Is Power?. Probability of rejecting a false H 0 Probability that you’ll find difference that’s really there

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Power

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  1. Power

  2. Importance of Power • Assume that a theory is true. • If we conduct experiments to test that theory, will the results always support the theory?

  3. What Is Power? • Probability of rejecting a false H0 • Probability that you’ll find difference that’s really there • 1 - b, where b = probability of Type II error

  4. Uses of Power • Two Primary Uses: • Estimate sample size required to detect a specified effect with a specified probability. • E.g., how many participants do I need to have a high probability (e.g., .90) of detecting a moderate effect? • Estimate probability of detecting a specified effect after an experiment has been conducted and the null hypothesis is not rejected

  5. What Controls Power? • The significance level (a) • True difference between null and alternative hypotheses • m1 - m2 • Sample size • Population variance • The particular test being used

  6. Distributions Under m1 and m0

  7. Effect Size • The degree to which the null is false • Depends on distance between m1and m2 • Also depends on standard error (of mean or of difference between means)

  8. Estimating Effect Size • Past research • What you consider important • Cohen’s conventions

  9. Combining Effect Size and n • We put them together and then evaluate power from the result. • General formula • where f (n) is some function of n • exact function depends on the test

  10. Power for One-Sample t • Applies to difference scores (related samples) as well • where n = size of sampleand d is effect size • Look power up in table using d and significance level (a)

  11. Power for Related-Sample t • Same as for one-sample t • The sample is the set of difference scores. • Use related-sample example to cover both situations.

  12. Power for Bushman’s Study • One sample t • Compared violent video group with population mean = 5.65 • Used 100 subjects • Assume he expected sample mean of 7.0 Cont.

  13. Bushman--cont. • d = 0.30 • n = 100 • d = 0.30100 = 3.0 • We are testing at a = .05

  14. This table is severely abbreviated. Power for d = 3.0, a = .05

  15. Power for Two Independent Groups • What changes from preceding? • Effect size deals with two sample means • Take into account both values of n • Effect size Cont.

  16. Estimating d • We could estimate d directly if we knew populations. • We could estimate from previous data. • Here we will calculate using Bushman’s sample statistics --assumes Bushman’s estimates of parameters are exact. Cont.

  17. Two Independent Groups--cont. • Then calculate d from effect size g Cont.

  18. Two Independent Groups--cont. • For our data Cont.

  19. This table is severely abbreviated. Power for d = 2.66, a = .05 Estimate = .76 ?

  20. Conclusions • If the parameters are as Bushman’s estimates would suggest, then if this study were run repeatedly, 76% of the time the result would be significant.

  21. How Many Subjects Do I Really Need? • Run calculations backward • Start with anticipated effect size (d) • Determine d required for power = .80. • Why .80? • Calculate n • What if Bushman wanted to rerun study, and wants power = .80?

  22. Calculating n • Bushman estimates d = 0.38 • Power table shows we need d = 2.80 • Calculations on next slide

  23. Bushman’s n

  24. Formulas for estimating n One sample/related samples N = (delta/d)2 Two sample N (each group) = 2(delta2)/d2

  25. Power as a Function of delta and significance Level (a)

  26. Sample problem: Estimating n • Avoidance behavior in rabbits. Over many studies, RT for a task is 5.8 s with SD = 2. E expects lesion in amygdala to decrease RT by 1 s. How many Ps needed to have 50/50 chance of detecting this difference? • How many Ps needed to have 80% chance of detecting this difference?

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