Wednesday November 16 Statistical Power If you are

Wednesday, November 16 Statistical Power If you are interested in testing for the statistical significance of an effect that is of a particular magnitude of practical significance, what should the sample size be?

Why Statistical Power? • It teaches you about the importance of effect size. = d x f (N)

Statistical Power • It teaches you about the importance of effect size. • It helps put the risk of Type I error, (alpha) into perspective. = d x f (N)

Statistical Power • It teaches you about the importance of effect size. • It helps put the risk of Type I error, (alpha) into perspective. • It helps you appreciate the value of the sample size, N. = d x f (N)

Statistical Power • It teaches you about the importance of effect size. • It helps put the risk of Type I error, (alpha) into perspective. • It helps you appreciate the value of the sample size, N. • It simply makes you a better person. = d x f (N)

“Reality” Decis io n H 0 True Reject H 0 Don’t Reject H 0 Type I Error Yeah! H 0 False Yeah!

“Reality” Decis io n H 0 True Reject H 0 Don’t Reject H 0 False Type I Error Yeah! Type II Error

1 - The ability to avoid Type II error (fail to reject H 0 that should be rejected).

σ = 100 σX= 100/12. 81 = 7. 81

Ordinarily, one is well advised to take the largest sample that is practical and then determine if this sample has adequate power for detecting a difference large enough to be of interest. Researchers often strive for power 80 with =. 05. More often, however, one finds that power is low even for detecting differences large enough to be of practical importance.

Problem You develop a new measure of social efficacy for adolescent girls, with 24 items on a 3 -point scale. The scale seems to have = 18, and = 16. You are asked to evaluate a new program to promote social efficacy in adolescent girls, and want to use your scale. You sample 16, but alas find that the sample mean of 22 does not allow you to reject the null hypothesis at =. 05. You’re really frustrated because you think that a 4 -point gain is meaningful. What should your next steps be?

= d x f (N) = d N 1/2 d = 4/16 =. 25 N = 16 = 1. 0 What would it take for power =. 80? N = ( / d )2 N = (2. 8 /. 25)2 = 125. 44

= d x f (N) = d (N-1) 1/2 = ρ (N-1) 1/2 d =. 5 N = 21 = 2. 24 What would it take for power =. 80? N = ( / d )2 N = (2. 8 /. 5)2 = 31. 36

= d x f (N) = d (N-1) 1/2 = ρ (N-1) 1/2 d =. 5 N = 21 = 2. 24 What would it take for power =. 90? N = ( / d )2 N = (3. 25/. 5)2 = 42. 25

What can you do to increase power? • Increase n

What can you do to increase power? • Increase n • Decrease measurement error

What can you do to increase power? • Increase n • Decrease measurement error • Increase , say, from. 05 to. 10 (or fiddle with tails*)

What can you do to increase power? • Increase n • Decrease measurement error • Increase , say, from. 05 to. 10 (or fiddle with tails*) *not advised

What can you do to increase power? • Increase n • Decrease measurement error • Increase , say, from. 05 to. 10 (or fiddle with tails*) • Increase the magnitude of the effect *not advised

In an independent samples t-test where the effect size d=. 5 and N=100, what is the expected power? (see p. 267)

In an independent samples t-test where the effect size d=. 5 and N=100, what is the expected power? (see p. 267)