1. 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?

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

3. It teaches you about the importance of effect size.
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)

4. It teaches you about the importance of effect size.
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)

5. It teaches you about the importance of effect size.
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)

6. “Reality”
H0 True
H0 False
Type I Error 
Reject H0
Yeah!
Decision
Yeah!
Don’t Reject H0
Yeah!

7. “Reality”
H0 True
H0 False
Yeah!
Type I Error 
Reject H0
Yeah!
Decision
Yeah!
Type II Error 
Don’t Reject H0
Yeah!

8. Statistical Power 1 -  The ability to avoid Type II error
(fail to reject H0 that should be rejected).

9. σ = 100
σX= 100/12.81
= 7.81

10. 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  = More often,
however, one finds that power is low even for detecting differences
large enough to be of practical importance.

11. 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 really frustrated because you think that a 4-point
gain is meaningful. What should your next steps be?

12. What would it take for power = .80?
 = 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 =

13. What would it take for power = .80?
 = 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

14. What would it take for power = .90?
 = 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

15. What can you do to increase power?
Increase n

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

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

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

19. 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

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

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