1. Power and Effect Size

2. I factor 4 levels

3. Testing?
Null True
Null false
Reject Null
Retain Null

4. Null True
Null false
Reject Null
Type I
(α)
Correct
(1-β)
Retain Null
(1-α)
Type II
(β)

5. effect
TREATMENT
NULL
power β
1 - β
1- α
α/2
α/2

8. What determines power?
Effect size
Sample size
Variability
Significance level
1 or 2 tail choice
Kind of test

10. effect
NULL
TREATMENT
power β
1 - β
1- α
α/2
α/2

11. Change significance level

12. 1 or 2 tail

13. Feature
Increase
power
Decrease power
Effect size
large
small
Population σ
small σ
big σ
Sample size (n)
big
significance
Lenient (0.05)
Strict
(0.01)
1 or 2 tail
one
two

14. power is in the sampling distributions, whereas effect size is in the population distributions

15. assumptions

16. Effect Size
The extent to which 2 populations do not overlap
d =( μ1 - μ2)/ σ
Cohen’s d
0.2 is small effect
0.5 medium
0.8 large

17. Effect size Small (f =0.1) Medium (f=0.25) Large(f=0.4) 3 groups
Approximate number of participants in each group (equal variances) to achieve 80% power for one-way ANOVA at 0.05 significance level
Effect size
Small (f =0.1)
Medium (f=0.25)
Large(f=0.4)
3 groups
(dfbetween=2)
322 52 21
4 groups
(dfbetween =3)
274 45 18
5 groups
(dfbetween =4)
240 39 16
How many?

18. Degrees of freedom
2 factor
Factor A has a levels and df= a-1
Factor B has b levels and df = b-1
Interaction df = (a-1)(b-1)
Error df = N - ab