Power and Effect Size

I factor 4 levels

Testing?

Null True Null false

Reject Null

Retain Null

Null True Null false

Reject Null Type I

(α)

Correct

(1-β)

Retain Null Correct

(1-α)

Type II

(β)

effect

power 1 - β β

α/2 α/21- α

TREATMENT NULL

What determines power?

1) Effect size

2) Sample size

3) Variability

4) Significance level

5) 1 or 2 tail choice

6) Kind of test

0 10 20 30 40 50 60 70 80 900

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 10 20 30 40 50 60 70 80 900

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 10 20 30 40 50 60 70 80 900

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 10 20 30 40 50 60 70 80 900

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 10 20 30 40 50 60 70 80 900

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

effect

power 1 - β β

α/2 α/21- α

TREATMENTNULL

Change significance level

1 or 2 tail

Feature Increase

power

Decrease power

Effect size large small

Population

σ

small σ big σ

Sample size (n)

big small

significance Lenient (0.05)

Strict

(0.01)

1 or 2 tail one two

• power is in the sampling distributions, whereas effect size is in the population distributions

assumptions

Effect Size

The extent to which 2 populations do not overlap

d =( μ1 - μ2)/ σ

Cohen’s d

0.2 is small effect0.5 medium0.8 large

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?

Degrees of freedom

2 factor

Factor A has a levels and df= a-1Factor B has b levels and df = b-1Interaction df = (a-1)(b-1)

Error df = N - ab