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 (1-α) Type II (β)

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

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

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

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 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 effect 0.5 medium 0.8 large

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?

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