1. Power Analysis for Traditional and Modern Hypothesis Tests
Kevin R. Murphy
Pennsylvania State University

2. Power Analysis Helps you plan better studies
Helps you make better sense of existing studies
Is not limited to traditional null hypothesis tests
Application of power analysis to minimum-effect tests will be discussed

3. Errors in Null Hypothesis Tests
True State of Affairs
No Effect (H0)
Some Effect
Reject Null
Type I Error - reject null when it is true
(a)
Power= 1- 
Fail to Reject Null
Type II Error - fail to reject null when you should ()
Your
Decision

4. Power Depends On Effect Size Sample Size (N) Decision Criteria - 
How large is the effect in the population?
Sample Size (N)
You are using a sample to make inferences about the population. How large is the sample?
Decision Criteria - 
How do you define “significant” and why?

5. Power Analysis and the F Distribution
The power of most statistical tests in social sciences (e.g., ANOVA, regression, t-tests, other linear model statistics) can be evaluated via the familiar F distribution
F is a ratio of observed effect to error
F= MS treatments / MS error
F = (True Effect + Error) / Error
The larger the true treatment effect, the larger F you expect to find
If the null hypothesis is correct, E(F) = 1.0

6. How Does Power Analysis Work?
In the familiar F distribution below, 95% of the
values are below (distribution for df = 7,200)
F=2.0 represents cutoff for rejecting H0

7. The Noncentral F Distribution
If the null hypothesis is false, the Noncentral F distribution is needed. In the Noncentral F distribution below, 75% of the values are below Therefore, power = .25

8. A Larger Effect
In the Noncentral F distribution below, in which the effect is larger, 30% of the values are below Therefore power = .70