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Power Analysis for Traditional and Modern Hypothesis Tests

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Presentation on theme: "Power Analysis for Traditional and Modern Hypothesis Tests"— Presentation transcript:

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


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