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Published byGeoffrey Arron Simpson Modified over 9 years ago
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Power Analysis for Traditional and Modern Hypothesis Tests
Kevin R. Murphy Pennsylvania State University
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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
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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
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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?
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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
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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
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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
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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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