Effect Sizes and Power Analyses - Statistics
Effect Sizes and Power Analyses
Nathaniel E. Helwig Assistant Professor of Psychology and Statistics
University of Minnesota (Twin Cities)
Updated 04-Jan-2017
Nathaniel E. Helwig (U of Minnesota)
Effect Sizes and Power Analyses
Updated 04-Jan-2017 : Slide 1
Copyright
Copyright ? 2017 by Nathaniel E. Helwig
Nathaniel E. Helwig (U of Minnesota)
Effect Sizes and Power Analyses
Updated 04-Jan-2017 : Slide 2
Outline of Notes
1) Effect Sizes: Definition and Overview Correlation ES Family Some Examples Difference ES Family Some Examples
2) Power Analyses: Definition and Overview One sample t test Two sample t test One-Way ANOVA Multiple regression
Nathaniel E. Helwig (U of Minnesota)
Effect Sizes and Power Analyses
Updated 04-Jan-2017 : Slide 3
Effect Sizes
Effect Sizes
Nathaniel E. Helwig (U of Minnesota)
Effect Sizes and Power Analyses
Updated 04-Jan-2017 : Slide 4
Effect Sizes Definition and Overview
What is an Effect Size?
An effect size (ES) measures the strength of some phenomenon: Correlation coefficient Regression slope coefficient Difference between means
ES are related to statistical tests, and are crucial for Power analyses (see later slides) Sample size planning (needed for grants) Meta-analyses (which combine ES from many studies)
Nathaniel E. Helwig (U of Minnesota)
Effect Sizes and Power Analyses
Updated 04-Jan-2017 : Slide 5
Effect Sizes Definition and Overview
Population versus Sample Effect Sizes
Like many other concepts in statistics, we distinguish between ES in the population versus ES in a given sample of data:
Correlation: versus r Regression: versus ^ Mean Difference: (?1 - ?2) versus (x?1 - x?2)
Typically reserve Greek letter for population parameters (ES) and Roman letter (or Greek-hat) to denote sample estimates.
Nathaniel E. Helwig (U of Minnesota)
Effect Sizes and Power Analyses
Updated 04-Jan-2017 : Slide 6
Effect Sizes Definition and Overview
Effect Sizes versus Test Statistics
Sample ES measures are related to (but distinct from) test statistics. ES measures strength of relationship TS provides evidence against H0
Unlike test statistics, measures of ES are not directly related to significance () levels or null hypotheses.
Nathaniel E. Helwig (U of Minnesota)
Effect Sizes and Power Analyses
Updated 04-Jan-2017 : Slide 7
Effect Sizes Definition and Overview
Standardized versus Unstandardized Effect Sizes
Standardized ES are unit free Correlation coefficient Standardized regression coefficient Cohen's d
Unstandardized ES depend on unit of measurement Covariance Regression coefficient (unstandardized) Mean difference
Nathaniel E. Helwig (U of Minnesota)
Effect Sizes and Power Analyses
Updated 04-Jan-2017 : Slide 8
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