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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