Statistical Power Analysis: A Simple and General Model for Traditional and Modern Hypothesis Tests

Cover
Half Title
Title Page
Copyright Page
Contents
Acknowledgments
Preface
	Changes in the New Edition
1. The Power of Statistical Tests
	The Structure of Statistical Tests
		What Determines the Outcomes of Statistical Tests?
		Effects of Sensitivity, Effect Size, and Decision Criteria on Power
	The Mechanics of Power Analysis
		Sensitivity and Power
		Effect Size and Power
		Decision Criteria and Power
		Power Analysis and the General Linear Model
	Statistical Power of Research in the Social and Behavioral Sciences
	Using Power Analysis
		Determining the Effect Size
		Determining the Desired Level of Power
		Applying Power Analysis
	Hypothesis Tests vs. Confidence Intervals
		Do We Really Need Null Hypotheses Tests or Power Analysis?
	What Can You Learn from a Null Hypothesis Test?
	Notes
2. A Simple and General Model for Power Analysis
	The General Linear Model, the F Statistic, and Effect Size
	The F Distribution and Power
		The F Statistic and Effect Size Measures
		The Noncentral F
	Using the Noncentral F Distribution to Assess Power
	Translating Common Statistics and ES Measures into F
		Transforming from F to PV
	Defining Large, Medium, and Small Effects
	Nonparametric and Robust Statistics
	From F to Power Analysis
	Analytic and Tabular Methods of Power Analysis
		Analytic Methods
		Power Tables
	Using the One-Stop F Table
	Simple and General Software for Power Analysis
	A Web-Based App for Power Analysis
	Notes
3. Power Analyses for Minimum-Effect Tests
	Nil Hypothesis Testing
	The Nil Hypothesis Is Almost Always Wrong
		The Nil Is a Point Hypothesis
		The Nil Hypothesis Is Impossibly Precise
		The Domain of Alternative Hypotheses Is Infinitely Large
		Nil Treatment Effects Exist Only in the World of Abstractions
	Implications of the Conclusion That the Nil Hypothesis Is Almost Always Wrong
	The Nil May Not Be True, but It Is Often Fairly Accurate
	Minimum-Effect Tests as Alternatives to Traditional Null Hypothesis Tests
		Minimum-Effect Tests Are Meaningful
		The Minimum-Effect Hypothesis Has a Reasonable Chance of Being True
	Testing the Hypothesis That Treatment Effects Are Negligible
		An Example
		Defining a Minimum Effect
		Power of Minimum-Effect Tests
	Using the One-Stop Tables to Assess Power to Test Minimum-Effect Hypotheses
		Testing Minimum-Effect Hypotheses (PV = .01)
		Testing Minimum-Effect Hypotheses (PV = .05)
		Using R Code and the Shiny Web App to Test Minimum-Effect Tests
	Type I Errors in Minimum-Effect Tests
	Notes
4. Using Power Analyses
	Estimating the Effect Size
		Inductive Methods
		Deductive Methods
		Effect Size Conventions
	Four Applications of Statistical Power Analysis
	Calculating Power
	Determining Sample Sizes
	Determining the Sensitivity of Studies
	Determining Appropriate Decision Criteria
		Balancing Risks in Choosing Significance Levels
		Should You Ever Worry about Type I Errors?
	Post-Hoc Power Analysis Should Be Avoided
	Notes
5. Correlation and Regression
	The Perils of Working with Large Samples
		Traditional versus Minimum-Effect Tests
		Power Estimation
	Multiple Regression
		Multiple Regression Models
		Hierarchical Regression Models
		Power Estimation
		Sample Size Estimation
	Power in Testing for Moderators
		Why Are Most Moderator Effects Small?
	Implications of Low Power in Tests for Moderators
	If You Understand Regression, You Will Understand (Almost) Everything
	Notes
6. t-Tests and the One-Way Analysis of Variance
	The t-Test
	Independent Groups t Test
		Estimating Power for This Study
		Traditional versus Minimum-Effect Tests
		Power Estimation
		Sample Size Estimation
	One-Tailed versus Two-Tailed Tests
	Repeated Measures or Dependent t-Test
	The Analysis of Variance
		Power Analysis
	Which Means Differ?
		The Least Significant Difference (LSD) Procedure
		Power for the LSD Procedure
		Ryan's Procedure
	Designing a One-Way ANOVA Study
	Notes
7. Multifactor ANOVA Designs
	The Factorial Analysis of Variance
		Different Questions Imply Different Levels of Power
		Estimating Power in Multifactor ANOVA
		Estimating PV from F in a Multifactor ANOVA
	Factorial ANOVA from Means and Standard Deviations
		Power Estimation
	General Design Principles for Multifactor ANOVA
	Fixed, Mixed, and Random Models
	Note
8. Studies with Multiple Observations for Each Subject: Repeated-Measures and Multivariate Analyses
	Randomized Block ANOVA: An Introduction to Repeated Measures Designs
	Independent Groups versus Repeated Measures
		Why Doesn't Everyone Use Repeated-Measures Designs?
	Complexities in Estimating Power in Repeated-Measures Designs
	Mixed Designs: Split-Plot Factorial ANOVA
	Power for Within-Subject versus Between-Subject Factors
	Split-Plot Designs with Multiple Repeated-Measures Factors
	The Multivariate Analysis of Variance
9. Power Analysis for Multilevel Studies
	What Do Multilevel Analyses Tell You?
	The Multilevel Equation
	Are Multilevel Models Necessary? - The Intraclass Correlation
	An Illustration of Multilevel Analysis
	Remember, It's All Regression
	Effect Sizes in Multilevel Analysis
	Power for What?
	Using Changes in Model Fit as a Basis for Power Analysis in Multilevel Modeling
		The Ambiguity of N
		Power Analysis for our Quantitative Ability Study
	Sample Size - Some General Guidance
	Notes
10. The Implications of Power Analyses
	Tests of the Traditional Null Hypothesis
		You Cannot Have Too Much Power
		Maximizing Power: The Hard Way and the Easy Way
		Tests with Insufficient Power Should Never Be Done
	Tests of Minimum-Effect Hypotheses
		Accepting the Null
		Balancing Errors in Testing Minimum-Effect Hypotheses
	Power Analysis: Benefits, Costs, and Implications for Hypothesis Testing
	Direct Benefits of Power Analysis
		Planning Research
		Interpreting Research
	Indirect Benefits of Power Analysis
		Large Samples, Sensitive Procedures
		Focus on Effect Size
	Costs Associated with Power Analysis
	Implications of Power Analysis: Can Power Be Too High?
	Note
Appendix A. Translating Common Statistics into F-Equivalent and PV Values
Appendix B. One-Stop F Table
	R Code Used to Generate One-Stop F Table
Appendix C. One-Stop PV Table
	R Code Used to Generate One-Stop PV Table
Appendix D. dferr Needed for Power of .80 for Nil and Minimum-Effect Hypothesis Tests
	R Text for generating the dferr needed to test the traditional Null Hypothesis with power = .80, α = .05
	R Text for generating the dferr needed to test the Hypothesis that Treatments account for 1% or less of the variance with power =.80, α =.05
References
Index