Statistical Power Analysis explains the key concepts in statistical power analysis and illustrates their application in both tests of traditional null hypotheses. It provides readers with the tools to understand and perform power analyses for virtually all the statistical methods used in the social and behavioral sciences.
Statistical Power Analysis explains the key concepts in statistical power analysis and illustrates their application in both tests of traditional null hypotheses (that treatments or interventions have no effect in the population) and in tests of the minimum-effect hypotheses (that the population effects of treatments or interventions are so small that they can be safely treated as unimportant). It provides readers with the tools to understand and perform power analyses for virtually all the statistical methods used in the social and behavioral sciences.
Brett Myors and Kevin Murphy apply the latest approaches of power analysis to both null hypothesis and minimum-effect testing using the same basic unified model. This book starts with a review of the key concepts that underly statistical power. It goes on to show how to perform and interpret power analyses, and the ways to use them to diagnose and plan research. We discuss the uses of power analysis in correlation and regression, in the analysis of experimental data, and in multilevel studies. This edition includes new material and new power software. The programs used for power analysis in this book have been re-written in R, a language that is widely used and freely available. The authors include R codes for all programs, and we have also provided a web-based app that allows users who are not comfortable with R to perform a wide range of analyses using any computer or device that provides access to the web.
Statistical Power Analysis helps readers design studies, diagnose existing studies, and understand why hypothesis tests come out the way they do. The fifth edition includes updates to all chapters to accommodate the most current scholarship, as well as recalculations of all examples. This book is intended for graduate students and faculty in the behavioral and social sciences; researchers in other fields will find the concepts and methods laid out here valuable and applicable to studies in many domains.
1. The Power of Statistical Tests 1.1 The Structure of Statistical Tests
1.1.1 Null Hypotheses vs. Nil Hypotheses1.1.2 Understanding Conditional
Probability 1.2 The Mechanics of Power Analysis 1.2.1 Understanding Sampling
1.2.2 Distributions d vs. delta vs. g 1.3 Statistical Power of Research in
the Social and Behavioral Sciences Power and the Replication Crisis 1.4 Using
Power Analysis The Meaning of Statistical Significance 1.5 Hypothesis Tests
vs. Confidence Intervals Accuracy in Parameter Estimation 1.6 What Can We
Learn from a Null Hypothesis Test? 1.7 Summary
2. A Simple and General Model
for Power Analysis 2.1 The General Linear Model, the F Statistic, and Effect
Size 2.1.1 Effect Size 2.2 Understanding Linear Models 2.3 The F Distribution
and Power 2.3.1 Confidence Intervals for PV and d 2.4 Using the Noncentral F
Distribution to Assess Power 2.5 Translating Common Statistics and ES
Measures into F 2.5.1 Worked Example Hierarchical Regression 2.5.2 Worked
Examples Using the d Statistic 2.6 Defining Large, Medium and Small Effects
2.7 Nonparametric and Robust Statistics 2.8 From F to Power Analysis 2.9
Analytic and Tabular Methods of Power Analysis 2.10 Using the One-Stop F
Table 2.11 Simple and General Software for Power Analysis 2.12 R code for
Power Analysis for Traditional and Modern Hypothesis Tests 2.13 Summary
3.
Power Analyses for Minimum-Effect Tests 3.1 Nil Hypothesis Testing 3.2 The
Nil Hypothesis is Almost Always Wrong 3.2.1 Polar Bear Traps: Why Type I
Error Control is a Bad Investment 3.3 The Nil may not be True, but it is
Often Fairly Accurate 3.4 Minimum-Effect tests as Alternatives to Traditional
Null Hypothesis Tests 3.5 Sometimes a Point Hypothesis is also a Range
Hypothesis 3.6 How do you Know the Effect Size? 3.7 Testing the Hypothesis
that Treatment Effects are Negligible 3.8 Using the One-Stop Tables to Assess
Power for Minimum-Effect Tests 3.9 A Worked Example of Minimum-Effect Testing
3.10 Type I Errors in Minimum-Effect Tests 3.11 Summary
4. Using Power
Analyses 4.1 Estimating the Effect Size 4.2 Using the One-Stop Tables and the
R Code/Shiny Web app to Perform Power Analyses 4.2.1 Worked Example:
Calculating F-equivalents and Power 4.3 Four Applications of Statistical
Power Analysis 4.4 Calculating Power 4.5 Determining Sample Sizes 4.6 A Few
Simple Approximations for Determining Sample Size Needed 4.7 Determining the
Sensitivity of Studies 4.8 Determining Appropriate Decision Criteria 4.8.1
Finding a Sensible Alpha 4.9 Post-Hoc Power Analysis Should be Avoided 4.10
Summary
5. Correlation and Regression 5.1 The Perils of Working with Large
Samples 5.2 Multiple Regression 5.2.1 Testing Minimum-Effect Hypotheses in
Multiple Regression 5.3 Power in Testing for Moderators 5.3.1 Power Analysis
for Moderators 5.4 Implications of Low Power in Tests for Moderators 5.5 If
You Understand Regression, You Will Understand (Almost) Everything 5.6
Summary
6. t-Tests and the One-Way Analysis of Variance 6.1 The t Test 6.2
The t distribution vs the Normal Distribution 6.3 Independent Groups t Test
6.3.1 Determining an Appropriate Sample Size 6.4 One- Versus Two Tailed Tests
6.4.1 Re-analysis of Smoking Reduction Treatments: One-Tailed Tests 6.5
Repeated Measures or Dependent t Test 6.6 The Analysis of Variance 6.6.1
Retrieving Effect Size Information from F Ratios 6.7 Which Means Differ? 6.8
Designing a One-way ANOVA Study 6.9 Summary
7. Multi-Factor ANOVA Designs 7.1
The Factorial Analysis of Variance 7.1.2 Calculating PV from F and df in
Multi-Factor ANOVA: Worked Example 7.2 Factorial ANOVA from Means and
Standard Deviations 7.2.1 Reconstructing ANOVA results from descriptive
statistics: A Worked Example 7.2.2 Eta squared vs. partial eta squared 7.3
General Design Principles for Multifactor ANOVA 7.4 Fixed, Mixed and Random
Models 7.5 Summary
8. Studies with Multiple Observations for Each Subject:
Repeated-Measures and Multivariate Analyses 8.1 Randomized Block ANOVA: An
Introduction to Repeated Measures Designs 8.2 Independent Groups versus
Repeated Measures 8.3 Complexities in Estimating Power in Repeated-Measures
Designs 8.4 Mixed Designs: Split Plot Factorial ANOVA 8.4.1 Estimating Power
for a Split Plot Factorial ANOVA 8.5 Power for Within-Subject vs.
Between-Subject Factors 8.6 Split-Plot Designs with Multiple
Repeated-Measures Factors 8.7 The Multivariate Analysis of Variance 8.8
Summary
9. Power Analysis for Multilevel Studies 9.1 What do Multilevel
Analyses Tell You? 9.2 The Multilevel Equation 9.3 Are Multilevel Models
Necessary? The Intraclass Correlation 9.4 An Illustration of Multilevel
Analysis 9.5 Remember, Its All Regression 9.6 Effect Sizes in Multilevel
Analysis 9.6.1 R code for obtaining R2 and pseudo-R2 estimates 9.7 Power for
What? 9.8 Using Changes in Model Fit as a Basis for Power Analysis in
Multilevel Modeling 9.9 R code for calculating critical chi squared values
and power for minimum-effect comparisons of models 9.10 Sample Size Some
General Guidance 9.11 Summary
10. The Implications of Power Analyses 10.1
Tests of the Traditional Null Hypothesis 10.2 Tests of Minimum-Effect
Hypotheses 10.2.1 Type I Errors in Minimum-Effect Tests Revisited 10.2.2
Statistical Power and the Replication Crisis 10.3 Power Analysis: Benefits,
Costs, and Implications for Hypothesis Testing 10.4 Direct Benefits of Power
Analysis 10.4.1 Is HARKing a Serious Problem? 10.5 Indirect Benefits of Power
Analysis 10.6 Costs Associated With Power Analysis 10.7 Implications of Power
Analysis: Can Power be too High? 10.8 Summary
11. Appendix A Translating
Statistics into F and PV Values 12 Appendix B - One Stop F Table
13. Appendix
C- One Stop PV Table
14. Appendix D dferr Needed for Power of .80 for Nil
and Minimum-Effect Hypothesis Tests
Kevin Murphy is a professor emeritus, University of Limerick, and an Organizational Psychologist. He is an author and editor of over 13 books and over 200 articles and chapters, in areas ranging from data analysis and research design to performance appraisal and performance management
Brett Myors received his PhD in Psychology from University of New South Wales, with a Postdoctoral appointment at Colorado State University. He served as director of organisational psychology at Griffith University and has published methodological research in several leading journals. He currently resides in the United Kingdom.
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