Statistical Power Analysis, 5th Edition

Statistical Power Analysis, 5th Edition

by Brett Myors, Kevin R. Murphy
Released March 2023
Publisher(s): Routledge
ISBN: 9781000843255

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Book description

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.

Table of contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Contents
  6. Acknowledgments
  7. Preface
    1. Changes in the New Edition
  8. 1 The Power of Statistical Tests
    1. The Structure of Statistical Tests
      1. What Determines the Outcomes of Statistical Tests?
      2. Effects of Sensitivity, Effect Size, and Decision Criteria on Power
    2. The Mechanics of Power Analysis
      1. Sensitivity and Power
      2. Effect Size and Power
      3. Decision Criteria and Power
      4. Power Analysis and the General Linear Model
    3. Statistical Power of Research in the Social and Behavioral Sciences
    4. Using Power Analysis
      1. Determining the Effect Size
      2. Determining the Desired Level of Power
      3. Applying Power Analysis
    5. Hypothesis Tests vs. Confidence Intervals
      1. Do We Really Need Null Hypotheses Tests or Power Analysis?
    6. What Can You Learn from a Null Hypothesis Test?
    7. Notes
  9. 2 A Simple and General Model for Power Analysis
    1. The General Linear Model, the F Statistic, and Effect Size
    2. The F Distribution and Power
      1. The F Statistic and Effect Size Measures
      2. The Noncentral F
    3. Using the Noncentral F Distribution to Assess Power
    4. Translating Common Statistics and ES Measures into F
      1. Transforming from F to PV
    5. Defining Large, Medium, and Small Effects
    6. Nonparametric and Robust Statistics
    7. From F to Power Analysis
    8. Analytic and Tabular Methods of Power Analysis
      1. Analytic Methods
      2. Power Tables
    9. Using the One-Stop F Table
    10. Simple and General Software for Power Analysis
    11. A Web-Based App for Power Analysis
    12. Notes
  10. 3 Power Analyses for Minimum-Effect Tests
    1. Nil Hypothesis Testing
    2. The Nil Hypothesis Is Almost Always Wrong
      1. The Nil Is a Point Hypothesis
      2. The Nil Hypothesis Is Impossibly Precise
      3. The Domain of Alternative Hypotheses Is Infinitely Large
      4. Nil Treatment Effects Exist Only in the World of Abstractions
    3. Implications of the Conclusion That the Nil Hypothesis Is Almost Always Wrong
    4. The Nil May Not Be True, but It Is Often Fairly Accurate
    5. Minimum-Effect Tests as Alternatives to Traditional Null Hypothesis Tests
      1. Minimum-Effect Tests Are Meaningful
      2. The Minimum-Effect Hypothesis Has a Reasonable Chance of Being True
    6. Testing the Hypothesis That Treatment Effects Are Negligible
      1. An Example
      2. Defining a Minimum Effect
      3. Power of Minimum-Effect Tests
    7. Using the One-Stop Tables to Assess Power to Test Minimum-Effect Hypotheses
      1. Testing Minimum-Effect Hypotheses (PV = .01)
      2. Testing Minimum-Effect Hypotheses (PV = .05)
      3. Using R Code and the Shiny Web App to Test Minimum-Effect Tests
    8. Type I Errors in Minimum-Effect Tests
    9. Notes
  11. 4 Using Power Analyses
    1. Estimating the Effect Size
      1. Inductive Methods
      2. Deductive Methods
      3. Effect Size Conventions
    2. Four Applications of Statistical Power Analysis
    3. Calculating Power
    4. Determining Sample Sizes
    5. Determining the Sensitivity of Studies
    6. Determining Appropriate Decision Criteria
      1. Balancing Risks in Choosing Significance Levels
      2. Should You Ever Worry about Type I Errors?
    7. Post-Hoc Power Analysis Should Be Avoided
    8. Notes
  12. 5 Correlation and Regression
    1. The Perils of Working with Large Samples
      1. Traditional versus Minimum-Effect Tests
      2. Power Estimation
    2. Multiple Regression
      1. Multiple Regression Models
      2. Hierarchical Regression Models
      3. Power Estimation
      4. Sample Size Estimation
    3. Power in Testing for Moderators
      1. Why Are Most Moderator Effects Small?
    4. Implications of Low Power in Tests for Moderators
    5. If You Understand Regression, You Will Understand (Almost) Everything
    6. Notes
  13. 6 t-Tests and the One-Way Analysis of Variance
    1. The t-Test
    2. Independent Groups t Test
      1. Estimating Power for This Study
      2. Traditional versus Minimum-Effect Tests
      3. Power Estimation
      4. Sample Size Estimation
    3. One-Tailed versus Two-Tailed Tests
    4. Repeated Measures or Dependent t-Test
    5. The Analysis of Variance
      1. Power Analysis
    6. Which Means Differ?
      1. The Least Significant Difference (LSD) Procedure
      2. Power for the LSD Procedure
      3. Ryan's Procedure
    7. Designing a One-Way ANOVA Study
    8. Notes
  14. 7 Multifactor ANOVA Designs
    1. The Factorial Analysis of Variance
      1. Different Questions Imply Different Levels of Power
      2. Estimating Power in Multifactor ANOVA
      3. Estimating PV from F in a Multifactor ANOVA
    2. Factorial ANOVA from Means and Standard Deviations
      1. Power Estimation
    3. General Design Principles for Multifactor ANOVA
    4. Fixed, Mixed, and Random Models
    5. Note
  15. 8 Studies with Multiple Observations for Each Subject: Repeated-Measures and Multivariate Analyses
    1. Randomized Block ANOVA: An Introduction to Repeated Measures Designs
    2. Independent Groups versus Repeated Measures
      1. Why Doesn't Everyone Use Repeated-Measures Designs?
    3. Complexities in Estimating Power in Repeated-Measures Designs
    4. Mixed Designs: Split-Plot Factorial ANOVA
    5. Power for Within-Subject versus Between-Subject Factors
    6. Split-Plot Designs with Multiple Repeated-Measures Factors
    7. The Multivariate Analysis of Variance
  16. 9 Power Analysis for Multilevel Studies
    1. What Do Multilevel Analyses Tell You?
    2. The Multilevel Equation
    3. Are Multilevel Models Necessary? – The Intraclass Correlation
    4. An Illustration of Multilevel Analysis
    5. Remember, It's All Regression
    6. Effect Sizes in Multilevel Analysis
    7. Power for What?
    8. Using Changes in Model Fit as a Basis for Power Analysis in Multilevel Modeling
      1. The Ambiguity of N
      2. Power Analysis for our Quantitative Ability Study
    9. Sample Size – Some General Guidance
    10. Notes
  17. 10 The Implications of Power Analyses
    1. Tests of the Traditional Null Hypothesis
      1. You Cannot Have Too Much Power
      2. Maximizing Power: The Hard Way and the Easy Way
      3. Tests with Insufficient Power Should Never Be Done
    2. Tests of Minimum-Effect Hypotheses
      1. Accepting the Null
      2. Balancing Errors in Testing Minimum-Effect Hypotheses
    3. Power Analysis: Benefits, Costs, and Implications for Hypothesis Testing
    4. Direct Benefits of Power Analysis
      1. Planning Research
      2. Interpreting Research
    5. Indirect Benefits of Power Analysis
      1. Large Samples, Sensitive Procedures
      2. Focus on Effect Size
    6. Costs Associated with Power Analysis
    7. Implications of Power Analysis: Can Power Be Too High?
    8. Note
  18. Appendix A: Translating Common Statistics into F-Equivalent and PV Values
  19. Appendix B: One-Stop F Table
    1. R Code Used to Generate One-Stop F Table
  20. Appendix C: One-Stop PV Table
    1. R Code Used to Generate One-Stop PV Table
  21. Appendix D: dferr Needed for Power of .80 for Nil and Minimum-Effect Hypothesis Tests
    1. R Text for generating the dferr needed to test the traditional Null Hypothesis with power = .80, α = .05
    2. 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
  22. References
  23. Index

Product information

  • Title: Statistical Power Analysis, 5th Edition
  • Author(s): Brett Myors, Kevin R. Murphy
  • Release date: March 2023
  • Publisher(s): Routledge
  • ISBN: 9781000843255