Analysis of Covariance and Alternatives

Bradley E. Huitema, PhD, is Professor of Psychology in the Industrial/Organizational Program at Western Michigan University. He also serves as a statistical consultant in the behavioral sciences for Western Michigan University and Children's Memorial Hospital, the pediatric training center of the Northwestern University Feinberg School of Medicine. Dr. Huitema has published extensively in his areas of research interest, which include applied time series analysis, single-case and quasi-experimental design, and the evaluation of health practices.

• Preface xv PART I BASIC EXPERIMENTAL DESIGN AND ANALYSIS1 Review of Basic Statistical Methods 31.1 Introduction, 31.2 Elementary Statistical Inference, 41.3 Elementary Statistical Decision Theory, 71.4 Effect Size, 101.5 Measures of Association, 141.6 A Practical Alternative to Effect Sizes and Measures of Association That Is Relevant to the Individual: p(YTx > YControl), 171.7 Generalization of Results, 191.8 Control of Nuisance Variation, 201.9 Software, 221.10 Summary, 242 Review of Simple Correlated Samples Designs and Associated Analyses 252.1 Introduction, 252.2 Two-Level Correlated Samples Designs, 252.3 Software, 322.4 Summary, 323 ANOVA Basics for One-Factor Randomized Group, Randomized Block, and Repeated Measurement Designs 353.1 Introduction, 353.2 One-Factor Randomized Group Design and Analysis, 353.3 One-Factor Randomized Block Design and Analysis, 513.4 One-Factor Repeated Measurement Design and Analysis, 563.5 Summary, 60PART II ESSENTIALS OF REGRESSION ANALYSIS4 Simple Linear Regression 634.1 Introduction, 634.2 Comparison of Simple Regression and ANOVA, 634.3 Regression Estimation, Inference, and Interpretation, 684.4 Diagnostic Methods: Is the Model Apt?, 804.5 Summary, 825 Essentials of Multiple Linear Regression 855.1 Introduction, 855.2 Multiple Regression: Two-Predictor Case, 865.3 General Multiple Linear Regression: m Predictors, 1055.4 Alternatives to OLS Regression, 1155.5 Summary, 119PART III ESSENTIALS OF SIMPLE AND MULTIPLE ANCOVA6 One-Factor Analysis of Covariance 1236.1 Introduction, 1236.2 Analysis of Covariance Model, 1276.3 Computation and Rationale, 1286.4 Adjusted Means, 1336.5 ANCOVA Example 1: Training Effects, 1406.6 Testing Homogeneity of Regression Slopes, 1446.7 ANCOVA Example 2: Sexual Activity Reduces Lifespan, 1486.8 Software, 1506.9 Summary, 1577 Analysis of Covariance Through Linear Regression 1597.1 Introduction, 1597.2 Simple Analysis of Variance Through Linear Regression, 1597.3 Analysis of Covariance Through Linear Regression, 1727.4 Computation of Adjusted Means, 1777.5 Similarity of ANCOVA to Part and Partial Correlation Methods, 1777.6 Homogeneity of Regression Test Through General Linear Regression, 1787.7 Summary, 1798 Assumptions and Design Considerations 1818.1 Introduction, 1818.2 Statistical Assumptions, 1828.3 Design and Data Issues Related to the Interpretation of ANCOVA, 2008.4 Summary, 2139 Multiple Comparison Tests and Confidence Intervals 2159.1 Introduction, 2159.2 Overview of Four Multiple Comparison Procedures, 2159.3 Tests on All Pairwise Comparisons: Fisher–Hayter, 2169.4 All Pairwise Simultaneous Confidence Intervals and Tests: Tukey–Kramer, 2199.5 Planned Pairwise and Complex Comparisons: Bonferroni, 2229.6 Any or All Comparisons: Scheff´e, 2259.7 Ignore Multiple Comparison Procedures?, 2279.8 Summary, 22810 Multiple Covariance Analysis 22910.1 Introduction, 22910.2 Multiple ANCOVA Through Multiple Regression, 23210.3 Testing Homogeneity of Regression Planes, 23410.4 Computation of Adjusted Means, 23610.5 Multiple Comparison Procedures for Multiple ANCOVA, 23710.6 Software: Multiple ANCOVA and Associated Tukey–Kramer Multiple Comparison Tests Using Minitab, 24310.7 Summary, 246PART IV ALTERNATIVES FOR ASSUMPTION DEPARTURES11 Johnson–Neyman and Picked-Points Solutions for Heterogeneous Regression 24911.1 Introduction, 24911.2 J–N and PPA Methods for Two Groups, One Covariate, 25111.3 A Common Method That Should Be Avoided, 26911.4 Assumptions, 27011.5 Two Groups, Multiple Covariates, 27211.6 Multiple Groups, One Covariate, 27711.7 Any Number of Groups, Any Number of Covariates, 27811.8 Two-Factor Designs, 27811.9 Interpretation Problems, 27911.10 Multiple Dependent Variables, 28111.11 Nonlinear Johnson-Neyman Analysis, 28211.12 Correlated Samples, 28211.13 Robust Methods, 28211.14 Software, 28311.15 Summary, 28312 Nonlinear ANCOVA 28512.1 Introduction, 28512.2 Dealing with Nonlinearity, 28612.3 Computation and Example of Fitting Polynomial Models, 28812.4 Summary, 29513 Quasi-ANCOVA: When Treatments Affect Covariates 29713.1 Introduction, 29713.2 Quasi-ANCOVA Model, 29813.3 Computational Example of Quasi-ANCOVA, 30013.4 Multiple Quasi-ANCOVA, 30413.5 Computational Example of Multiple Quasi-ANCOVA, 30413.6 Summary, 30814 Robust ANCOVA/Robust Picked Points 31114.1 Introduction, 31114.2 Rank ANCOVA, 31114.3 Robust General Linear Model, 31414.4 Summary, 32015 ANCOVA for Dichotomous Dependent Variables 32115.1 Introduction, 32115.2 Logistic Regression, 32315.3 Logistic Model, 32415.4 Dichotomous ANCOVA Through Logistic Regression, 32515.5 Homogeneity of Within-Group Logistic Regression, 32815.6 Multiple Covariates, 32815.7 Multiple Comparison Tests, 33015.8 Continuous Versus Forced Dichotomy Results, 33115.9 Summary, 33116 Designs with Ordered Treatments and No Covariates 33316.1 Introduction, 33316.2 Qualitative, Quantitative, and Ordered Treatment Levels, 33316.3 Parametric Monotone Analysis, 33716.4 Nonparametric Monotone Analysis, 34616.5 Reversed Ordinal Logistic Regression, 35016.6 Summary, 35317 ANCOVA for Ordered Treatments Designs 35517.1 Introduction, 35517.2 Generalization of the Abelson–Tukey Method to Include One Covariate, 35517.3 Abelson–Tukey: Multiple Covariates, 35817.4 Rank-Based ANCOVA Monotone Method, 35917.5 Rank-Based Monotone Method with Multiple Covariates, 36217.6 Reversed Ordinal Logistic Regression with One or More Covariates, 36217.7 Robust R-Estimate ANCOVA Monotone Method, 36317.8 Summary, 364PART V SINGLE-CASE DESIGNS18 Simple Interrupted Time-Series Designs 36718.1 Introduction, 36718.2 Logic of the Two-Phase Design, 37018.3 Analysis of the Two-Phase (AB) Design, 37118.4 Two Strategies for Time-Series Regression Intervention Analysis, 37418.5 Details of Strategy II, 37518.6 Effect Sizes, 38518.7 Sample Size Recommendations, 38918.8 When the Model Is Too Simple, 39318.9 Summary, 39419 Examples of Single-Case AB Analysis 40319.1 Introduction, 40319.2 Example I: Cancer Death Rates in the United Kingdom, 40319.3 Example II: Functional Activity, 41119.4 Example III: Cereal Sales, 41419.5 Example IV: Paracetamol Poisoning, 42419.6 Summary, 43020 Analysis of Single-Case Reversal Designs 43320.1 Introduction, 43320.2 Statistical Analysis of Reversal Designs, 43420.3 Computational Example: Pharmacy Wait Time, 44120.4 Summary, 45221 Analysis of Multiple-Baseline Designs 45321.1 Introduction, 45321.2 Case I Analysis: Independence of Errors Within and Between Series, 45521.3 Case II Analysis: Autocorrelated Errors Within Series, Independence Between Series, 46121.4 Case III Analysis: Independent Errors Within Series, Cross-Correlation Between Series, 46121.5 Intervention Versus Control Series Design, 46721.6 Summary, 471PART VI ANCOVA EXTENSIONS22 Power Estimation 47522.1 Introduction, 47522.2 Power Estimation for One-Factor ANOVA, 47522.3 Power Estimation for ANCOVA, 48022.4 Power Estimation for Standardized Effect Sizes, 48222.5 Summary, 48223 ANCOVA for Randomized-Block Designs 48323.1 Introduction, 48323.2 Conventional Design and Analysis Example, 48423.3 Combined Analysis (ANCOVA and Blocking Factor), 48623.4 Summary, 48824 Two-Factor Designs 48924.1 Introduction, 48924.2 ANCOVA Model and Computation for Two-Factor Designs, 49424.3 Multiple Comparison Tests for Adjusted Marginal Means, 51224.4 Two-Factor ANOVA and ANCOVA for Repeated-Measurement Designs, 51924.5 Summary, 53025 Randomized Pretest–Posttest Designs 53125.1 Introduction, 53125.2 Comparison of Three ANOVA Methods, 53125.3 ANCOVA for Pretest–Posttest Designs, 53425.4 Summary, 53926 Multiple Dependent Variables 54126.1 Introduction, 54126.2 Uncorrected Univariate ANCOVA, 54326.3 Bonferroni Method, 54426.4 Multivariate Analysis of Covariance (MANCOVA), 54426.5 MANCOVA Through Multiple Regression Analysis: Two Groups Only, 55326.6 Issues Associated with Bonferroni F and MANCOVA, 55426.7 Alternatives to Bonferroni and MANCOVA, 55526.8 Example Analyses Using Minitab, 55726.9 Summary, 564PART VII QUASI-EXPERIMENTS AND MISCONCEPTIONS27 Nonrandomized Studies: Measurement Error Correction 56727.1 Introduction, 56727.2 Effects of Measurement Error: Randomized-Group Case, 56827.3 Effects of Measurement Error in Exposure and Covariates: Nonrandomized Design, 56927.4 Measurement Error Correction Ideas, 57027.5 Summary, 57328 Design and Analysis of Observational Studies 57528.1 Introduction, 57528.2 Design of Nonequivalent Group/Observational Studies, 57928.3 Final (Outcome) Analysis, 58728.4 Propensity Design Advantages, 59228.5 Evaluations of ANCOVA Versus Propensity-Based Approaches, 59428.6 Adequacy of Observational Studies, 59628.7 Summary, 59729 Common ANCOVA Misconceptions 59929.1 Introduction, 59929.2 SSAT Versus SSIntuitive AT: Single Covariate Case, 59929.3 SSAT Versus SSIntuitive AT: Multiple Covariate Case, 60129.4 ANCOVA Versus ANOVA on Residuals, 60629.5 ANCOVA Versus Y/X Ratio, 60629.6 Other Common Misconceptions, 60729.7 Summary, 60830 Uncontrolled Clinical Trials 60930.1 Introduction, 60930.2 Internal Validity Threats Other Than Regression, 61030.3 Problems with Conventional Analyses, 61330.4 Controlling Regression Effects, 61530.5 Naranjo–Mckean Dual Effects Model, 61630.6 Summary, 617Appendix: Statistical Tables 619References 643Index 655