The Analysis of Covariance and Alternatives -- Contents -- Preface -- PART I BASIC EXPERIMENTAL DESIGN AND ANALYSIS -- 1 Review of Basic Statistical Methods -- 1.1 Introduction -- 1.2 Elementary Statistical Inference -- 1.3 Elementary Statistical Decision Theory -- 1.4 Effect Size -- 1.5 Measures of Association -- 1.6 A Practical Alternative to Effect Sizes and Measures of Association That Is Relevant to the Individual: p(YTx > YControl) -- 1.7 Generalization of Results -- 1.8 Control of Nuisance Variation -- 1.9 Software -- 1.10 Summary -- 2 Review of Simple Correlated Samples Designs and Associated Analyses -- 2.1 Introduction -- 2.2 Two-Level Correlated Samples Designs -- 2.3 Software -- 2.4 Summary -- 3 ANOVA Basics for One-Factor Randomized Group, Randomized Block, and Repeated Measurement Designs -- 3.1 Introduction -- 3.2 One-Factor Randomized Group Design and Analysis -- 3.3 One-Factor Randomized Block Design and Analysis -- 3.4 One-Factor Repeated Measurement Design and Analysis -- 3.5 Summary -- PART II ESSENTIALS OF REGRESSION ANALYSIS -- 4 Simple Linear Regression -- 4.1 Introduction -- 4.2 Comparison of Simple Regression and ANOVA -- 4.3 Regression Estimation, Inference, and Interpretation -- 4.4 Diagnostic Methods: Is the Model Apt? -- 4.5 Summary -- 5 Essentials of Multiple Linear Regression -- 5.1 Introduction -- 5.2 Multiple Regression: Two-Predictor Case -- 5.3 General Multiple Linear Regression: m Predictors -- 5.4 Alternatives to OLS Regression -- 5.5 Summary -- PART III ESSENTIALS OF SIMPLE AND MULTIPLE ANCOVA -- 6 One-Factor Analysis of Covariance -- 6.1 Introduction -- 6.2 Analysis of Covariance Model -- 6.3 Computation and Rationale -- 6.4 Adjusted Means -- 6.5 ANCOVA Example 1: Training Effects -- 6.6 Testing Homogeneity of Regression Slopes -- 6.7 ANCOVA Example 2: Sexual Activity Reduces Lifespan -- 6.8 Software.

6.9 Summary -- 7 Analysis of Covariance Through Linear Regression -- 7.1 Introduction -- 7.2 Simple Analysis of Variance Through Linear Regression -- 7.3 Analysis of Covariance Through Linear Regression -- 7.4 Computation of Adjusted Means -- 7.5 Similarity of ANCOVA to Part and Partial Correlation Methods -- 7.6 Homogeneity of Regression Test Through General Linear Regression -- 7.7 Summary -- 8 Assumptions and Design Considerations -- 8.1 Introduction -- 8.2 Statistical Assumptions -- 8.3 Design and Data Issues Related to the Interpretation of ANCOVA -- 8.4 Summary -- 9 Multiple Comparison Tests and Confidence Intervals -- 9.1 Introduction -- 9.2 Overview of Four Multiple Comparison Procedures -- 9.3 Tests on All Pairwise Comparisons: Fisher-Hayter -- 9.4 All Pairwise Simultaneous Confidence Intervals and Tests: Tukey-Kramer -- 9.5 Planned Pairwise and Complex Comparisons: Bonferroni -- 9.7 Ignore Multiple Comparison Procedures? -- 9.8 Summary -- 10 Multiple Covariance Analysis -- 10.1 Introduction -- 10.2 Multiple ANCOVA Through Multiple Regression -- 10.3 Testing Homogeneity of Regression Planes -- 10.4 Computation of Adjusted Means -- 10.5 Multiple Comparison Procedures for Multiple ANCOVA -- 10.6 Software: Multiple ANCOVA and Associated Tukey-Kramer Multiple Comparison Tests Using Minitab -- 10.7 Summary -- PART IV ALTERNATIVES FOR ASSUMPTION DEPARTURES -- 11 Johnson-Neyman and Picked-Points Solutions for Heterogeneous Regression -- 11.1 Introduction -- 11.2 J-N and PPA Methods for Two Groups, One Covariate -- 11.3 A Common Method That Should Be Avoided -- 11.4 Assumptions -- 11.5 Two Groups, Multiple Covariates -- 11.6 Multiple Groups, One Covariate -- 11.7 Any Number of Groups, Any Number of Covariates -- 11.8 Two-Factor Designs -- 11.9 Interpretation Problems -- 11.10 Multiple Dependent Variables -- 11.11 Nonlinear Johnson-Neyman Analysis.

11.12 Correlated Samples -- 11.13 Robust Methods -- 11.14 Software -- 11.15 Summary -- 12 Nonlinear ANCOVA -- 12.1 Introduction -- 12.2 Dealing with Nonlinearity -- 12.3 Computation and Example of Fitting Polynomial Models -- 12.4 Summary -- 13 Quasi-ANCOVA: When Treatments Affect Covariates -- 13.1 Introduction -- 13.2 Quasi-ANCOVA Model -- 13.3 Computational Example of Quasi-ANCOVA -- 13.4 Multiple Quasi-ANCOVA -- 13.5 Computational Example of Multiple Quasi-ANCOVA -- 13.6 Summary -- 14 Robust ANCOVA/Robust Picked Points -- 14.1 Introduction -- 14.2 Rank ANCOVA -- 14.3 Robust General Linear Model -- 14.4 Summary -- 15 ANCOVA for Dichotomous Dependent Variables -- 15.1 Introduction -- 15.2 Logistic Regression -- 15.3 Logistic Model -- 15.4 Dichotomous ANCOVA Through Logistic Regression -- 15.5 Homogeneity of Within-Group Logistic Regression -- 15.6 Multiple Covariates -- 15.7 Multiple Comparison Tests -- 15.8 Continuous Versus Forced Dichotomy Results -- 15.9 Summary -- 16 Designs with Ordered Treatments and No Covariates -- 16.1 Introduction -- 16.2 Qualitative, Quantitative, and Ordered Treatment Levels -- 16.3 Parametric Monotone Analysis -- 16.4 Nonparametric Monotone Analysis -- 16.5 Reversed Ordinal Logistic Regression -- 16.6 Summary -- 17 ANCOVA for Ordered Treatments Designs -- 17.1 Introduction -- 17.2 Generalization of the Abelson-Tukey Method to Include One Covariate -- 17.3 Abelson-Tukey: Multiple Covariates -- 17.4 Rank-Based ANCOVA Monotone Method -- 17.5 Rank-Based Monotone Method with Multiple Covariates -- 17.6 Reversed Ordinal Logistic Regression with One or More Covariates -- 17.7 Robust R-Estimate ANCOVA Monotone Method -- 17.8 Summary -- PART V SINGLE-CASE DESIGNS -- 18 Simple Interrupted Time-Series Designs -- 18.1 Introduction -- 18.2 Logic of the Two-Phase Design -- 18.3 Analysis of the Two-Phase (AB) Design.

18.4 Two Strategies for Time-Series Regression Intervention Analysis -- 18.5 Details of Strategy II -- 18.6 Effect Sizes -- 18.7 Sample Size Recommendations -- 18.8 When the Model Is Too Simple -- 18.9 Summary -- 19 Examples of Single-Case AB Analysis -- 19.1 Introduction -- 19.2 Example I: Cancer Death Rates in the United Kingdom -- 19.3 Example II: Functional Activity -- 19.4 Example III: Cereal Sales -- 19.5 Example IV: Paracetamol Poisoning -- 19.6 Summary -- 20 Analysis of Single-Case Reversal Designs -- 20.1 Introduction -- 20.2 Statistical Analysis of Reversal Designs -- 20.3 Computational Example: Pharmacy Wait Time -- 20.4 Summary -- 21 Analysis of Multiple-Baseline Designs -- 21.1 Introduction -- 21.2 Case I Analysis: Independence of Errors Within and Between Series -- 21.3 Case II Analysis: Autocorrelated Errors Within Series, Independence Between Series -- 21.4 Case III Analysis: Independent Errors Within Series, Cross-Correlation Between Series -- 21.5 Intervention Versus Control Series Design -- 21.6 Summary -- PART VI ANCOVA EXTENSIONS -- 22 Power Estimation -- 22.1 Introduction -- 22.2 Power Estimation for One-Factor ANOVA -- 22.3 Power Estimation for ANCOVA -- 22.4 Power Estimation for Standardized Effect Sizes -- 22.5 Summary -- 23 ANCOVA for Randomized-Block Designs -- 23.1 Introduction -- 23.2 Conventional Design and Analysis Example -- 23.3 Combined Analysis (ANCOVA and Blocking Factor) -- 23.4 Summary -- 24 Two-Factor Designs -- 24.1 Introduction -- 24.2 ANCOVA Model and Computation for Two-Factor Designs -- 24.3 Multiple Comparison Tests for Adjusted Marginal Means -- 24.4 Two-Factor ANOVA and ANCOVA for Repeated-Measurement Designs -- 24.5 Summary -- 25 Randomized Pretest-Posttest Designs -- 25.1 Introduction -- 25.2 Comparison of Three ANOVA Methods -- 25.3 ANCOVA for Pretest-Posttest Designs -- 25.4 Summary.

26 Multiple Dependent Variables -- 26.1 Introduction -- 26.2 Uncorrected Univariate ANCOVA -- 26.3 Bonferroni Method -- 26.4 Multivariate Analysis of Covariance (MANCOVA) -- 26.5 MANCOVA Through Multiple Regression Analysis: Two Groups Only -- 26.6 Issues Associated with Bonferroni F and MANCOVA -- 26.7 Alternatives to Bonferroni and MANCOVA -- 26.8 Example Analyses Using Minitab -- 26.9 Summary -- PART VII QUASI-EXPERIMENTS AND MISCONCEPTIONS -- 27 Nonrandomized Studies: Measurement Error Correction -- 27.1 Introduction -- 27.2 Effects of Measurement Error: Randomized-Group Case -- 27.3 Effects of Measurement Error in Exposure and Covariates: Nonrandomized Design -- 27.4 Measurement Error Correction Ideas -- 27.5 Summary -- 28 Design and Analysis of Observational Studies -- 28.1 Introduction -- 28.2 Design of Nonequivalent Group/Observational Studies -- 28.3 Final (Outcome) Analysis -- 28.4 Propensity Design Advantages -- 28.5 Evaluations of ANCOVA Versus Propensity-Based Approaches -- 28.6 Adequacy of Observational Studies -- 28.7 Summary -- 29 Common ANCOVA Misconceptions -- 29.1 Introduction -- 29.2 SSAT Versus SSIntuitive AT: Single Covariate Case -- 29.3 SSAT Versus SSIntuitive AT: Multiple Covariate Case -- 29.4 ANCOVA Versus ANOVA on Residuals -- 29.5 ANCOVA Versus Y/X Ratio -- 29.6 Other Common Misconceptions -- 29.7 Summary -- 30 Uncontrolled Clinical Trials -- 30.1 Introduction -- 30.2 Internal Validity Threats Other Than Regression -- 30.3 Problems with Conventional Analyses -- 30.4 Controlling Regression Effects -- 30.5 Naranjo-Mckean Dual Effects Model -- 30.6 Summary -- Appendix: Statistical Tables -- References -- Index -- WILEY SERIES IN PROBABILITY AND STATISTICS.