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The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies, 2nd Edition

ISBN: 978-0-471-74896-0
688 pages
November 2011
The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies, 2nd Edition (047174896X) cover image
A complete guide to cutting-edge techniques and best practices for applying covariance analysis methods

The Second Edition of Analysis of Covariance and Alternatives sheds new light on its topic, offering in-depth discussions of underlying assumptions, comprehensive interpretations of results, and comparisons of distinct approaches. The book has been extensively revised and updated to feature an in-depth review of prerequisites and the latest developments in the field.

The author begins with a discussion of essential topics relating to experimental design and analysis, including analysis of variance, multiple regression, effect size measures and newly developed methods of communicating statistical results. Subsequent chapters feature newly added methods for the analysis of experiments with ordered treatments, including two parametric and nonparametric monotone analyses as well as approaches based on the robust general linear model and reversed ordinal logistic regression. Four groundbreaking chapters on single-case designs introduce powerful new analyses for simple and complex single-case experiments. This Second Edition also features coverage of advanced methods including:

  • Simple and multiple analysis of covariance using both the Fisher approach and the general linear model approach
  • Methods to manage assumption departures, including heterogeneous slopes, nonlinear functions, dichotomous dependent variables, and covariates affected by treatments
  • Power analysis and the application of covariance analysis to randomized-block designs, two-factor designs, pre- and post-test designs, and multiple dependent variable designs
  • Measurement error correction and propensity score methods developed for quasi-experiments, observational studies, and uncontrolled clinical trials

Thoroughly updated to reflect the growing nature of the field, Analysis of Covariance and Alternatives is a suitable book for behavioral and medical scineces courses on design of experiments and regression and the upper-undergraduate and graduate levels. It also serves as an authoritative reference work for researchers and academics in the fields of medicine, clinical trials, epidemiology, public health, sociology, and engineering.

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Preface xv

PART I BASIC EXPERIMENTAL DESIGN AND ANALYSIS

1 Review of Basic Statistical Methods 3

1.1 Introduction, 3

1.2 Elementary Statistical Inference, 4

1.3 Elementary Statistical Decision Theory, 7

1.4 Effect Size, 10

1.5 Measures of Association, 14

1.6 A Practical Alternative to Effect Sizes and Measures of Association That Is Relevant to the Individual: p(YTx > YControl), 17

1.7 Generalization of Results, 19

1.8 Control of Nuisance Variation, 20

1.9 Software, 22

1.10 Summary, 24

2 Review of Simple Correlated Samples Designs and Associated Analyses 25

2.1 Introduction, 25

2.2 Two-Level Correlated Samples Designs, 25

2.3 Software, 32

2.4 Summary, 32

3 ANOVA Basics for One-Factor Randomized Group, Randomized Block, and Repeated Measurement Designs 35

3.1 Introduction, 35

3.2 One-Factor Randomized Group Design and Analysis, 35

3.3 One-Factor Randomized Block Design and Analysis, 51

3.4 One-Factor Repeated Measurement Design and Analysis, 56

3.5 Summary, 60

PART II ESSENTIALS OF REGRESSION ANALYSIS

4 Simple Linear Regression 63

4.1 Introduction, 63

4.2 Comparison of Simple Regression and ANOVA, 63

4.3 Regression Estimation, Inference, and Interpretation, 68

4.4 Diagnostic Methods: Is the Model Apt?, 80

4.5 Summary, 82

5 Essentials of Multiple Linear Regression 85

5.1 Introduction, 85

5.2 Multiple Regression: Two-Predictor Case, 86

5.3 General Multiple Linear Regression: m Predictors, 105

5.4 Alternatives to OLS Regression, 115

5.5 Summary, 119

PART III ESSENTIALS OF SIMPLE AND MULTIPLE ANCOVA

6 One-Factor Analysis of Covariance 123

6.1 Introduction, 123

6.2 Analysis of Covariance Model, 127

6.3 Computation and Rationale, 128

6.4 Adjusted Means, 133

6.5 ANCOVA Example 1: Training Effects, 140

6.6 Testing Homogeneity of Regression Slopes, 144

6.7 ANCOVA Example 2: Sexual Activity Reduces Lifespan, 148

6.8 Software, 150

6.9 Summary, 157

7 Analysis of Covariance Through Linear Regression 159

7.1 Introduction, 159

7.2 Simple Analysis of Variance Through Linear Regression, 159

7.3 Analysis of Covariance Through Linear Regression, 172

7.4 Computation of Adjusted Means, 177

7.5 Similarity of ANCOVA to Part and Partial Correlation Methods, 177

7.6 Homogeneity of Regression Test Through General Linear Regression, 178

7.7 Summary, 179

8 Assumptions and Design Considerations 181

8.1 Introduction, 181

8.2 Statistical Assumptions, 182

8.3 Design and Data Issues Related to the Interpretation of ANCOVA, 200

8.4 Summary, 213

9 Multiple Comparison Tests and Confidence Intervals 215

9.1 Introduction, 215

9.2 Overview of Four Multiple Comparison Procedures, 215

9.3 Tests on All Pairwise Comparisons: Fisher–Hayter, 216

9.4 All Pairwise Simultaneous Confidence Intervals and Tests: Tukey–Kramer, 219

9.5 Planned Pairwise and Complex Comparisons: Bonferroni, 222

9.6 Any or All Comparisons: Scheff´e, 225

9.7 Ignore Multiple Comparison Procedures?, 227

9.8 Summary, 228

10 Multiple Covariance Analysis 229

10.1 Introduction, 229

10.2 Multiple ANCOVA Through Multiple Regression, 232

10.3 Testing Homogeneity of Regression Planes, 234

10.4 Computation of Adjusted Means, 236

10.5 Multiple Comparison Procedures for Multiple ANCOVA, 237

10.6 Software: Multiple ANCOVA and Associated Tukey–Kramer Multiple Comparison Tests Using Minitab, 243

10.7 Summary, 246

PART IV ALTERNATIVES FOR ASSUMPTION DEPARTURES

11 Johnson–Neyman and Picked-Points Solutions for Heterogeneous Regression 249

11.1 Introduction, 249

11.2 J–N and PPA Methods for Two Groups, One Covariate, 251

11.3 A Common Method That Should Be Avoided, 269

11.4 Assumptions, 270

11.5 Two Groups, Multiple Covariates, 272

11.6 Multiple Groups, One Covariate, 277

11.7 Any Number of Groups, Any Number of Covariates, 278

11.8 Two-Factor Designs, 278

11.9 Interpretation Problems, 279

11.10 Multiple Dependent Variables, 281

11.11 Nonlinear Johnson-Neyman Analysis, 282

11.12 Correlated Samples, 282

11.13 Robust Methods, 282

11.14 Software, 283

11.15 Summary, 283

12 Nonlinear ANCOVA 285

12.1 Introduction, 285

12.2 Dealing with Nonlinearity, 286

12.3 Computation and Example of Fitting Polynomial Models, 288

12.4 Summary, 295

13 Quasi-ANCOVA: When Treatments Affect Covariates 297

13.1 Introduction, 297

13.2 Quasi-ANCOVA Model, 298

13.3 Computational Example of Quasi-ANCOVA, 300

13.4 Multiple Quasi-ANCOVA, 304

13.5 Computational Example of Multiple Quasi-ANCOVA, 304

13.6 Summary, 308

14 Robust ANCOVA/Robust Picked Points 311

14.1 Introduction, 311

14.2 Rank ANCOVA, 311

14.3 Robust General Linear Model, 314

14.4 Summary, 320

15 ANCOVA for Dichotomous Dependent Variables 321

15.1 Introduction, 321

15.2 Logistic Regression, 323

15.3 Logistic Model, 324

15.4 Dichotomous ANCOVA Through Logistic Regression, 325

15.5 Homogeneity of Within-Group Logistic Regression, 328

15.6 Multiple Covariates, 328

15.7 Multiple Comparison Tests, 330

15.8 Continuous Versus Forced Dichotomy Results, 331

15.9 Summary, 331

16 Designs with Ordered Treatments and No Covariates 333

16.1 Introduction, 333

16.2 Qualitative, Quantitative, and Ordered Treatment Levels, 333

16.3 Parametric Monotone Analysis, 337

16.4 Nonparametric Monotone Analysis, 346

16.5 Reversed Ordinal Logistic Regression, 350

16.6 Summary, 353

17 ANCOVA for Ordered Treatments Designs 355

17.1 Introduction, 355

17.2 Generalization of the Abelson–Tukey Method to Include One Covariate, 355

17.3 Abelson–Tukey: Multiple Covariates, 358

17.4 Rank-Based ANCOVA Monotone Method, 359

17.5 Rank-Based Monotone Method with Multiple Covariates, 362

17.6 Reversed Ordinal Logistic Regression with One or More Covariates, 362

17.7 Robust R-Estimate ANCOVA Monotone Method, 363

17.8 Summary, 364

PART V SINGLE-CASE DESIGNS

18 Simple Interrupted Time-Series Designs 367

18.1 Introduction, 367

18.2 Logic of the Two-Phase Design, 370

18.3 Analysis of the Two-Phase (AB) Design, 371

18.4 Two Strategies for Time-Series Regression Intervention Analysis, 374

18.5 Details of Strategy II, 375

18.6 Effect Sizes, 385

18.7 Sample Size Recommendations, 389

18.8 When the Model Is Too Simple, 393

18.9 Summary, 394

19 Examples of Single-Case AB Analysis 403

19.1 Introduction, 403

19.2 Example I: Cancer Death Rates in the United Kingdom, 403

19.3 Example II: Functional Activity, 411

19.4 Example III: Cereal Sales, 414

19.5 Example IV: Paracetamol Poisoning, 424

19.6 Summary, 430

20 Analysis of Single-Case Reversal Designs 433

20.1 Introduction, 433

20.2 Statistical Analysis of Reversal Designs, 434

20.3 Computational Example: Pharmacy Wait Time, 441

20.4 Summary, 452

21 Analysis of Multiple-Baseline Designs 453

21.1 Introduction, 453

21.2 Case I Analysis: Independence of Errors Within and Between Series, 455

21.3 Case II Analysis: Autocorrelated Errors Within Series, Independence Between Series, 461

21.4 Case III Analysis: Independent Errors Within Series, Cross-Correlation Between Series, 461

21.5 Intervention Versus Control Series Design, 467

21.6 Summary, 471

PART VI ANCOVA EXTENSIONS

22 Power Estimation 475

22.1 Introduction, 475

22.2 Power Estimation for One-Factor ANOVA, 475

22.3 Power Estimation for ANCOVA, 480

22.4 Power Estimation for Standardized Effect Sizes, 482

22.5 Summary, 482

23 ANCOVA for Randomized-Block Designs 483

23.1 Introduction, 483

23.2 Conventional Design and Analysis Example, 484

23.3 Combined Analysis (ANCOVA and Blocking Factor), 486

23.4 Summary, 488

24 Two-Factor Designs 489

24.1 Introduction, 489

24.2 ANCOVA Model and Computation for Two-Factor Designs, 494

24.3 Multiple Comparison Tests for Adjusted Marginal Means, 512

24.4 Two-Factor ANOVA and ANCOVA for Repeated-Measurement Designs, 519

24.5 Summary, 530

25 Randomized Pretest–Posttest Designs 531

25.1 Introduction, 531

25.2 Comparison of Three ANOVA Methods, 531

25.3 ANCOVA for Pretest–Posttest Designs, 534

25.4 Summary, 539

26 Multiple Dependent Variables 541

26.1 Introduction, 541

26.2 Uncorrected Univariate ANCOVA, 543

26.3 Bonferroni Method, 544

26.4 Multivariate Analysis of Covariance (MANCOVA), 544

26.5 MANCOVA Through Multiple Regression Analysis: Two Groups Only, 553

26.6 Issues Associated with Bonferroni F and MANCOVA, 554

26.7 Alternatives to Bonferroni and MANCOVA, 555

26.8 Example Analyses Using Minitab, 557

26.9 Summary, 564

PART VII QUASI-EXPERIMENTS AND MISCONCEPTIONS

27 Nonrandomized Studies: Measurement Error Correction 567

27.1 Introduction, 567

27.2 Effects of Measurement Error: Randomized-Group Case, 568

27.3 Effects of Measurement Error in Exposure and Covariates: Nonrandomized Design, 569

27.4 Measurement Error Correction Ideas, 570

27.5 Summary, 573

28 Design and Analysis of Observational Studies 575

28.1 Introduction, 575

28.2 Design of Nonequivalent Group/Observational Studies, 579

28.3 Final (Outcome) Analysis, 587

28.4 Propensity Design Advantages, 592

28.5 Evaluations of ANCOVA Versus Propensity-Based Approaches, 594

28.6 Adequacy of Observational Studies, 596

28.7 Summary, 597

29 Common ANCOVA Misconceptions 599

29.1 Introduction, 599

29.2 SSAT Versus SSIntuitive AT: Single Covariate Case, 599

29.3 SSAT Versus SSIntuitive AT: Multiple Covariate Case, 601

29.4 ANCOVA Versus ANOVA on Residuals, 606

29.5 ANCOVA Versus Y/X Ratio, 606

29.6 Other Common Misconceptions, 607

29.7 Summary, 608

30 Uncontrolled Clinical Trials 609

30.1 Introduction, 609

30.2 Internal Validity Threats Other Than Regression, 610

30.3 Problems with Conventional Analyses, 613

30.4 Controlling Regression Effects, 615

30.5 Naranjo–Mckean Dual Effects Model, 616

30.6 Summary, 617

Appendix: Statistical Tables 619

References 643

Index 655

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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.

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