Description
Book SynopsisA 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 experimentswith orderedtreatments, including two parametric and nonparametric monotone analyses as well as approaches based on the robust general linear model and reversed ordin
Table of Contents
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
