Bradley Huitema
Covariance 2E
Bradley Huitema
Covariance 2E
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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…mehr
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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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Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: John Wiley & Sons / Wiley
- Artikelnr. des Verlages: 14674896000
- 2nd edition
- Seitenzahl: 688
- Erscheinungstermin: 1. November 2011
- Englisch
- Abmessung: 240mm x 161mm x 41mm
- Gewicht: 1191g
- ISBN-13: 9780471748960
- ISBN-10: 047174896X
- Artikelnr.: 33260305
- Verlag: John Wiley & Sons / Wiley
- Artikelnr. des Verlages: 14674896000
- 2nd edition
- Seitenzahl: 688
- Erscheinungstermin: 1. November 2011
- Englisch
- Abmessung: 240mm x 161mm x 41mm
- Gewicht: 1191g
- ISBN-13: 9780471748960
- ISBN-10: 047174896X
- Artikelnr.: 33260305
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 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
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
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
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