Analyzing Within-Subjects Experiments

Most behavioral scientists know two important concepts -- how to analyze continuous data from randomly assigned treatment groups of subjects and how to assess practice effects for a single group of subjects given a constant treatment at each of several stages of practice. However, except in the case of the repeated measures Latin square design, researchers are not facile in analyzing data from different subjects receiving different treatments at various times in an experiment. This book helps fill the void.

PREFACE

xv

Chapter 1 AN ORIENTATION TO WITHIN-SUBJECTS DESIGNS

1

(11)

Introduction

1

(1)

Types of Within-Subjects Designs

2

(3)

Background on Analysis of Within-Subjects Designs

5

(3)

Tools of the Present Book: ANOVA and the SAS(R) GLM Statistical Package

8

(1)

The Idea of the General Linear Model

9

(3)

Chapter 2 TWO-WAY EXPERIMENTAL PLANS: SPLITPLOT AND RANDOMIZED BLOCK DESIGNS

12

(35)

Introduction to Models With Practice or Treatment Effects, but Not Both

12

(1)

Analyzing One-Group Split-Plot Data

12

(20)

Analyzing Multigroup Data Without Time-Related Effects

32

(12)

Method C: Randomization Tests Appropriate in Randomized Block Designs Without Random Selection of Subjects

44

(1)

Things to Remember

45

(1)

Exercises

46

(1)

Chapter 3 ANALYZING DATA FROM A RANDOMIZED BLOCK DESIGN EXPERIMENT THAT MAY EXHIBIT TIME-RELATED EFFECTS

47

(32)

Introduction

47

(1)

Crossover Design Approach to Mental Rotation Data

47

(28)

Other Tests of Experimental Effects When Sphericity Does Not Hold

75

(2)

Things to Remember

77

(1)

Exercises

78

(1)

Chapter 4 INTERPRETING ESTIMABILITY INFORMATION AND REPORTED ESTIMATES OF PARAMETERS IN SAS(R) GLM PROGRAMS

79

(13)

Introduction

79

(1)

Interpreting Estimability Tables in SAS(R) GLM Output

80

(5)

"Solution" Versus "Estimate" Commands

85

(4)

More About Expected Mean Squares

89

(1)

Things to Remember

90

(1)

Exercises

91

(1)

Chapter 5 ANALYZING DATA FROM WITHIN-SUBJECT FACTORIAL DESIGNS, TAKING INTO ACCOUNT STAGE-OF-PRACTICE EFFECTS

92

(42)

Introduction

92

(1)

Analyzing a 2 X 2 Within-Subjects Example

93

(21)

Analyzing a 2 X 2 Within-Subjects Example Without Complete Balance

114

(14)

Judging If a Given Within-Subjects Factorial Design Will Lead to Interpretable Results

128

(3)

Things to Remember

131

(2)

Exercises

133

(1)

Chapter 6 PRETEST-POSTTEST CONTROL GROUP DESIGNS: COMPARING DIFFERENT TREATMENT GROUPS AFTER PRETESTING

134

(29)

Introduction

134

(1)

Method A: Analyzing Data From a Simple Design--AA Versus AB Sequences

135

(4)

Method B: Comparing A(3)A(3) and A(3) B(3) Sequences

139

(6)

Generalizing This Design

145

(2)

Exercises

147

(1)

Optional Theory, Examples, and Exercises Involving BMDP(TM), SPSS(R), and SYSTAT(TM)

147

(14)

Things to Remember

161

(2)

Chapter 7 SWITCHING TREATMENTS IN BLOCKS: A(m)A(m), A(m)B(m), B(m)A(m), OR B(m)B(m) PATTERNS WITH m STAGES

163

(21)

Introduction

163

(1)

Method A: Analyzing Data From an AA Versus AB Versus BA Versus BB Experiment

164

(9)

Method B: Analyzing Data From Three-Stage Blocks: A(3)A(3), A(3)B(3), B(3)A(3), and B(3)B(3) Sequences

173

(9)

Final Thoughts

182

(1)

Things to Remember

182

(1)

Exercises

183

(1)

Chapter 8 ANALYZING DATA FROM VARIANTS OF ALTERNATING TREATMENT DESIGNS

184

(29)

Introduction

184

(1)

Analyzing Data From an ABAB Versus BABA Reversal Design

185

(16)

Analyzing Data From a More General Design: A(m1)B(m2)A(m3)B(m4) Versus B(m1)A(m2)B(m3)A(m4)

201

(9)

Final Thoughts

210

(1)

Things to Remember

211

(1)

Exercises

212

(1)

Chapter 9 DATA ANALYSIS FOR MULTIPLE-BASELINE DESIGNS

213

(17)

Introduction

213

(1)

Method A: Analyzing Data From a Multiple-Baseline Experiment Interpreted by a Crossover Design Model

214

(5)

Method B: Computing Efficiencies and Variances of Estimators (in XXX Units) for the Current Example

219

(2)

Related Multiple-Baseline Designs

221

(7)

Final Thoughts

228

(1)

Things to Remember

228

(1)

Exercises

229

(1)

Chapter 10 DATA ANALYSIS FOR DUAL-BALANCED MULTIPLE-BASELINE DESIGNS

230

(14)

Introduction

230

(2)

A Hypothetical Dual-Balanced Multiple-Baseline Experiment on Elation Versus Depression Effects

232

(7)

Related Designs

239

(3)

Final Thoughts

242

(1)

Things to Remember

242

(1)

Exercises

243

(1)

Chapter 11 BLOCK-RANDOMIZATION EXPERIMENTS WITH MULTIPLE TREATMENTS, EACH ONCE PER BLOCK OF STAGES

244

(16)

Introduction

244

(1)

Method A: Data Analysis Assuming Classical Carryover Effects

244

(8)

Method B1: Data Analysis Assuming Transitional Carryover Effects

252

(2)

Method B2: Finding Direct Plus Transitional Carryover Effects

254

(1)

Final Thoughts

255

(2)

Things to Remember

257

(1)

Exercises

257

(3)

Chapter 12 ANALYZING DATA FROM AN ABBA VERSUS BAAB COUNTERBALANCED DESIGN

260

(16)

Introduction

260

(2)

Method A: Data Analysis Assuming Linear Stage Effects

262

(7)

Method B: Data With Possibly Nonlinear Stage Effects

269

(5)

Final Thoughts

274

(1)

Things to Remember

274

(1)

Exercises

275

(1)

Chapter 13 SHOULD "OPTIMAL DESIGNS" BE PREFERRED IN BEHAVIOR SCIENCE CROSSOVER EXPERIMENTS?

276

(21)

Introduction

276

(1)

Optimal Design for Two-Treatment Experiments

277

(8)

Optimal Design With More Than Two Treatments

285

(2)

Possible Difficulties With Some Optimal Designs

287

(4)

Final Thoughts: Comparison of Efficiencies of Different Classes of Possible Psychological Designs

291

(3)

Things to Remember

294

(2)

Exercises

296

(1)

Appendix 1 A LITTLE ABOUT MATRICES AND VECTORS

297

(11)

Introduction

297

(1)

Some Matrix Operations and Properties

297

(11)

Appendix 2 USING THE GAUSS MATRIX PROGRAMMING LANGUAGE

308

(11)

A GAUSS(TM) Program for Estimating Parameters for ABBA Versus BAAB Design Data With Linear Slope

308

(6)

A GAUSS(TM) Program for Finding Contrasts for ABBA Versus BAAB Design Data With Linear Slope

314

(1)

Relation to SAS(R) Definitions of Contrasts Based on Table 12.2

315

(2)

Finding Contrasts for Data Without Linear Slope

317

(1)

Use of GAUSS(TM) in Efficiency Estimation

318

(1)

GAUSS(TM) Is Just One Option

318

(1)

REFERENCES

319

(8)

AUTHOR INDEX

327

(4)

SUBJECT INDEX

331

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