Preface x

**1 Psychophysics I: Introduction and Thresholds 1**

1.1 Introduction and Terminology 1

1.2 Absolute Sensitivity 4

1.3 Methods for Measuring Absolute Thresholds 8

1.4 Differential Sensitivity 13

1.5 A Look Ahead: Fechner’s Contribution 17

Appendix 1.A: Relationship of Proportions, Areas Under the Normal

Distribution, and Z-Scores 18

Appendix 1.B: Worked Example: Fitting a Logistic Function to Threshold Data 20

References 22

**2 Psychophysics II: Scaling and Psychophysical Functions 24**

2.1 Introduction 24

2.2 History: Cramer, Bernoulli, Weber, and Fechner 26

2.3 Partition Scales and Categories 27

2.4 Magnitude Estimation and the Power Law 28

2.5 Cross-Modality Matching; Attempts at Validation 32

2.6 Two-Stage Models and Judgment Processes 35

2.7 Empirical Versus Theory-Based Functions 39

2.8 Hybrid Scales and Indirect Scales: A Look Ahead 40

2.9 Summary and Conclusions 41

Appendix 2.A: Decibels and Sones 42

Appendix 2.B: Worked Example: Transformations Applied to Non-Modulus

Magnitude Estimation Data 44

References 45

**3 Basics of Signal Detection Theory 47**

3.1 Introduction 48

3.2 The Yes/No Experiment 49

3.3 Connecting the Design to Theory 52

3.4 The ROC Curve 57

3.5 ROC Curves from Rating Scales; the R-Index 62

3.6 Conclusions and Implications for Sensory Testing 67

Appendix 3.A: Table of p and Z 68

Appendix 3.B: Test for the Significance of Differences Between d′ Values 69

References 69

**4 Thurstonian Models for Discrimination and Preference 71**

4.1 The Simple Paired-Choice Model 71

4.2 Extension into n-AFC: The Byer and Abrams “Paradox” 78

4.3 A Breakthrough: Power Analysis and Sample Size Determination 80

4.4 Tau Versus Beta Criteria: The Same–Different Test 84

4.5 Extension to Preference and Nonforced Preference 89

4.6 Limitations and Issues in Thurstonian Modeling 90

4.7 Summary and Conclusions 94

Appendix 4.A: The Bradley–Terry–Luce Model: An Alternative to Thurstone 95

Appendix 4.B: Tables for delta Values from Proportion Correct 96

References 97

**5 Progress in Discrimination Testing 99**

5.1 Introduction 99

5.2 Metrics for Degree of Difference 104

5.3 Replication in Choice Tests 108

5.4 Current Variations 110

5.5 Summary and Conclusions 118

Appendix 5.A: Psychometric Function for the Dual Pair Test, Power

Equations, and Sample Size 119

Appendix 5.B: Fun with g 120

References 121

**6 Similarity and Equivalence Testing 124**

6.1 Introduction: Issues in Type II Error 124

6.2 Commonsense Approaches to Equivalence 126

6.3 Allowable Differences and Effect Size 133

6.4 Further Significance Testing 138

6.5 Summary and Conclusions 140

References 141

**7 Progress in Scaling 143**

7.1 Introduction 143

7.2 Labeled Magnitude Scales for Intensity 147

7.3 Adjustable and Relative Scales 153

7.4 Explicit Anchoring 155

7.5 Post Hoc Adjustments 158

7.6 Summary and Conclusions 161

Appendix 7.A: Examples of Individual Rescaling for Magnitude Estimation 162

References 164

**8 Progress in Affective Testing: Preference/Choice and Hedonic Scaling 167**

8.1 Introduction 167

8.2 Preference Testing Options 168

8.3 Replication 173

8.4 Alternative Models: Ferris k-visit, Dirichlet multinomial 176

8.5 Affective Scales 181

8.6 Ranking and Partial Ranking 185

8.7 Conclusions 188

Appendix 8.A: Proof that the McNemar Test is Equivalent to the Binomial

Approximation Z-Test (AKA Sign Test) 188

References 190

**9 Using Subjects as Their Own Controls 194**

Part I: Designs using Parametric Statistics 195

9.1 Introduction to Part I 195

9.2 Dependent Versus Independent t-Tests 198

9.3 Within-Subjects ANOVA (“Repeated Measures”) 203

9.4 Issues 206

Part II: Nonparametric Statistics 208

9.5 Introduction to Part II 208

9.6 Applications of the McNemar Test: A–not-A and

Same–Different Methods 209

9.7 Examples of the Stuart–Maxwell 212

9.8 Further Extensions of the Stuart Test Comparisons 218

9.9 Summary and Conclusions 220

Appendix 9.A: R code for the Stuart Test 221

References 222

**10 Frequency Counts and Check-All-That-Apply (CATA) 224**

10.1 Frequency Count Data: Situations — Open Ends, CATA 224

10.2 Simple Data Handling 227

10.3 Repeated or Within-Subjects Designs 228

10.4 Multivariate Analyses 230

10.5 Difference from Ideal and Penalty Analysis 231

10.6 Frequency Counts in Advertising Claims 235

10.7 Conclusions 236

Appendix 10.A: Proof Showing Equivalence of Binomial Approximation

Z-Test and c2 Test for Differences of Proportions 237

References 239

**11 Time–Intensity Modeling 240**

11.1 Introduction: Goals and Applications 240

11.2 Parameters Versus Average Curves 245

11.3 Other Methods and Analyses 250

11.4 Summary and Conclusions 254

References 254

**12 Product Stability and Shelf-Life Measurement 257**

12.1 Introduction 257

12.2 Strategies, Measurements, and Choices 258

12.3 Study Designs 261

12.4 Hazard Functions and Failure Distributions 261

12.5 Reaction Rates and Kinetic Modeling 267

12.6 Summary and Conclusions 271

References 272

**13 Product Optimization, Just-About-Right (Jar ) Scales, and ****Ideal Profiling 273**

13.1 Introduction 273

13.2 Basic Equations, Designed Experiments, and Response Surfaces 276

13.3 Just-About-Right Scales 279

13.4 Ideal Profiling 285

13.5 Summary and Conclusions 292

References 294

**14 Perceptual Mapping, Multivariate Tools, and Graph Theory 297**

14.1 Introduction 297

14.2 Common Multivariate Methods 299

14.3 Shortcuts for Data Collection: Sorting and Projective Mapping 308

14.4 Preference Mapping Revisited 309

14.5 Cautions and Concerns 311

14.6 Introduction to Graph Theory 314

References 319

**15 Segmentation 323**

15.1 Introduction 323

15.2 Case Studies 326

15.3 Cluster Analysis 330

15.4 Other Analyses and Methods 336

15.5 Women, Fire, and Dangerous Things 337

References 338

**16 An Introduction to Bayesian Analysis 340**

16.1 Some Binomial-Based Examples 340

16.2 General Bayesian Models 347

16.3 Bayesian Inference Using Beta Distributions for Preference Tests 349

16.4 Proportions of Discriminators 352

16.5 Modeling Forced-Choice Discrimination Tests 353

16.6 Replicated Discrimination Tests 355

16.7 Bayesian Networks 356

16.8 Conclusions 359

References 360

Appendix A: Overview of Sensory Evaluation 361

A.1 Introduction 361

A.2 Discrimination and Simple Difference Tests 363

A.3 Descriptive Analysis 367

A.4 Affective Tests 372

A.5 Summary and Conclusions 375

References 375

Appendix B: Overview of Experimental Design 377

B.1 General Considerations 377

B.2 Factorial Designs 379

B.3 Fractional Factorials and Screening 380

B.4 Central Composite and Box–Behnken Designs 383

B.5 Mixture Designs 385

B.6 Summary and Conclusions 385

References 386

Appendix C: Glossary 387

Index 398