Dr Harry T. Lawless is Professor Emeritus at the Department of FoodScience, Cornell University, Ithaca, New York, USA.

• Preface x 1 Psychophysics I: Introduction and Thresholds 11.1 Introduction and Terminology 11.2 Absolute Sensitivity 41.3 Methods for Measuring Absolute Thresholds 81.4 Differential Sensitivity 131.5 A Look Ahead: Fechner’s Contribution 17Appendix 1.A: Relationship of Proportions, Areas Under the NormalDistribution, and Z-Scores 18Appendix 1.B: Worked Example: Fitting a Logistic Function to Threshold Data 20References 222 Psychophysics II: Scaling and Psychophysical Functions 242.1 Introduction 242.2 History: Cramer, Bernoulli, Weber, and Fechner 262.3 Partition Scales and Categories 272.4 Magnitude Estimation and the Power Law 282.5 Cross-Modality Matching; Attempts at Validation 322.6 Two-Stage Models and Judgment Processes 352.7 Empirical Versus Theory-Based Functions 392.8 Hybrid Scales and Indirect Scales: A Look Ahead 402.9 Summary and Conclusions 41Appendix 2.A: Decibels and Sones 42Appendix 2.B: Worked Example: Transformations Applied to Non-ModulusMagnitude Estimation Data 44References 453 Basics of Signal Detection Theory 473.1 Introduction 483.2 The Yes/No Experiment 493.3 Connecting the Design to Theory 523.4 The ROC Curve 573.5 ROC Curves from Rating Scales; the R-Index 623.6 Conclusions and Implications for Sensory Testing 67Appendix 3.A: Table of p and Z 68Appendix 3.B: Test for the Significance of Differences Between d′ Values 69References 694 Thurstonian Models for Discrimination and Preference 714.1 The Simple Paired-Choice Model 714.2 Extension into n-AFC: The Byer and Abrams “Paradox” 784.3 A Breakthrough: Power Analysis and Sample Size Determination 804.4 Tau Versus Beta Criteria: The Same–Different Test 844.5 Extension to Preference and Nonforced Preference 894.6 Limitations and Issues in Thurstonian Modeling 904.7 Summary and Conclusions 94Appendix 4.A: The Bradley–Terry–Luce Model: An Alternative to Thurstone 95Appendix 4.B: Tables for delta Values from Proportion Correct 96References 975 Progress in Discrimination Testing 995.1 Introduction 995.2 Metrics for Degree of Difference 1045.3 Replication in Choice Tests 1085.4 Current Variations 1105.5 Summary and Conclusions 118Appendix 5.A: Psychometric Function for the Dual Pair Test, PowerEquations, and Sample Size 119Appendix 5.B: Fun with g 120References 1216 Similarity and Equivalence Testing 1246.1 Introduction: Issues in Type II Error 1246.2 Commonsense Approaches to Equivalence 1266.3 Allowable Differences and Effect Size 1336.4 Further Significance Testing 1386.5 Summary and Conclusions 140References 1417 Progress in Scaling 1437.1 Introduction 1437.2 Labeled Magnitude Scales for Intensity 1477.3 Adjustable and Relative Scales 1537.4 Explicit Anchoring 1557.5 Post Hoc Adjustments 1587.6 Summary and Conclusions 161Appendix 7.A: Examples of Individual Rescaling for Magnitude Estimation 162References 1648 Progress in Affective Testing: Preference/Choice and Hedonic Scaling 1678.1 Introduction 1678.2 Preference Testing Options 1688.3 Replication 1738.4 Alternative Models: Ferris k-visit, Dirichlet multinomial 1768.5 Affective Scales 1818.6 Ranking and Partial Ranking 1858.7 Conclusions 188Appendix 8.A: Proof that the McNemar Test is Equivalent to the BinomialApproximation Z-Test (AKA Sign Test) 188References 1909 Using Subjects as Their Own Controls 194Part I: Designs using Parametric Statistics 1959.1 Introduction to Part I 1959.2 Dependent Versus Independent t-Tests 1989.3 Within-Subjects ANOVA (“Repeated Measures”) 2039.4 Issues 206Part II: Nonparametric Statistics 2089.5 Introduction to Part II 2089.6 Applications of the McNemar Test: A–not-A andSame–Different Methods 2099.7 Examples of the Stuart–Maxwell 2129.8 Further Extensions of the Stuart Test Comparisons 2189.9 Summary and Conclusions 220Appendix 9.A: R code for the Stuart Test 221References 22210 Frequency Counts and Check-All-That-Apply (CATA) 22410.1 Frequency Count Data: Situations — Open Ends, CATA 22410.2 Simple Data Handling 22710.3 Repeated or Within-Subjects Designs 22810.4 Multivariate Analyses 23010.5 Difference from Ideal and Penalty Analysis 23110.6 Frequency Counts in Advertising Claims 23510.7 Conclusions 236Appendix 10.A: Proof Showing Equivalence of Binomial ApproximationZ-Test and c2 Test for Differences of Proportions 237References 23911 Time–Intensity Modeling 24011.1 Introduction: Goals and Applications 24011.2 Parameters Versus Average Curves 24511.3 Other Methods and Analyses 25011.4 Summary and Conclusions 254References 25412 Product Stability and Shelf-Life Measurement 25712.1 Introduction 25712.2 Strategies, Measurements, and Choices 25812.3 Study Designs 26112.4 Hazard Functions and Failure Distributions 26112.5 Reaction Rates and Kinetic Modeling 26712.6 Summary and Conclusions 271References 27213 Product Optimization, Just-About-Right (Jar ) Scales, and Ideal Profiling 27313.1 Introduction 27313.2 Basic Equations, Designed Experiments, and Response Surfaces 27613.3 Just-About-Right Scales 27913.4 Ideal Profiling 28513.5 Summary and Conclusions 292References 29414 Perceptual Mapping, Multivariate Tools, and Graph Theory 29714.1 Introduction 29714.2 Common Multivariate Methods 29914.3 Shortcuts for Data Collection: Sorting and Projective Mapping 30814.4 Preference Mapping Revisited 30914.5 Cautions and Concerns 31114.6 Introduction to Graph Theory 314References 31915 Segmentation 32315.1 Introduction 32315.2 Case Studies 32615.3 Cluster Analysis 33015.4 Other Analyses and Methods 33615.5 Women, Fire, and Dangerous Things 337References 33816 An Introduction to Bayesian Analysis 34016.1 Some Binomial-Based Examples 34016.2 General Bayesian Models 34716.3 Bayesian Inference Using Beta Distributions for Preference Tests 34916.4 Proportions of Discriminators 35216.5 Modeling Forced-Choice Discrimination Tests 35316.6 Replicated Discrimination Tests 35516.7 Bayesian Networks 35616.8 Conclusions 359References 360Appendix A: Overview of Sensory Evaluation 361A.1 Introduction 361A.2 Discrimination and Simple Difference Tests 363A.3 Descriptive Analysis 367A.4 Affective Tests 372A.5 Summary and Conclusions 375References 375Appendix B: Overview of Experimental Design 377B.1 General Considerations 377B.2 Factorial Designs 379B.3 Fractional Factorials and Screening 380B.4 Central Composite and Box–Behnken Designs 383B.5 Mixture Designs 385B.6 Summary and Conclusions 385References 386Appendix C: Glossary 387Index 398

Dr Harry T. Lawless is Professor Emeritus at the Department of FoodScience, Cornell University, Ithaca, New York, USA.

• Preface x 1 Psychophysics I: Introduction and Thresholds 11.1 Introduction and Terminology 11.2 Absolute Sensitivity 41.3 Methods for Measuring Absolute Thresholds 81.4 Differential Sensitivity 131.5 A Look Ahead: Fechner’s Contribution 17Appendix 1.A: Relationship of Proportions, Areas Under the NormalDistribution, and Z-Scores 18Appendix 1.B: Worked Example: Fitting a Logistic Function to Threshold Data 20References 222 Psychophysics II: Scaling and Psychophysical Functions 242.1 Introduction 242.2 History: Cramer, Bernoulli, Weber, and Fechner 262.3 Partition Scales and Categories 272.4 Magnitude Estimation and the Power Law 282.5 Cross-Modality Matching; Attempts at Validation 322.6 Two-Stage Models and Judgment Processes 352.7 Empirical Versus Theory-Based Functions 392.8 Hybrid Scales and Indirect Scales: A Look Ahead 402.9 Summary and Conclusions 41Appendix 2.A: Decibels and Sones 42Appendix 2.B: Worked Example: Transformations Applied to Non-ModulusMagnitude Estimation Data 44References 453 Basics of Signal Detection Theory 473.1 Introduction 483.2 The Yes/No Experiment 493.3 Connecting the Design to Theory 523.4 The ROC Curve 573.5 ROC Curves from Rating Scales; the R-Index 623.6 Conclusions and Implications for Sensory Testing 67Appendix 3.A: Table of p and Z 68Appendix 3.B: Test for the Significance of Differences Between d′ Values 69References 694 Thurstonian Models for Discrimination and Preference 714.1 The Simple Paired-Choice Model 714.2 Extension into n-AFC: The Byer and Abrams “Paradox” 784.3 A Breakthrough: Power Analysis and Sample Size Determination 804.4 Tau Versus Beta Criteria: The Same–Different Test 844.5 Extension to Preference and Nonforced Preference 894.6 Limitations and Issues in Thurstonian Modeling 904.7 Summary and Conclusions 94Appendix 4.A: The Bradley–Terry–Luce Model: An Alternative to Thurstone 95Appendix 4.B: Tables for delta Values from Proportion Correct 96References 975 Progress in Discrimination Testing 995.1 Introduction 995.2 Metrics for Degree of Difference 1045.3 Replication in Choice Tests 1085.4 Current Variations 1105.5 Summary and Conclusions 118Appendix 5.A: Psychometric Function for the Dual Pair Test, PowerEquations, and Sample Size 119Appendix 5.B: Fun with g 120References 1216 Similarity and Equivalence Testing 1246.1 Introduction: Issues in Type II Error 1246.2 Commonsense Approaches to Equivalence 1266.3 Allowable Differences and Effect Size 1336.4 Further Significance Testing 1386.5 Summary and Conclusions 140References 1417 Progress in Scaling 1437.1 Introduction 1437.2 Labeled Magnitude Scales for Intensity 1477.3 Adjustable and Relative Scales 1537.4 Explicit Anchoring 1557.5 Post Hoc Adjustments 1587.6 Summary and Conclusions 161Appendix 7.A: Examples of Individual Rescaling for Magnitude Estimation 162References 1648 Progress in Affective Testing: Preference/Choice and Hedonic Scaling 1678.1 Introduction 1678.2 Preference Testing Options 1688.3 Replication 1738.4 Alternative Models: Ferris k-visit, Dirichlet multinomial 1768.5 Affective Scales 1818.6 Ranking and Partial Ranking 1858.7 Conclusions 188Appendix 8.A: Proof that the McNemar Test is Equivalent to the BinomialApproximation Z-Test (AKA Sign Test) 188References 1909 Using Subjects as Their Own Controls 194Part I: Designs using Parametric Statistics 1959.1 Introduction to Part I 1959.2 Dependent Versus Independent t-Tests 1989.3 Within-Subjects ANOVA (“Repeated Measures”) 2039.4 Issues 206Part II: Nonparametric Statistics 2089.5 Introduction to Part II 2089.6 Applications of the McNemar Test: A–not-A andSame–Different Methods 2099.7 Examples of the Stuart–Maxwell 2129.8 Further Extensions of the Stuart Test Comparisons 2189.9 Summary and Conclusions 220Appendix 9.A: R code for the Stuart Test 221References 22210 Frequency Counts and Check-All-That-Apply (CATA) 22410.1 Frequency Count Data: Situations — Open Ends, CATA 22410.2 Simple Data Handling 22710.3 Repeated or Within-Subjects Designs 22810.4 Multivariate Analyses 23010.5 Difference from Ideal and Penalty Analysis 23110.6 Frequency Counts in Advertising Claims 23510.7 Conclusions 236Appendix 10.A: Proof Showing Equivalence of Binomial ApproximationZ-Test and c2 Test for Differences of Proportions 237References 23911 Time–Intensity Modeling 24011.1 Introduction: Goals and Applications 24011.2 Parameters Versus Average Curves 24511.3 Other Methods and Analyses 25011.4 Summary and Conclusions 254References 25412 Product Stability and Shelf-Life Measurement 25712.1 Introduction 25712.2 Strategies, Measurements, and Choices 25812.3 Study Designs 26112.4 Hazard Functions and Failure Distributions 26112.5 Reaction Rates and Kinetic Modeling 26712.6 Summary and Conclusions 271References 27213 Product Optimization, Just-About-Right (Jar ) Scales, and Ideal Profiling 27313.1 Introduction 27313.2 Basic Equations, Designed Experiments, and Response Surfaces 27613.3 Just-About-Right Scales 27913.4 Ideal Profiling 28513.5 Summary and Conclusions 292References 29414 Perceptual Mapping, Multivariate Tools, and Graph Theory 29714.1 Introduction 29714.2 Common Multivariate Methods 29914.3 Shortcuts for Data Collection: Sorting and Projective Mapping 30814.4 Preference Mapping Revisited 30914.5 Cautions and Concerns 31114.6 Introduction to Graph Theory 314References 31915 Segmentation 32315.1 Introduction 32315.2 Case Studies 32615.3 Cluster Analysis 33015.4 Other Analyses and Methods 33615.5 Women, Fire, and Dangerous Things 337References 33816 An Introduction to Bayesian Analysis 34016.1 Some Binomial-Based Examples 34016.2 General Bayesian Models 34716.3 Bayesian Inference Using Beta Distributions for Preference Tests 34916.4 Proportions of Discriminators 35216.5 Modeling Forced-Choice Discrimination Tests 35316.6 Replicated Discrimination Tests 35516.7 Bayesian Networks 35616.8 Conclusions 359References 360Appendix A: Overview of Sensory Evaluation 361A.1 Introduction 361A.2 Discrimination and Simple Difference Tests 363A.3 Descriptive Analysis 367A.4 Affective Tests 372A.5 Summary and Conclusions 375References 375Appendix B: Overview of Experimental Design 377B.1 General Considerations 377B.2 Factorial Designs 379B.3 Fractional Factorials and Screening 380B.4 Central Composite and Box–Behnken Designs 383B.5 Mixture Designs 385B.6 Summary and Conclusions 385References 386Appendix C: Glossary 387Index 398

Dr Harry T. Lawless is Professor Emeritus at the Department of FoodScience, Cornell University, Ithaca, New York, USA.

• Preface x 1 Psychophysics I: Introduction and Thresholds 11.1 Introduction and Terminology 11.2 Absolute Sensitivity 41.3 Methods for Measuring Absolute Thresholds 81.4 Differential Sensitivity 131.5 A Look Ahead: Fechner’s Contribution 17Appendix 1.A: Relationship of Proportions, Areas Under the NormalDistribution, and Z-Scores 18Appendix 1.B: Worked Example: Fitting a Logistic Function to Threshold Data 20References 222 Psychophysics II: Scaling and Psychophysical Functions 242.1 Introduction 242.2 History: Cramer, Bernoulli, Weber, and Fechner 262.3 Partition Scales and Categories 272.4 Magnitude Estimation and the Power Law 282.5 Cross-Modality Matching; Attempts at Validation 322.6 Two-Stage Models and Judgment Processes 352.7 Empirical Versus Theory-Based Functions 392.8 Hybrid Scales and Indirect Scales: A Look Ahead 402.9 Summary and Conclusions 41Appendix 2.A: Decibels and Sones 42Appendix 2.B: Worked Example: Transformations Applied to Non-ModulusMagnitude Estimation Data 44References 453 Basics of Signal Detection Theory 473.1 Introduction 483.2 The Yes/No Experiment 493.3 Connecting the Design to Theory 523.4 The ROC Curve 573.5 ROC Curves from Rating Scales; the R-Index 623.6 Conclusions and Implications for Sensory Testing 67Appendix 3.A: Table of p and Z 68Appendix 3.B: Test for the Significance of Differences Between d′ Values 69References 694 Thurstonian Models for Discrimination and Preference 714.1 The Simple Paired-Choice Model 714.2 Extension into n-AFC: The Byer and Abrams “Paradox” 784.3 A Breakthrough: Power Analysis and Sample Size Determination 804.4 Tau Versus Beta Criteria: The Same–Different Test 844.5 Extension to Preference and Nonforced Preference 894.6 Limitations and Issues in Thurstonian Modeling 904.7 Summary and Conclusions 94Appendix 4.A: The Bradley–Terry–Luce Model: An Alternative to Thurstone 95Appendix 4.B: Tables for delta Values from Proportion Correct 96References 975 Progress in Discrimination Testing 995.1 Introduction 995.2 Metrics for Degree of Difference 1045.3 Replication in Choice Tests 1085.4 Current Variations 1105.5 Summary and Conclusions 118Appendix 5.A: Psychometric Function for the Dual Pair Test, PowerEquations, and Sample Size 119Appendix 5.B: Fun with g 120References 1216 Similarity and Equivalence Testing 1246.1 Introduction: Issues in Type II Error 1246.2 Commonsense Approaches to Equivalence 1266.3 Allowable Differences and Effect Size 1336.4 Further Significance Testing 1386.5 Summary and Conclusions 140References 1417 Progress in Scaling 1437.1 Introduction 1437.2 Labeled Magnitude Scales for Intensity 1477.3 Adjustable and Relative Scales 1537.4 Explicit Anchoring 1557.5 Post Hoc Adjustments 1587.6 Summary and Conclusions 161Appendix 7.A: Examples of Individual Rescaling for Magnitude Estimation 162References 1648 Progress in Affective Testing: Preference/Choice and Hedonic Scaling 1678.1 Introduction 1678.2 Preference Testing Options 1688.3 Replication 1738.4 Alternative Models: Ferris k-visit, Dirichlet multinomial 1768.5 Affective Scales 1818.6 Ranking and Partial Ranking 1858.7 Conclusions 188Appendix 8.A: Proof that the McNemar Test is Equivalent to the BinomialApproximation Z-Test (AKA Sign Test) 188References 1909 Using Subjects as Their Own Controls 194Part I: Designs using Parametric Statistics 1959.1 Introduction to Part I 1959.2 Dependent Versus Independent t-Tests 1989.3 Within-Subjects ANOVA (“Repeated Measures”) 2039.4 Issues 206Part II: Nonparametric Statistics 2089.5 Introduction to Part II 2089.6 Applications of the McNemar Test: A–not-A andSame–Different Methods 2099.7 Examples of the Stuart–Maxwell 2129.8 Further Extensions of the Stuart Test Comparisons 2189.9 Summary and Conclusions 220Appendix 9.A: R code for the Stuart Test 221References 22210 Frequency Counts and Check-All-That-Apply (CATA) 22410.1 Frequency Count Data: Situations — Open Ends, CATA 22410.2 Simple Data Handling 22710.3 Repeated or Within-Subjects Designs 22810.4 Multivariate Analyses 23010.5 Difference from Ideal and Penalty Analysis 23110.6 Frequency Counts in Advertising Claims 23510.7 Conclusions 236Appendix 10.A: Proof Showing Equivalence of Binomial ApproximationZ-Test and c2 Test for Differences of Proportions 237References 23911 Time–Intensity Modeling 24011.1 Introduction: Goals and Applications 24011.2 Parameters Versus Average Curves 24511.3 Other Methods and Analyses 25011.4 Summary and Conclusions 254References 25412 Product Stability and Shelf-Life Measurement 25712.1 Introduction 25712.2 Strategies, Measurements, and Choices 25812.3 Study Designs 26112.4 Hazard Functions and Failure Distributions 26112.5 Reaction Rates and Kinetic Modeling 26712.6 Summary and Conclusions 271References 27213 Product Optimization, Just-About-Right (Jar ) Scales, and Ideal Profiling 27313.1 Introduction 27313.2 Basic Equations, Designed Experiments, and Response Surfaces 27613.3 Just-About-Right Scales 27913.4 Ideal Profiling 28513.5 Summary and Conclusions 292References 29414 Perceptual Mapping, Multivariate Tools, and Graph Theory 29714.1 Introduction 29714.2 Common Multivariate Methods 29914.3 Shortcuts for Data Collection: Sorting and Projective Mapping 30814.4 Preference Mapping Revisited 30914.5 Cautions and Concerns 31114.6 Introduction to Graph Theory 314References 31915 Segmentation 32315.1 Introduction 32315.2 Case Studies 32615.3 Cluster Analysis 33015.4 Other Analyses and Methods 33615.5 Women, Fire, and Dangerous Things 337References 33816 An Introduction to Bayesian Analysis 34016.1 Some Binomial-Based Examples 34016.2 General Bayesian Models 34716.3 Bayesian Inference Using Beta Distributions for Preference Tests 34916.4 Proportions of Discriminators 35216.5 Modeling Forced-Choice Discrimination Tests 35316.6 Replicated Discrimination Tests 35516.7 Bayesian Networks 35616.8 Conclusions 359References 360Appendix A: Overview of Sensory Evaluation 361A.1 Introduction 361A.2 Discrimination and Simple Difference Tests 363A.3 Descriptive Analysis 367A.4 Affective Tests 372A.5 Summary and Conclusions 375References 375Appendix B: Overview of Experimental Design 377B.1 General Considerations 377B.2 Factorial Designs 379B.3 Fractional Factorials and Screening 380B.4 Central Composite and Box–Behnken Designs 383B.5 Mixture Designs 385B.6 Summary and Conclusions 385References 386Appendix C: Glossary 387Index 398