Statistical Methods in Food and Consumer Research (eBook)

Front Cover 1
Statistical Methods in Food and Consumer Research 4
Copyright Page 5
Dedication Page 6
Table of Contents 8
Preface to the Second Edition 14
Chapter 1: Introduction 16
1.1 A Brief Review of Tools for Statistical Inference 16
Notation and Symbolism 17
The Normal Distribution 19
Estimation 23
Testing of Hypotheses 24
Experimental Significance 31
1.2 Principles of Experimental Design 31
Randomization 32
Replication 32
Local Control 32
Blinding 33
Planning the Test Program 34
1.3 The Role of the Statistician in Research 36
Partnership 36
Client-Consultant Relationship 36
Exercises 37
Chapter 2: Statistical Sensory Testing 40
2.1 Psychophysical Aspects of Sensory Data 40
Weber´s Law 42
Fechner´s Law 42
Stevens´ Power Law 43
Thurstone´s Law of Comparative Judgment 44
2.2 Scales of Measurement 45
Hedonic Scale 47
Intensity Rating Scale 49
Rankings 50
2.3 Scale Structures 50
2.4 Construction of a Scale 52
Edwards´ Method of Successive Intervals 53
Scaling of Categories 61
2.5 Distribution of Sensory Data 65
Measures of Shape Distribution 65
Statistical Properties of Subjective Data 67
Transformation 70
2.6 Selection of Panel Members 72
Criteria Based on Binomial Response 72
Criteria Based on Rating Scale 78
Sequential Analysis 79
Quality Control Chart for Degree of Difference 84
Exercises 89
Chapter 3: The Analysis of Variance and Multiple Comparison Tests 92
3.1 Analysis of Variance 92
Assumptions in the Analysis of Variance 95
Fixed- and Random-Effects Models 96
3.2 Multiple-Comparison Tests 113
Least Significant Difference Test 114
Dunnett's Test for Multiple Comparisons with a Control 115
Tukey's Studentized Range Test 116
Duncan's Multiple-Range Test 118
Choice of Multiple-Comparison Tests 120
3.3 Sample Size Estimation 122
Sample Size for Confidence Interval Estimation 124
Sample Size for Dichotomous Responses 125
Exercises 126
Chapter 4: Experimental Design 128
4.1 Simple Comparative Experiments 128
Group-Comparison Designs 128
Paired Comparison Designs 130
4.2 Completely Randomized Designs 136
4.3 Randomized Complete Block Designs 139
Randomized Complete Block Designs with More Than One Observation per Experimental Unit 143
4.4 Latin Square Designs 146
Replicating LS Designs 149
Partially Replicated Latin Square 153
4.5 Cross-Over Designs 157
4.6 Split Plot Designs 168
Exercises 181
Chapter 5: Incomplete Block Experimental Designs 184
5.1 Balanced Incomplete Block Designs 184
Parameters of Balanced Incomplete Block Designs 185
Intrablock Analysis 186
Interblock Analysis 192
Combining Intrablock and Interblock Estimates 192
5.2 Balanced Incomplete Block Designs Augmented with a Control 197
5.3 Doubly Balanced Incomplete Block Designs 202
5.4 Composite Complete-Incomplete Block Designs 209
Intrablock Analysis 213
Exercises 217
Chapter 6: Factorial Experiments 220
6.1 The 2n Factorial Experiments 221
6.2 The 3n Factorial Experiments 231
6.3 The p x q and p x q x k Factorial Experiments 240
Confounding in 2n Factorial Experiments 249
Fractional Factorial 252
Exercises 259
Chapter 7: Response Surface Designs and Analysis 262
7.1 General Concepts 262
Construction of Response Surfaces 266
7.2 Fitting of Response Surfaces and Some Design Considerations 271
7.3 Illustrations of Fittings of First- and Second-Order Models 278
7.4 Composite Designs 290
Composite Designs from Fractional Factorials 297
A 1/2 Replicate of 24 297
A 1/2 Replicate of 26 298
7.5 Rotatable Designs 301
Composite Rotatable Designs 307
Arrangements of Composite Designs in Blocks 309
7.6 A Response Surface Analysis Approach for Sensory Data 319
Exercises 323
Chapter 8: Shelf Life Testing Experiments 326
8.1 Hazard Function 327
8.2 Shelf Life Models 331
Normal Distribution 332
Lognormal Distribution 333
Weibull Distribution 335
Graphical Test for Failure Distributions 343
8.3 Regression Analysis 346
Confidence Intervals 355
Nonlinear Relationships 360
Exercises 363
Chapter 9: Nonparametric Statistical Methods 366
9.1 Some Methods for Binary Data 366
Tests for Independent Proportions 366
Tests for Dependent Proportions 374
Combining 2 x 2 Contingency Tables 379
Measure of Association for 2 x 2 Tables 384
9.2 Some Methods Based on Ranks 385
Rank Tests for Single and Paired Samples 386
Rank Tests for Two Independent Samples 393
Rank Tests for Multiple Independent Samples 404
Rank Tests for Multiple Related Samples 410
Measures of Association for Ranking Data 419
9.3 Some Methods for Categorical Data 429
Contingency Tables and Chi-square Statistics 429
Goodness of Fit Tests 433
Analysis of r x c Contingency Tables 437
Measures of Association for r x c Contingency Tables 445
Analysis of Square (r x r) Contingency Tables 448
9.4 Multidimensional Contingency Tables 453
Introduction 453
Simpson´s Paradox 454
Tests for Independence 456
Numerical Example for Tests for Independence 458
Exercises 464
Chapter 10: Sensory Difference and Similarity Tests 470
10.1 Sensory Difference Tests 470
Triangle Test 470
Duo-Trio Test 486
Pair Difference Test (2-AFC) 488
Three-Alternative Forced-Choice Test (3-AFC) 492
A-Not A Test 493
Same-Different Test 499
Comparisons of Difference Test Designs 500
10.2 Sensory Similarity (Equivalence) Tests 511
Introduction 511
Similarity Tests Using Forced-Choice Methods 512
Similarity Tests Using the Paired Comparison Method 513
Similarity Tests Using A-Not A and Same-Different Methods 516
Similarity Tests for Continuous Data 518
Similarity Tests for Correlated Data 521
Hypothesis Test and Confidence Interval for Similarity Evaluation 525
10.3 Replicated Difference and Similarity Tests 529
Introduction 529
The Beta-Binomial (BB) Model 530
Tests Based on the BB Model 537
The Corrected Beta-Binomial (CBB) Model 547
Tests Based on the CBB Model 551
The Dirichlet-Multinomial (DM) Model 555
Tests Based on the DM Model 560
Exercises 567
Chapter 11: The Method of Paired Comparisons in Sensory Tests and Thurstonian Scaling 574
11.1 Paired Comparison Designs 574
Completely Balanced Paired Comparison Designs 574
Incomplete Balanced Paired Comparison Designs 579
11.2 Paired Comparison Models 586
The Scheffacute Model 586
The Bradley-Terry Model 597
The Thurstone-Mosteller Model 611
Choice of Models 620
11.3 Thurstonian Discriminal Distance d´ 622
Introduction 622
Estimation of d´ 624
Variance of d´ 629
Tables and S-PLUS Codes for d´ and Variance of d´ 635
Confidence Intervals and Tests for d´ 636
11.4 Area Under ROC Curve and R-Index 639
Introduction 639
Estimating R-Index and Its Variance 640
Difference Testing Using R-Index 642
Similarity Testing Using R-Index 644
Linking R-Index with d´ 645
Same-Different Area Theorem 647
Exercises 650
Chapter 12: Descriptive Analysis and Perceptual Mapping 656
12.1 Descriptive Analysis 656
12.2 Consumer Tests 657
In-House Consumer Test 657
Home-Use Consumer Test 658
Central Location Consumer Test 659
12.3 Hedonic and Intensity Rating Scales 659
Just-About-Right Rating Scale 660
Signal-to-Noise Ratio 661
Questionnaire Design 668
12.4 Perceptual Mapping 674
Factor Analysis 675
Principal Component Analysis 689
12.5 Preference Mapping 694
Exercises 700
Chapter 13: Sensory Evaluation in Cosmetic Studies 702
13.1 Experimental Designs 702
Clinical Study Data 703
Self-Controlled Design 706
Parallel Design 713
Cross-Over Design 716
13.2 Regression Analysis 721
Polynomial Regression 721
Nonlinear Regression 725
Fit of Nonlinear Regression Model 733
Exercises 734
Appendix: Statistical Tables 736
Tables 736
References 844
Index 860
Food Science and Technology International Series 866