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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
Sensory testing and measurement are the main functions of sensory analysis. In recent years, the sensory and consumer field has evolved to include both difference testing and similarity testing, and new sensory discrimination methods such as the tetrads have received more attention in the literature.
This second edition of Sensory Discrimination Tests and Measurements is updated throughout and responds to these changes and includes:
- A wide range of sensory measurements:
- Measurements of sensory effect (d', R-index and Gini-index);
- Measurements of performance of trained sensory panel (Intraclass correlation coefficients and Cronbach�s coefficient alpha);
- Measurements of relative importance of correlated sensory and consumer attributes (drivers of consumer liking or purchase intent);
- Measurements of consumer emotions and psychographics;
- Measurements of time-intensity;
- Measurements of sensory thresholds;
- Measurements of sensory risk with negative sensory effects (Benchmark Dose, BMD, methodology)
- Measurements of sensory shelf life (SSL).
- A balanced introduction of sensory discrimination tests including difference tests and similarity tests.
- Bayesian approach to sensory discrimination tests.
- Modified and multiple-sample discrimination tests.
- Replicated discrimination tests using the beta-binomial (BB), corrected beta-binomial (CBB), and Dirichlet-multinomial (DM) models.
- Sensory discrimination methods including the tetrads and the �M+N�.
- R and S-Plus codes for all the measurements and tests introduced in the book.
Mainly intended for researchers and practitioners in the sensory and consumer field, the book is a useful reference for modern sensory analysis and consumer research, especially for sensometrics.
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Veröffentlichungsjahr: 2015
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Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
References
Acknowledgments
About the companion website
Chapter 1: Introduction
1.1 Sensometrics
1.2 Sensory tests and measurements
1.3 A brief review of sensory analysis methodologies
1.4 Method, test, and measurement
1.5 Commonly used discrimination methods
1.6 Classification of sensory discrimination methods
Chapter 2: Measurements of sensory difference/similarity: Thurstonian discriminal distance
2.1 Measurement of sensory difference/similarity
2.2 Thurstonian discriminal distance, δ or
d
′
2.3 Variance of
d
′
2.4 Tables and R/S-Plus codes for
d
′ and variance of
d
′
2.5 Computer-intensive approach to Thurstonian models of the “M + N” test
2.6 Estimates of population and group
d
′
Chapter 3: Measurements of sensory difference/similarity: area under ROC curve in Signal Detection Theory
3.1 Area measure of sensory difference/similarity
3.2 ROC curve functions
3.3 Estimations of the parameters of ROC curves
3.4 Estimations of variances of estimators
3.5 R/S-Plus codes for estimations of parameters for the three ratings methods
3.6 Estimates of population
R
-index in replicated ratings
Chapter 4: Difference testing
4.1 Binomial model for difference testing
4.2 Difference tests using forced-choice methods
4.3 Power analysis for tests for one proportion
4.4 Discrimination tests using methods with response bias
4.5 Power analysis of tests for two proportions
4.6 Efficiency comparisons of difference tests
4.7 Difference tests for
d
′ and
R
-index
Chapter 5: Similarity (equivalence) testing
5.1 Introduction
5.2 Similarity tests using the Two-Alternative Forced Choice (2-AFC) method
5.3 Similarity testing using forced-choice methods
5.4 Similarity tests using methods with response bias
5.5 Similarity tests using ratings of the A–Not A, Same–Different, and A–Not AR
5.6 Similarity tests for continuous data
5.7 Similarity tests for correlated data
5.8 Confidence interval for similarity evaluation
5.9 Controversy over similarity (equivalence) tests in statistical and sensory literature
Chapter 6: Bayesian approach to discrimination tests
6.1 Introduction
6.2 One-proportion two-sided tests
6.3 One-proportion one-sided tests
6.4 Two-proportion tests
6.5 Thurstonian
d′
for Bayesian estimate of proportion
Chapter 7: Modified discrimination tests
7.1 Modified Triangular test
7.2 Degree of Difference test
7.3 Double discrimination tests
7.4 Preference tests with a “no preference” option
7.5 Discrimination tests with pseudo-correct responses (forgiveness)
Chapter 8: Multiple-sample discrimination tests
8.1 Multiple-sample comparison based on proportions
8.2 Multiple-sample comparison based on ranks
8.3 Multiple-sample comparison based on categories
8.4 Multiple-sample comparison based on ratings
8.5 Multiple-sample comparison based on paired comparisons
Chapter 9: Replicated discrimination tests: beta-binomial model
9.1 Introduction
9.2 BB distribution
9.3 Estimation of the parameters
9.4 Applications of the BB model in replicated tests
9.5 Testing power and sample size
Chapter 10: Replicated discrimination tests: corrected beta-binomial model
10.1 Introduction
10.2 CBB distribution
10.3 Estimation of parameters in the CBB model
10.4 Statistical testing for parameters in a CBB model
10.5 Testing power and sample size
10.6 CBB and Thurstonian models for replicated discrimination methods
Chapter 11: Replicated discrimination tests: Dirichlet–multinomial (DM) model
11.1 DM distribution
11.2 Estimation of the parameters of a DM model
11.3 Applications of the DM model in replicated ratings and discrimination tests
11.4 Testing power for DM tests
11.5 DM model in a meta-analysis for usage and attitudinal (U&A) data
Chapter 12: Measurements of sensory thresholds
12.1 Introduction
12.2 Standard dose–response model
12.3 Model for responses with an independent background effect
12.4 Model for overdispersed responses
Chapter 13: Measurements of sensory risk with negative sensory effects
13.1 Benchmark dose methodology
13.2 Estimation of BMD from quantal data
13.3 Estimation of BMD from replicated quantal data
13.4 Estimation of BMD from continuous data
Chapter 14: Measurements of time intensity
14.1 Introduction
14.2 Smoothing and graphical presentation of T-I data
14.3 Analysis based on parameters of smoothed T-I curves
14.4 Multivariate data analysis for T-I data
14.5 Functional data analysis for T-I data
Chapter 15: Measurements of sensory shelf life
15.1 Introduction
15.2 Determination of SSL using R package and R codes
15.3 Numerical examples
Chapter 16: Measurements of the performance of a trained sensory panel and panelists
16.1 Criteria for assessing performance
16.2 Estimations of ICC from different types of data
16.3 Statistical tests for ICCs
16.4 Other indices for evaluation of panel data
16.5 Assessing the discriminability of trained sensory panelists and panels
References
Chapter 17: Measurements of consumer emotions and psychographics
17.1 Introduction
17.2 Measurements of consumer positive and negative emotions
17.3 Psychographics
17.4 Propensity score analysis
Chapter 18: Measurements of the relative importance of attributes
18.1 Introduction
18.2 Determination of the relative importance of attributes based on averaging over orderings
18.3 Determination of the relative importance of attributes based on variable transformation
18.4 Determination of the relative importance of attributes based on Breiman's RF
18.5 Determination of the relative importance of attributes based on fuzzy measures and the Choquet integral
18.6 Meta-analysis of the relative importances of attributes
18.7 Adaptive penalty analysis combining both directional effects and the relative importance of JAR attributes to overall liking
Appendix A: List of R/S-Plus codes, data files, and packages used in the book
References
Author Index
Subject Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 2: Measurements of sensory difference/similarity: Thurstonian discriminal distance
Figure 2.1 Theoretical and empirical psychometric functions.
Figure 2.2 Empirical psychometric functions for the Specified and Unspecified “” test with M = N.
Chapter 3: Measurements of sensory difference/similarity: area under ROC curve in Signal Detection Theory
Figure 3.1 Geometric presentation of ROC and indices: in normal-deviate (z) scales, AUC, and Gini-index.
Chapter 4: Difference testing
Figure 4.1 Powers of statistical tests using forced-choice methods. TR, Triangular; 2AFC, Two-Alternative Forced Choice; 3AFC, Three-Alternative Forced Choice; 4AFC, Four-Alternative Forced Choice; DUTR, Duo–Trio; TETU, Unspecified Tetrad; TETS, Specified Tetrad; DUPAR, Dual Pair (4IAX).
Figure 4.2 Powers of statistical tests using methods with response bias
Figure 4.3 Difference testing powers for three versions of ratings methods
Chapter 5: Similarity (equivalence) testing
Figure 5.1 Power of similarity testing using the 2-AFC method .
Figure 5.6 Power of similarity testing using the 2-AFC method (, 100, 200, or 300).
Figure 5.7 Statistical powers of similarity tests using the four forced-choice methods (2-AFC, Duo–Trio, 3-AFC, and Triangular) with , , , with a step of 0.01, and .
Figure 5.8 Powers for similarity tests using the 2-AFC method for , , and sample sizes , based on (a) exact binomial and (b) normal approximation with a continuity correction.
Figure 5.9 Similarity test powers for ratings of three methods (similarity limit ).
Chapter 6: Bayesian approach to discrimination tests
Figure 6.1 Beta prior distributions.
Figure 6.2 Highest posterior density (HPD) interval. Note: For a specified credible level, we can find a density value and two points and in a posterior beta distribution such that the density at and equals and the area (the probability) under the density curve and between and approximately equals the specified credible level.
Figure 6.3 Prior and posterior beta distributions. Note: The prior distribution is a beta distribution with mean and variance . The posterior distribution is a beta distribution with and . The observations are and the sample size is .
Figure 6.4 Posterior distribution of in a 3-AFC test. Note: The prior distribution of
p
is noninformative. The observed number of correct responses is and the total number of responses is
n
= 100. The independent background effect is .
Figure 6.5 Posterior distribution of log-odds ratio . Note: The posterior distribution with = 0.6 and = 0.0804. The posterior probability of is 0.983.
Figure 6.6 Posterior distribution of the difference of proportions . Note: The posterior distribution with and . The posterior probability of is 0.958.
Chapter 7: Modified discrimination tests
Figure 7.1 Powers of conventional and double discrimination methods .
Figure 7.2 Thurstonian model for the 2-AC with both placebo pairs and test pairs.
Figure 7.3 Comparisons of the powers of Two-out-of-Five difference tests with true correct and pseudo-correct responses .
Figure 7.4 Comparison of the powers of Two-out-of-Five similarity tests with true correct and pseudo-correct responses (, similarity limit ).
Chapter 8: Multiple-sample discrimination tests
Figure 8.1 Multiple comparisons in Example 8.4.2.
Figure 8.2 Predicted probabilities of response for product purchase intent.
Figure 8.3 Estimated relative abilities (worths) of products.
Chapter 12: Measurements of sensory thresholds
Figure 12.1 Fit of the logit model to the data in Table 12.1.
Figure 12.2 Fit of the logit model to the data in Table 12.2.
Figure 12.3 Fit of logit model to the data in Table 12.3.
Chapter 13: Measurements of sensory risk with negative sensory effects
Figure 13.1 Log-logit model for BMD and BMDL based on the data in Table 13.1.
Figure 13.2 Log-logit model combining a CBB log-likelihood for BMD and BMDL based on the replicated testing data in Table 13.2.
Figure 13.3 Output of BMDS for the data in Table 13.3.
Figure 13.4 Output of BMDS for the data in Table 13.4.
Chapter 14: Measurements of time intensity
Figure 14.1 T-I curve for the data in Table 14.1.
Figure 14.2 T-I curve and its 95% confidence intervals for the data in Table 14.1.
Figure 14.3 First and second principal curves.
Figure 14.4 Loadings on the first and second principal curves.
Figure 14.5 Three groups of curves and their averages.
Figure 14.6 Values of GCV for selection of the smooth parameter .
Figure 14.7 Fit to function of the data in Table 14.1.
Figure 14.8 Charts for the functional data objects “tidat5fd” and “tidat123fd.”
Figure 14.9 Mean and standard deviation curves for the functional data object “tidat5fd.”
Figure 14.10 First and the second derivatives of the functional data object “cexa.fd.”
Figure 14.11 First and the second derivatives of the mean of the functional data object “tidat5fd.”
Figure 14.12 Ninth curve in the functional data object “tidat5fd.”
Figure 14.13 Estimated variance–covariance surface and contour plot for the bivariate functional data object “tidat5bifd.”
Figure 14.14 First two principal component functions or harmonics in Example 14.5.11.
Figure 14.15 Effect of the first two principal component functions or harmonics as perturbations of the mean curve (the solid line).
Figure 14.16 Scores of nine curves on the first two principal components.
Figure 14.17 First two pairs of canonical weight functions in Example 14.5.2. Solid curves correspond to attribute A and dotted curves to attribute B.
Figure 14.18 Scores for the first two pairs of canonical variables plotted against each other.
Figure 14.19 Regression coefficients estimated in order to predict T-I for all products and for each product invidually.
Figure 14.20 Predicted mean for each product.
Figure 14.21 Predicted mean for each of three products.
Figure 14.22 Fittings for each of three products.
Figure 14.23 Observed pointwise statistic values and critical values for a functional F-test.
Figure 14.24 fANOVA for three groups of curves.
Figure 14.25 Observed pointwise statistic values and critical value for a functional t-test.
Figure 14.26 fANOVA for first derivative curves.
Figure 14.27 fANOVA for second derivative curves.
Chapter 15: Measurements of sensory shelf life
Figure 15.1 Failure curve based on Weibull distribution for the “ssldat” data.
Figure 15.2 Survival curve based on the nonparametric KM model for the “ssldat” data. Note: The thicker line is the estimate and the thinner lines pointwise 95% confidence interval.
Figure 15.3 Failure curve based on Weibull distribution for the “ssldat2” data.
Figure 15.4 Survival curve based on nonparametric KM model for the “ssldat2” data. Note: The thicker line is the estimate and the thinner lines pointwise 95% confidence interval.
Chapter 16: Measurements of the performance of a trained sensory panel and panelists
Figure 16.1 Ratings quality for 10 attributes.
Figure 16.2 Ratings quality for 10 panelists.
Chapter 17: Measurements of consumer emotions and psychographics
Figure 17.1 Loadings of factors on PA and NA items.
Figure 17.2 Multiple comparisons for well-being rating means for the four regions.
Figure 17.3 Approximate weight of evidence (AWE) for clusters and clustering tree.
Figure 17.4 Range of PSs, by treatment group .
Chapter 18: Measurements of the relative importance of attributes
Figure 18.1 Relative importance of attributes in Example 18.2.1.
Figure 18.2 Relative importance of attributes in Example 18.2.2.
Figure 18.3 Relative importance of attributes in Example 18.4.1.
Figure 18.4 Relative importance of attributes in Example 18.4.2.
Figure 18.5 Relative-importance values of JAR attributes to overall liking for a product in Example 18.7.1
List of Tables
Chapter 1: Introduction
Table 1.1 Classifications of sensory discrimination methods
Chapter 2: Measurements of sensory difference/similarity: Thurstonian discriminal distance
Table 2.1
d
′ and
B
value for variance of
d
′ for the 2-AFC method
Table 2.8
d
′ and
B
value for variance of
d
′ for the Dual Pair method
Table 2.9
d
′ and
B
value for variance of
d
′ for the double 2-AFC method
Table 2.12
d
′ and
B
value for variance of
d
′ for the double Triangular method
Table 2.11
d
′ and
B
value for variance of
d
′ for the double Duo–Trio method
Table 2.13 R/S-Plus codes for forced-choice methods
Table 2.14 R/S-Plus codes for A–Not A and Same–Different methods
Table 2.15 Different versions of the “M + N” test
Table 2.16 Theoretical chance probabilities of the “M + N” test
Table 2.17
d
′ and
B
values for the Specified Two-out-of-Five test (“dp321f”)
Table 2.18
d
′ and
B
values for the Unspecified Two-out-of-Five test (“dp322f”)
Table 2.19
d
′ and
B
values for the Unspecified “M + N” with M = 3 and N = 1 test (“dp312”)
Table 2.20
d
′ and B values for the Specified Hexagon test (M = N = 3)(“dp331f”)
Table 2.21
d
′ and B values for the Unspecified Hexagon test (M = N = 3) (“dp332f”)
Table 2.22
d
′ and
B
values for the Specified Octad test (M = N = 4) (“dp441f”)
Table 2.23
d
′ and B values for the Unspecified Octad test (M = N = 4)(“dp442f”)
Table 2.24 R/S-Plus codes used to produce some simulation-derived psychometric functions
Table 2.25
Table 2.26
Chapter 3: Measurements of sensory difference/similarity: area under ROC curve in Signal Detection Theory
Table 3.1 Practical meanings of the values of the measures
Table 3.2
Chapter 4: Difference testing
Table 4.1 2 × 2 Table for data from a monadic A–Not A test
Table 4.2 Data for Example 4.6
Table 4.3 2 × 2 Table for data from a mixed A–Not A test
Table 4.4 Data for Example 4.9
Table 4.6 Data for Example 4.4.5
Table 4.7 Sample sizes (
N
) required for a power of 0.8 using mixed-design A–Not A and Same–Different tests
Table 4.8 Expectations under a null hypothesis
Table 4.9 Expectations under an alternative hypothesis
Table 4.5 2 × 2 Table for data from a paired A–Not A test
Table 4.10 Sample sizes for significance at
α
≤ 0.05 and power at 0.8 using the paired design A–Not A and Same–Different tests (McNemar's test, one-sided test)
Table 4.11 Sample sizes for significance at
α
≤ 0.1 and power at 0.8 using the paired design A–Not A and Same–Different tests (McNemar's test, one-sided test)
Table 4.12 Power efficiencies for discrimination methods (
α
= 0.05, power = 0.8)
Table 4.13 Generalized power efficiencies for forced-choice methods
Chapter 5: Similarity (equivalence) testing
Table 5.1 Critical number selecting a product in similarity testing using the 2-AFC method (α = 0.05)
Table 5.2 Critical number selecting a product in similarity testing using the 2-AFC method (α = 0.1)
Table 5.3 Sample size (pairs) required for similarity testing using the 2-AFC method at 0.8 testing power (α = 0.05)
Table 5.4 Sample size (pairs) required for similarity testing using the 2-AFC method for 0.8 testing power (α = 0.1)
Table 5.5 Powers for similarity testing using the 2-AFC method for , and sample sizes
n
= 57–70
Table 5.6 Sample sizes required to reach 0.8 power for similarity testing using the A–Not A and Same–Different methods (α = 0.05,
h
= 1)
Table 5.7 Sample sizes required to reach 0.8 power for similarity testing using the A–Not A and Same–Different methods (α = 0.1,
h
= 1)
Table 5.8 Critical values for paired
t
-tests for similarity (α = 0.05)
Table 5.9 Overall liking for new and current products (Example 5.7.1)
Table 5.10 Purchase intent for new and current products (Example 5.7.2)
Chapter 6: Bayesian approach to discrimination tests
Table 6.1 Interpretations of the Bayes factor
Table 6.2
Table 6.3 Data of a numerical example for an equivalence test using the A–Not A method
Chapter 7: Modified discrimination tests
Table 7.1 Data for the Gridgeman model
Table 7.2 Expanded Table for the Gridgeman two-stage Triangular test
Table 7.3 Probabilities of weight total
w
T
(
N
= 2)
Table 7.4 Total probabilities of weight total
w
T
(
N
= 2)
Table 7.5 Data for Example 7.1.2
Table 7.6 Ratings in Example 7.2.1
Table 7.7 Frequencies of ratings for 100 subjects in a monadic Degree of Difference test
Table 7.8 Frequencies of ratings for 250 subjects in a mixed Degree of Difference test
Table 7.9 Frequencies of ratings for 100 subjects in a paired Degree of Difference test
Table 7.10 Sample sizes required to reach 0.8 power (with a continuity correction) (
α
= 0.05) in double discrimination methods
Table 7.11 Proportions of correct responses (
p
c
) corresponding to Thurstonian
δ
(or
d
′) in forced-choice methods
Table 7.12 Categories in the two-visit method
Table 7.13 Data for Example 7.4.1
Table 7.14 Data in Example 7.4.11
Chapter 8: Multiple-sample discrimination tests
Table 8.1 Upper
α
point of the range of
m
independent and identically distributed standard normal variables
Table 8.2 Data for Example 8.1.2
Table 8.3 Critical values for the Friedman test
Table 8.4 Upper
α
point of the studentized range distribution with parameter
t
and degrees of freedom
Table 8.5 Rank data for Example 8.2.1
Table 8.6 Ranked data in a BIB design (
t
= 7,
k
= 3,
n
= 7,
r
= 3,
λ
= 1)
Table 8.7 Anderson Table for ranked data
Table 8.8 Ranking numbers of three varieties of snap beans (Example 8.2.3)
Table 8.9 Homeowner rankings of four grasses (Example 8.2.4)
Table 8.10
Table 8.11
Table 8.12 Frequencies for the ratings in Table 8.11 by panelist
Table 8.13 Frequencies for the ratings in Table 8.11 by product
Table 8.14 Predicted probabilities of responses concerning product aftertaste
Table 8.15 Predicted probabilities of response for product purchase intent
Table 8.16 Aggregated forced-choice preference data (number of panelists who prefer a product in a given row to a product in a given column)
Table 8.17 Predicted preference probabilities for each pair among four products
Table 8.18 Data for Example 8.5.2
Table 8.19 Predicted probabilities of preferences
Table 8.20 Table for the Thurstonian model of Torgerson's method of triads
Chapter 9: Replicated discrimination tests: beta-binomial model
Table 9.1 Data for Example 9.1.1
Table 9.2 Data for Example 9.1.2
Table 9.3 Data in Example 9.3.2
Table 9.5 Critical proportions for replicated similarity testing using the paired comparison method (
Δ
= 0.1,
α
= 0.05)
Table 9.4 Numbers preferring sample A in a replicated similarity test using the paired comparison method (
k
= 100,
n
= 4) (Example 9.4.5)
Table 9.6 Data for a replicated monadic A–Not A test (Example 9.4.6)
Table 9.7 Pooled data for a replicated monadic A–Not A test (Example 9.4.6)
Table 9.8 Distribution of purchases of a brand over 12 weeks (Example 9.4.7)
Table 9.9 Sample sizes (
k
) required to reach 0.8 power for a replicated similarity preference test and a nondirectional 2-AFC test (
α
= 0.1)
Chapter 10: Replicated discrimination tests: corrected beta-binomial model
Table 10.1
Table 10.2
Table 10.3 Data for a replicated Triangular test where
n
= 3,
k
= 30 (Example 10.3.5)
Chapter 11: Replicated discrimination tests: Dirichlet–multinomial (DM) model
Table 11.1 Probabilities of a DM distribution (
n
= 3,
m
= 3,
g
= 9,
π
= (0.5, 0.2, 0.3))
Table 11.2 Data for a replicated preference test with a “no preference” option (
k
= 30,
n
= 4,
m
= 3)
Table 11.3 Housing satisfaction data
Table 11.4 Summary of data in Table 11.3
Table 11.5 Frequencies of ratings for 25 subjects with 4 replications in a replicated paired designed Degree of Difference test
Table 11.6 Summary of data in Table 11.5
Table 11.7 Data for a replicated mixed A–Not A test
Table 11.8 Pooled data for a replicated mixed A–Not A test
Table 11.9 Evaluations of three products by 10 panelists with five replications (1 = “ acceptable, ” 0 = “ unaccepTable ”)
Table 11.10 Response patterns for three products (1 = “ acceptable, ” 0 = “ unaccepTable ”)
Table 11.11 Numbers of response patterns for each panelist
Table 11.12 Counts of responses for a CO (Check One) question
Table 11.13 Example of a CATA (Check All That Apply) question
Table 11.14 Responses to the first item, “Morning, just after waking up,” and the last item, “Just before going to bed,” in the CATA question in Table 11.13
Chapter 12: Measurements of sensory thresholds
Table 12.1 Dose response data for Example 12.2.1 (from Bliss 1935, Prentice 1976)
Table 12.2 Data for Example 12.2.2
Table 12.3 Data in Example 12.3.1
Table 12.4 Data for Example 12.3.2 (Hoekstra 1987, Morgan 1992, p. 95)
Table 12.5 Neonatal acute toxicity to trichloromethane (Example 12.4.1)
Table 12.6 Maximum-likelihood parameter estimates and variance–covariance matrix for the parameters of the dose–response model based on a beta-binomial distribution
Table 12.7 Maximum likelihood parameter estimates and variance–covariance matrix for the parameters of the dose–response model based on a CBB distribution
Table 12.8 Data for Examples 12.4.2 and 12.4.3
Chapter 13: Measurements of sensory risk with negative sensory effects
Table 13.1 Consumer response data for Example 13.2.1
Table 13.2 Data summary of consumer responses for Example 13.3.1
Table 13.3 Summarized data for Example 13.4.1
Table 13.4 Summarized data for Example 13.4.2
Chapter 14: Measurements of time intensity
Table 14.1 Data for Example 14.2.1
Table 14.2 Averaged
I
max
values for samples
Table 14.3 Alpha upper quantile for adaptive Neyman test for curves
Chapter 15: Measurements of sensory shelf life
Table 15.1 Data in Example 15.3.1 (“ssldat”) (“ 1 ” = “ yes ”; “ 2 ” = “ no ”)
Table 15.2 Data in Example 15.3.2 (“ssldat2”) (“ 1 ” = “ yes ”; “ 2 ” = “ no ”)
Chapter 16: Measurements of the performance of a trained sensory panel and panelists
Table 16.1 Ratings for
k
random samples given by
n
panelists in a panel
Table 16.2 ANOVA one-way random effects model
Table 16.3 Numerical example for continuous data
Table 16.4 Numerical example for ordinary data
Table 16.5 Ranks of ordinary data
Table 16.6 Numerical example for ranking data
Table 16.7 Numerical example for multiple-choice data
Table 16.8 ICCs (
r
I
) for Cronbach's coefficient alpha (
r
α
) = 0.70 and
n
= 3 : 15
Table 16.9 Ratings quality for 10 attributes
Table 16.10 Ratings quality for 10 panelists
Table 16.11 Format of the data summary for the “ M + N ” experiment
Table 16.12 Probabilities of making correct selections in Fisher's exact test using the specified “ M + N ” method with M = N
Table 16.13 Cumulative probabilities (
p
-values in a one-sided test) of making correct selections in Fisher's exact test using the specified “ M + N ” method with M = N
Table 16.14 Outcome of Fisher's “The Lady Tasting Tea” experiment
Chapter 17: Measurements of consumer emotions and psychographics
Table 17.1 Positive and Negative Affect Schedule (PANAS)
Table 17.2 Arizona Integrative Outcomes Scale (AIOS)
Table 17.3 Consumer involvement profile (CIP)
Table 17.4 Example of CIP
Table 17.5 Price–quality consciousness
Table 17.6 Food neophobia scale (FNS)
Table 17.7 General neophobia scale (GNS)
Table 17.8 Brief Sensation Seeking Scale, 4-Item (BSSS-4)
Table 17.9 Sensation Seeking, 2-Item (SS2)
Table 17.10 General self-efficacy (GSE)
Table 17.11 Medication Adherence Self-Efficacy Scale
Table 17.12 Resilience
Table 17.13 Well-being rating means of the four regions
Table 17.14 Treatment effects on overall liking
Chapter 18: Measurements of the relative importance of attributes
Table 18.1 Relative importance values and 95% confidence intervals of attributes in Example 18.2.1
Table 18.2 Relative importance of attributes to purchase intent in Example 18.2.2
Table 18.3 Relative importance of panel descriptive attributes for consumer overall liking, determined by Breiman's RF
Table 18.4 Data for Example 18.5.1
Table 18.5 Relative-importance vectors and covariance matrices for three studies (Example 18.6.1)
Table 18.6 Group and population relative-importance vectors and covariance matrices
Table 18.7 Results of a penalty analysis for a product (
n
= 120)
Table 18.8 Relative-importance values of JAR attributes to overall liking in Example 18.7.1
Appendix A: List of R/S-Plus codes, data files, and packages used in the book
Table .1 List of R/S-Plus codes used in the book
Table A.2 List of some data files used in the book
Table A.3 List of R/S-Plus packages used in the book
Sensory Discrimination Tests and Measurements
Sensometrics in Sensory Evaluation
Second Edition
Jian Bi
Sensometrics Research and Service
Richmond, Virginia, USA
This edition first published 2015 © 2015 by John Wiley & Sons, Ltd.
Registered office: John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK
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A catalogue record for this book is available from the British Library.
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To my family
Preface
The second edition of this book is similar to the first in that it focuses on sensory tests and measurements from a statistical perspective. However, it expands greatly upon the first in the following aspects:
The second edition extends the discussion of sensory measurement from Thurstonian discriminal distance
(
Chapter 2
) to the area (
R
-index and Gini-index) under the ROC curve in Signal Detection Theory (
Chapter 3
) and to wider sensory measurements, including sensory threshold (
Chapter 12
), sensory risk (
Chapter 13
), time-intensity (
Chapter 14
), sensory shelf life (
Chapter 15
), the performance of a trained sensory panel and panelists (
Chapter 16
), consumer emotions and psychographics (
Chapter 17
), and the relative importance of attributes (
Chapter 18
).
The second edition extends the discussion of sensory discrimination tests from main difference tests (
Chapter 4
) to similarity/equivalence tests (
Chapter 5
) and Bayesian tests (
Chapter 6
).
Chapters 7
–
11
discuss novel methods for modified discrimination tests, multiple-sample discrimination tests, and replicated discrimination tests.
More R/S-Plus built-in programs, packages, and codes are used in the second edition. Some of the tables for statistical tests used in the first edition are replaced by R/S-Plus codes. The R/S-Plus codes and some of the data files used in the book are listed in Tables A.
1
and A.
2
in Appendix A and are available from the companion Web site,
www.wiley.com/go/bi/SensoryDiscrimination
. The R packages (R Development Core Team 2013) used in the book are listed in Table A.
3
in Appendix A and can be downloaded from
www.r-project.org
.
The title of the book has been changed to reflect the expanded and changed contents of the second edition. The title of the first edition was
Sensory Discrimination Tests and Measurements: Statistical Principles, Procedures, and Tables
, while is the title of the second edition is
Sensory Discrimination Tests and Measurements: Sensometrics in Sensory Evaluation
.
The book is organized as follows:
Chapter 1
briefly describes sensory discrimination methods.
Chapter 2
and
3
discuss sensory effect measurement using distance index, Thurstonian
, and the area indices
R
-index and Gini-index.
Chapter 4
–
6
discuss sensory discrimination tests, including difference testing, similarity (equivalence) testing, and the Bayesian approach to discrimination testing.
Chapter 7
and
8
discuss modified and multiple-sample discrimination tests.
Chapter 9
–
11
discuss replicated discrimination tests based on the beta-binomial (BB) model, the corrected beta-binomial (CBB) model, and the Dirichlet–multinomial (DM) model, respectively.
Chapters 12
–
18
discuss diverse and specific sensory measurements in a broad sense, from measurements of sensory threshold (
Chapter 12
) to measurements of the relative importance of attributes (
Chapter 18
).
The assumed readers of the book are researchers and practitioners in the sensory and consumer field, as well as anyone who is interested in sensometrics. The book is intended to be a useful reference for modern sensory analysis and consumer research, especially for sensometrics. It is different in its objective from the textbooks widely used in the sensory field (e.g., Amerine et al. 1965, Stone and Sidel 2004, Meilgaard et al. 2006, Lawless and Heymann 2010) and from common guidebooks (e.g., Chambers and Wolf 1996, Kemp et al. 2009). It is also different in perspective and focus from the books on quantitative sensory analysis and applied statistics in sensory and consumer research (e.g., O'Mahony 1986b, Næs and Risvik 1996, Meullenet et al. 2007, Mazzocchi 2008, Gacula et al. 2009, Næs et al. 2010, Lawless 2013), although it has some topics in common with these.
References
Amerine, M. A., Pangborn, R. M., and Roessler, E. B. 1965.
Principles of Sensory Evaluation of Food
. Academic Press, New York.
Chambers, E. VI and Wolf, M. B. 1996.
Sensory Testing Methods
(2nd ed.). ASTM Manual Series MNL. ASTM International, West Conshohocken, PA.
Gacula, M., Singh, J., Bi, J., and Altan, S. 2009.
Statistical Methods in Food and Consumer Research
(2nd ed.). Elsevier/Academic Press, Amsterdam.
Kemp, S. E., Hollowood, T., and Hort, J. 2009.
Sensory Evaluation. A Practical Handbook
. John Wiley & Sons, Chichester.
Lawless, H. T. 2013.
Quantitative Sensory Analysis: Psychophysics, Models and Intelligent Design
. Wiley-Blackwell, Oxford.
Lawless, H. T. and Heymann, H. 2010.
Sensory Evaluation of Food: Principles and Practice
(2nd ed.). Springer, New York.
Mazzocchi, M. 2008.
Sensory for Marketing and Consumer Research
. Sage, Los Angeles, CA.
Meilgaard, M. C., Civille, G. V., and Carr B. T. 2006.
Sensory Evaluation Technique
(4th ed.). CRC Press, Boca Raton, FL.
Meullenet, J. F., Xiong, R., and Findlay, C. J. 2007.
Multivariate and probabilistic Analysis of Sensory Science Problems
. Blackwell, Ames, IA.
Næs, T. and Risvik, E. 1996.
Multivariate Analysis of Data in Sensory Science
. Elsevier, Amsterdam.
Næs, T., Brockhoff, P. B., and Tomic, O. 2010.
Statistics for Sensory and Consumer Science
. John Wiley & Sons, Chichester.
R Development Core Team. 2013.
R: A Language and Environment for Statistical Computing
. R Foundation for Statistical Computing, Vienna. Available from:
http://www.R-project.org
/ (last accessed April 14, 2015).
Stone, H. and Sidel, J. 2004.
Sensory Evaluation Practices
(3rd ed.). Academic Press, Amsterdam.
Acknowledgments
I am grateful to Professor Michael O'Mahony, Professor Hye-Seong Lee, Dr. Carla Kuesten, Dr. Herbert Meiselman, Julia Chung, Yaohua Feng, and Pooja Chopra, who are the co-authors of our papers published in recent years.
I would like to thank the Wiley editor David McDade and project editor Audrie Tan for their encouragement in the completion of this project.
I wish to dedicate this book to my wife, Yulin, and my daughter, Cindy.
Jian Bi
Richmond, Virginia
December 2014
About the companion website
This book is accompanied by a companion website:
www.wiley.com/go/bi/SensoryDiscrimination
The website includes:
R/S-Plus codes for downloading
Data files for downloading
The lists of R/S-Plus codes and data files available on the website are provided in Appendix A on page (insert page number) of this book.
Introduction
1.1 Sensometrics
This book is about sensometrics, focusing on sensory discrimination tests and measurements in the domain of sensory analysis. Sensometrics is a subfield of, or an area related to, sensory and consumer science. According to Brockhoff (2011), “Sensometrics is the scientific area that applies mathematical and statistical methods to model data from sensory and consumer science.” It is similar to psychometrics in psychology, biometrics in biology, chemometrics in chemistry, econometrics in economy, politimetrics in macropolitics, environmetrics in environmental sciences, and so on. Sensometrics has experienced rapid growth in both academia and industry within the last 2 or 3 decades. It plays an important role in modern sensory analysis and consumer research, especially in the coming Big Data era.
1.2 Sensory tests and measurements
The basic functions of sensory analysis are to provide reliable sensory measurements and to conduct valid tests. Statistical hypothesis testing is the theoretical basis of sensory tests. Statistical tests include both difference tests and similarity (equivalence) tests. The Thurstonian model (Thurstone 1927) and Signal Detection Theory (SDT) (Green and Swets 1966, Macmillan and Creelman 2005) are the theoretical basis for sensory effect measurement. Psychometric functions provide invariable indices that are independent of the methods used for measurements. Notably, the Thurstonian discriminal distance (or ) (ASTM 2012) and the area (R-index) under the receiver operating characteristic (ROC) curve in SDT have been widely accepted and are used in both food and sensory fields. Daniel M. Ennis (1993, 1998, 2003) and Michael O'Mahony (1979, 1992), among others, should be particularly thanked for their insight and foresight in introducing the methodologies into these fields and for tirelessly promoting their research and application over recent decades.
Sensory measurement takes on a broad range of meanings and contents. Besides sensory effect measurement using Thurstonian discriminal distance and area under ROC curve, the following measurements can also be regarded as different types of sensory measurement: sensory threshold measurement, sensory risk measurement, time intensity measurement, sensory shelf life measurement, trained sensory panel/panelist performance measurement, consumer emotions and psychographics measurement, and attribute relative importance measurement. Specific statistical methodologies are used for different types of sensory measurement.
1.3 A brief review of sensory analysis methodologies
Sensory analysis can be divided into two types: laboratory sensory analysis and consumer sensory analysis. In laboratory sensory analysis, a trained panel is used as an analytical instrument to measure the sensory properties of products. In consumer sensory analysis, a sample of a specified consumer population is used to test and predict consumer responses to products. These have different goals and functions, but share some methodologies.
Discriminative analysis and descriptive analysis are the main classes of methodology for both laboratory and consumer sensory analyses. Discriminative analysis includes discrimination tests and measurements. In this book, discrimination tests are used to determine whether a difference exists between treatments for confusable sensory properties of products (difference test), or whether a difference is smaller than a specified limit (similarity/equivalence test), usually using a two-point scale or a rating or ranking scale. Discrimination measurements are used to measure, on a particular index, the extent of the difference/similarity. There are two sources of sensory differences: intensity and preference. A discrimination test is used when testing difference/similarity of intensity; a preference test is used when testing difference/similarity of preference. Descriptive analysis is used to determine, on a rating scale, how much of a specific characteristic difference exists among products (quantitative descriptive analysis) or to characterize a product's sensory attributes (qualitative descriptive analysis). Quantitative descriptive analysis for preference is also called “acceptance testing.”
Acceptance or preference testing is of very limited value for a laboratory panel (Amerine et al. 1965) but is valuable in a consumer analysis setting. Laboratory discrimination testing, using a trained panel under controlled conditions, is referred to as “Sensory Evaluation I,” while consumer discrimination testing, using a sample of untrained consumers under ordinary consumption (eating) conditions, is referred to as “Sensory Evaluation II” (O'Mahony 1995). Confusion of the two will lead to misleading conclusions. Controversy over whether the consumer can be used for discrimination testing ignores the fact that laboratory and consumer discrimination tests have different goals and functions.
The distinction between discriminative analysis and quantitative descriptive analysis is not absolute from the viewpoint of modern sensory analysis. The Thurstonian model and SDT (see Chapters 2, 3) can be used for both discriminative analysis and quantitative descriptive analysis. The Thurstonian (or ), a measure of sensory difference/similarity, can be obtained from any kind of scale used in discriminative and descriptive analysis. A rating scale, typically used in descriptive analysis, is also used in some modified discrimination tests.
The following types of analysis are the important topics and methodologies of sensory analysis: sensory threshold analysis, sensory risk analysis, time intensity analysis, sensory shelf life analysis, trained sensory panel/panelist performance analysis, consumer emotions and psychographics analysis, and sensory attribute relative importance analysis.
This book is primarily concerned with methodology, mainly from a statistical point of view, of sensory discrimination tests and measurements, including laboratory and consumer sensory analyses.
1.4 Method, test, and measurement
In this book, a distinction is made among three terms: “sensory discrimination method,” “sensory discrimination test,” and “sensory discrimination measurement.”
In sensory discriminative analysis, certain procedures are used for experiments. These procedures are called discrimination methods (e.g., the Duo–Trio method, the Triangular method, the ratings method).
When discrimination procedures are used for statistical hypothesis testing, or when statistical testing is conducted for the data from a discrimination procedure, the procedure is called discrimination testing (e.g., the Duo–Trio test, the Triangular test, the ratings test). In this book, discrimination testing is referred to as both difference testing and similarity/equivalence testing for both preference and intensity (Chapters 4, 5). Bayesian statistical tests are also discussed, in Chapter 6. In Chapter 7, some modified discrimination tests are discussed. Multiple-sample discrimination tests are discussed in Chapter 8. Replicated discrimination tests are discussed in Chapters 9–11.
When discrimination procedures are used to measure, or, in other words, when an index (e.g., Thurstonian (or ) or R-index) is produced using the data from a discrimination procedure, the procedure is called a discrimination measurement (e.g., Duo–Trio measurement, Triangular measurement, ratings of the A–Not A measurement). Effect measurement includes distance measure and area measure R-index (or Gini-index). Besides the effect measurement discussed in Chapters 2, 3, other sensory measurements are discussed in Chapters 12–18. Both sensory testing and measurement are of importance and are useful. However, generally speaking, sensory measurement is more important and more useful in practice. Sensory measurements provide indices of the magnitude of sensory effects.
1.5 Commonly used discrimination methods
1.5.1 Forced-choice methods
The Two-Alternative Forced Choice (2-AFC) method (Green and Swets 1966): This method is also called the paired comparison method (Dawson and Harris 1951, Peryam 1958). With this method, the panelist receives a pair of coded samples, A and B, for comparison on the basis of some specified sensory characteristic. The possible pairs are AB and BA. The panelist is asked to select the sample with the strongest (or weakest) sensory characteristic. The panelist is required to select one even if he or she cannot detect the difference.
The Three-Alternative Forced Choice (3-AFC) method (Green and Swets 1966): Three samples of two products, A and B, are presented to each panelist. Two of them are the same. The possible sets of samples are AAB, ABA, BAA or ABB, BAB, BBA. The panelist is asked to select the sample with the strongest or the weakest characteristic. The panelist has to select a sample even if he or she cannot identify the one with the strongest or the weakest sensory characteristic.
The Four-Alternative Forced Choice (4-AFC) method (Swets 1959): Four samples of two products, A and B, are presented to each panelist. Three of them are the same. The possible sets of samples are AAAB, AABA, ABAA, BAAA or BBBA, BBAB, BABB, ABBB. The panelist is asked to select the sample with the strongest or the weakest characteristic. The panelist is required to select a sample even if he or she cannot identify the one with the strongest or weakest sensory characteristic.
The Triangular (Triangle) method (Dawson and Harris 1951, Peryam 1958): Three samples of two products, A and B, are presented to each panelist. Two of them are the same. The possible sets of samples are AAB, ABA, BAA, ABB, BAB, and BBA. The panelist is asked to select the odd sample. The panelist is required to select one sample even if he or she cannot identify the odd one.
The Duo–Trio method (Dawson and Harris 1951, Peryam 1958): Three samples of two products, A and B, are presented to each panelist. Two of them are the same. The possible sets of samples are A: AB, A: BA, B: AB, and B: BA. The first one is labeled as the “control.” The panelist is asked which of the two test samples is the same as the control sample. The panelist is required to select one sample to match the “control” sample even if he or she cannot identify which is the same as the control.
The Unspecified Tetrad method (Lockhart 1951): Four stimuli, two of A and two of B, are used, where A and B are confusable and vary in the relative strengths of their sensory attributes. Panelists are told that there are two pairs of putatively identical stimuli and to sort them into their pairs.
The Specified Tetrad method (Wood 1949): Four stimuli, two of A and two of B, are used, where A and B are confusable and vary in the relative strengths of their sensory attributes. Panelists are told that there are two pairs of putatively identical stimuli and to indicate the two stimuli of specified A or B.
The Dual Pair (4IAX) method (Macmillan
et al
. 1977): Two pairs of samples are presented simultaneously to the panelist. One pair is composed of samples of the same stimuli, AA or BB, while the other is composed of samples of different stimuli, AB or BA. The panelist is told to select the most different pair of the two pairs.
The “
” method (Lockhart 1951):
samples with M sample A and N sample B are presented. The panelist is told to divide the samples into two groups, of A and B. There are two versions of the method: specified and unspecified. This is a generalization of many forced-choice discrimination methods, including the Multiple-Alternative Forced Choice (m-AFC), Triangle, and Specified and Unspecified Tetrad. The “
” with larger M and N can be regarded as a specific discrimination method with a new model. Unlike the conventional difference tests using the “
” with small M and N based on a binomial model, the “
” with larger M and
can reach a statistical significance in a single trial for only one “
” sample set based on a hypergeometric model. The methods that use a new model are particularly useful for assessing the discriminability of sensory panels and panelists; these are discussed in Chapter 16.5.
1.5.2 Methods with response bias
The A–Not A method (Peryam 1958): Panelists are familiarized with samples A and Not A. One sample, which is either A or Not A, is presented to each panelist. The panelist is asked if the sample is A or Not A.
The A–Not A with Remind (A–Not AR) method (Macmillan and Creelman 2005): Unlike the A–Not A, which is a single-sample presentation, a reminder (e.g., sample A) is provided before each test sample (sample A or Not A) in order to jog the panelist's memory.
The Same–Different method (see, e.g., Pfaffmann 1954, Amerine
et al
. 1965, Macmillan
et al
. 1977, Meilgaard
et al
. 1991, among others, for the same method under different names): A pair of samples, A and B, is presented to each panelist. The four possible sample pairs are AA, BB, AB, and BA. The panelist is asked if the two samples that he or she received are the same or different.
The ratings methods discussed in the book include ratings of the A–Not A, A–Not AR, and Same–Different methods.
1.6 Classification of sensory discrimination methods
Sensory discrimination methods are typically classified according to the number of samples presented for evaluation, as single-sample (stimulus), two-sample, three-sample, or multiple-sample methods. This classification is natural, but it does not reflect the inherent characteristics of the methods. In this book, the discrimination methods are classified according to the decision rules and cognitive strategies they involve. This kind of classification may be more reasonable and profound. In the following chapters, we will see how methods in the same class correspond to the same types of statistical model and decision rules.
1.6.1 Methods requiring and not requiring the nature of difference
There are two different types of instruction in the discrimination method. One type involves asking the panelists to indicate the nature of difference in the products under evaluation; for example, “Which sample is sweeter?” (the 2-AFC and the 3-AFC methods); or “Is the sample A or Not A?” (the A–Not A method). The other type compares the distance of difference; for example, “Which of the two test samples is the same as the control sample?” (the Duo–Trio method); “Which of these three samples is the odd one out?” (the Triangular method); or “Are these two samples the ‘same’ or ‘different’?” (the Same–Different method). The two types involve different cognitive strategies and result in different percentages of correct responses. Hence, the discrimination methods can be divided into these two types: methods using the “skimming” strategy and methods using the “comparison of distance” strategy (O'Mahony et al. 1994). The two types of methods can also called specified or unspecified method.
1.6.2 Methods with and without response bias
Response bias is a basic problem with sensory discrimination methods. Many authors hav eaddressed this problem (e.g. Torgerson 1958, Green and Swets 1966, Macmillan and Creelman 2005, O'Mahony 1989, 1992, 1995). Sensory discrimination methods are designed for the detection and measurement of confusable sensory differences. There is no response bias if the difference is large enough, but response bias may occur when the difference between two products is so small that a panelist makes an uncertain judgment. In this situation, how large a difference can be judged as a difference may play a role in the decision process. Criterion variation (strictness or laxness of a criterion) causes response bias. A response bias is a psychological tendency to favor one side of a criterion. Response bias is independent of sensitivity. This is why the methods with response bias (e.g., the A–Not A and the Same–Different methods) can also be used for difference testing. However, response bias affects test effectiveness (power).
Forced-choice procedures can be used to stabilize decision criteria. Hence, most sensory discrimination methods are designed as forced-choice procedures. A forced-choice procedure must have at least three characteristics: (1) Two sides of a criterion must be presented. The two sides may be “strong” and “weak,” if the criterion is about the nature of the difference between products. The two sides may be “same” and “different,” if the criterion is about the distance of the difference between products. Because a single sample or two samples of the same type cannot contain two sides of a criterion, evaluating a single sample or the same type of sample is not a forced-choice procedure. Because a single pair of samples or a pair of samples of the same type cannot contain two sides of a criterion concerning the distance of a difference, evaluating a single sample pair or a pair of samples of the same type is not a forced-choice procedure, either. (2) A panelist should be instructed that the samples presented for evaluation contain the two sides of a criterion. (3) A response must be given in terms of one clearly defined category. The “don't know” response is not allowed.
1.6.3 Methods using multiple sets and only one set of samples
In conventional discrimination tests using forced-choice methods, such as the “” method with small M and N, we cannot get a statistical conclusion from a response for only one set of samples, because even for the perfect response for a set of the samples, the chance probability (e.g., 1/3 in the 3-AFC) is still larger than any acceptable significance level. Hence, multiple sets of “” samples are needed. A binomial model is used for analysis of the proportion of correct responses. However, we can get a conclusion based on responses in a table for only one set of “” samples with larger M and N in a Fisher's exact test.
1.6.4 Methods with binary and ratings data
The responses in forced-choice methods are binary. The responses in the methods with response bias may be binary or ratings. The ratings of the methods represent degrees of sureness of a judgment or different decision criteria. For example, the responses in an A–Not A test are “A”/“Not A” (i.e., 1 or 2). The responses in a ratings of the A–Not A test may be a six-point scale with (1, 2, 3, 4, 5, 6) corresponding to (A, A?, A??, N??, N?, N).
Table 1.1 describes the classifications of sensory discrimination methods.
Table 1.1 Classifications of sensory discrimination methods
Requiring the nature of difference
Comparing distance of difference
Forced-choice methods
Based on multiple sets of samples
2-AFC
Duo–Trio
3-AFC
Triangular
4-AFC
Unspecified Tetrad
Specified Tetrad
Dual-Pair (4IAX)
Based on one set of samples
Specified “
” with larger M and N
Unspecified “
” with larger M and N
Methods with response bias
Binary response
A–Not A
Same–Different
A–Not AR
Ratings response
Ratings of A–Not A
Ratings of Same–DifferentRatings of A–Not AR
