ASTM E2262-03(2014)

Standard Practice for Estimating Thurstonian Discriminal Distances

SIGNIFICANCE AND USE
5.1 Under the assumptions of the model, the Thurstonian model approach to measuring the perceived difference between two samples (whether overall or for a specific attribute) is independent of the sensory method used to collect the data. Converting results obtained from different test methods to d' values permits the assessment of relative differences among samples without requiring that the samples be compared to each other directly or that the same test methods be used for all pairs of samples.  
5.2 Thurstonian scaling has been applied to:  
5.2.1 Creating a historical database to track differences between production and reference samples over periods in which different test methods were used to measure the difference,  
5.2.2 Comparing the relative sensitivities of different user groups and consumer segments,  
5.2.3 Comparing trained panels that use different measuring techniques,  
5.2.4 Comparing the relative sensitivities of consumers versus trained panels,  
5.2.5 Comparing different methods of consumer testing (for example, CLT versus HUT, preference versus hedonic scales, etc.), and  
5.2.6 Comparing different discrimination test methods.
SCOPE
1.1 This practice describes procedures to estimate Thurstonian discriminal distances (that is, d' values) from data obtained on two samples. Procedures are presented for four forced-choice methods (that is, the triangle, the duo-trio, the 3-alternative-forced-choice (or 3-AFC) and the 2-AFC (also called the directional difference test)), the A/Not-A method, the Same-Different method and for data obtained from ordered category scales. Procedures for estimating the variance of d' are also presented. Thus, confidence intervals and statistical tests can be calculated for d'.  
1.2 The procedures in this document pertain only to the unidimensional, equal-variance model. Other, more complicated Thurstonian models, involving multiple dimensions and unequal variances exist but are not addressed in this standard. The procedure for forced-choice methods is limited to dichotomous responses. The procedure for the A/Not-A method assumes equal sample sizes for the two samples. The procedure for the Same-Different method assumes equal sample sizes for the matched and unmatched pairs of samples. For all methods, only unreplicated tests are considered. (Tests in which each assessor performs multiple (that is, replicated) evaluations require different analyses.)  
1.3 Thurstonian scaling is a method for measuring the perceptual difference between two samples based on a probabilistic model for categorical choice decision making. The magnitude of the perceived difference, δ, can be estimated from the assessors' categorical choices using the methods described in this practice (See Appendix X3 for a more detailed description of Thurstonian scaling).  
1.4 In theory, the Thurstonian δ does not depend on the method used to measure the difference between two samples. As such, δ provides a common scale of measure for comparing samples measured under a variety of test conditions. For example, Thurstonian scaling can be used to compare products measured under different test conditions, to compare panels (trained, consumer or both) that have evaluated the same samples (using the same or different test methods) and to compare test methods on their ability to discriminate samples that exhibit a fixed sensory difference.  
1.5 This standard may involve hazardous materials, operations and equipment. This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

General Information

• Status: Historical
• Publication Date: 31-Aug-2014
• ICS: 67.240 - Sensory analysis
• Technical Committee: E18 - Sensory Evaluation
• Drafting Committee: E18.03 - Sensory Theory and Statistics

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E2262 − 03 (Reapproved 2014)
Standard Practice for
Estimating Thurstonian Discriminal Distances
This standard is issued under the fixed designation E2262; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope (trained, consumer or both) that have evaluated the same
samples (using the same or different test methods) and to
1.1 This practice describes procedures to estimate Thursto-
compare test methods on their ability to discriminate samples
nian discriminal distances (that is, d’ values) from data
that exhibit a fixed sensory difference.
obtained on two samples. Procedures are presented for four
1.5 This standard may involve hazardous materials, opera-
forced-choice methods (that is, the triangle, the duo-trio, the
tions and equipment. This standard does not purport to address
3-alternative-forced-choice (or 3-AFC) and the 2-AFC (also
all of the safety concerns, if any, associated with its use. It is
calledthedirectionaldifferencetest)),theA/Not-Amethod,the
the responsibility of the user of this standard to establish
Same-Different method and for data obtained from ordered
appropriate safety and health practices and determine the
category scales. Procedures for estimating the variance of d’
applicability of regulatory limitations prior to use.
are also presented. Thus, confidence intervals and statistical
tests can be calculated for d’.
2. Referenced Documents
1.2 The procedures in this document pertain only to the
2.1 ASTM Standards:
unidimensional, equal-variance model. Other, more compli-
E253Terminology Relating to Sensory Evaluation of Mate-
cated Thurstonian models, involving multiple dimensions and
rials and Products
unequal variances exist but are not addressed in this standard.
E456Terminology Relating to Quality and Statistics
Theprocedureforforced-choicemethodsislimitedtodichoto-
E460Practice for Determining Effect of Packaging on Food
mous responses. The procedure for the A/Not-A method
and Beverage Products During Storage
assumesequalsamplesizesforthetwosamples.Theprocedure
E679Practice for Determination of Odor and Taste Thresh-
for the Same-Different method assumes equal sample sizes for
olds By a Forced-ChoiceAscending Concentration Series
the matched and unmatched pairs of samples. For all methods,
Method of Limits
only unreplicated tests are considered. (Tests in which each
E1432Practice for Defining and Calculating Individual and
assessor performs multiple (that is, replicated) evaluations
Group SensoryThresholds from Forced-Choice Data Sets
require different analyses.)
of Intermediate Size
1.3 Thurstonian scaling is a method for measuring the
E1593GuideforAssessingtheEfficacyofAirCareProducts
perceptual difference between two samples based on a proba-
in Reducing the Perception of Indoor Malodor
bilistic model for categorical choice decision making. The
E1627Practice for Sensory Evaluation of Edible Oils and
magnitude of the perceived difference, δ, can be estimated
Fats
from the assessors’ categorical choices using the methods
E1697Test Method for Unipolar Magnitude Estimation of
describedinthispractice(SeeAppendixX3foramoredetailed
Sensory Attributes
description of Thurstonian scaling).
E1810Practice for Evaluating Effects of Contaminants on
1.4 In theory, the Thurstonian δ does not depend on the Odor and Taste of Exposed Fish
method used to measure the difference between two samples. E1879Guide for Sensory Evaluation of Beverages Contain-
Assuch, δprovidesacommonscaleofmeasureforcomparing ing Alcohol
samples measured under a variety of test conditions. For E1885Test Method for Sensory Analysis—Triangle Test
example,Thurstonian scaling can be used to compare products E1958Guide for Sensory Claim Substantiation
measured under different test conditions, to compare panels E2049 Guide for Quantitative Attribute Evaluation of
Fragrance/Odors for Shampoos and Hair Conditioners by
Trained Assessors
This practice is under the jurisdiction of ASTM Committee E18 on Sensory
Evaluation and is the direct responsibility of Subcommittee E18.03 on Sensory
Theory and Statistics. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Sept. 1, 2014. Published September 2014. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 2003. Last previous edition approved in 2009 as E2262–03 (2009). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/E2262-03R14. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2262 − 03 (2014)
E2164Test Method for Directional Difference Test proportion of the “A” responses for the A sample (p ). The
a
2.2 ASTM Publication: same method is used to estimate the variance of d’, S (d’),
Manual 26Sensory Testing Methods, 2nd Edition using Table X1.10.
2.3 ISO Standard:
4.4 For the Same-Different method, tally the proportion of
ISO 5495Sensory Analysis—Methodology—Paired Com-
“same” responses for the matched pairs of samples (that is,
parison
A/A or B/B) and the proportion of “same” responses for the
unmatched pairs of samples (that is, A/B or B/A). Read the
3. Terminology
valueof d’fromTableX1.11inthecolumnthatcorrespondsto
3.1 For definitions of terms relating to sensory analysis, see
the observed proportion of “same” responses for the un-
Terminology E253, and for terms relating to statistics, see
matched pairs (p / ) and the row that corresponds to the
s u
Terminology E456.
observed proportion of the “same” responses for the matched
3.2 Definitions of Terms Specific to This Standard: pairs (p / ). The same method is used to estimate the variance
s m
of d’, S (d’), using Table X1.12.
3.2.1 δ—theThurstoniandiscriminaldistanceisthedistance
between the means of the distributions of sensory magnitudes
4.5 For ordered category scales, a rapid, table-look-up
of the two samples in the test (see Appendix X3).
approach is used. For each sample, the category scale data are
3.2.2 d’—the statistic used to estimate δ based on the data collapsed into two categories. One sample is selected to be the
obtained from the test. “A” sample and the other sample is selected to be the “Not-A”
sample. Choice proportions are tallied for each sample and the
3.2.3 choice proportion (P )—the expected proportion of
c
values of d’ and its variance, S (d’), are obtained from Tables
responsesfromaforced-choicemethod(forexample,ifthereis
X1.9 and X1.10, respectively, by the same techniques used in
noperceptibledifferencebetweenthesamplesinatriangletest,
the A/Not A method.
P = 1/3. If there is a perceptible difference, P > 1/3).
c c
3.2.4 observed choice proportion (p)—the statistic used to
c
5. Significance and Use
estimate choice proportion, P , where p = x/n, where x is the
c c
5.1 Under the assumptions of the model, the Thurstonian
observednumberofcorrectresponsesand nisthesamplesize.
modelapproachtomeasuringtheperceiveddifferencebetween
4. Summary of Practice
two samples (whether overall or for a specific attribute) is
independent of the sensory method used to collect the data.
4.1 Determinethetypeofdatacollectedonthetwosamples:
Converting results obtained from different test methods to d’
data from a forced-choice test, an A/Not A test, a same-
values permits the assessment of relative differences among
different test or an ordered category scale.
samples without requiring that the samples be compared to
4.2 For forced-choice tests, reference the table that corre-
eachotherdirectlyorthatthesametestmethodsbeusedforall
sponds to the test method (that is, triangle test—Tables X1.1
pairs of samples.
and X1.2; duo-trio test—Tables X1.3 and X1.4; 3-AFC test—
5.2 Thurstonian scaling has been applied to:
Tables X1.5 and X1.6; or 2-AFC test—Tables X1.7 and X1.8).
5.2.1 Creating a historical database to track differences
Identify the entry in the table closest to the observed choice
between production and reference samples over periods in
proportion (p ) from the test. Read the estimated value of δ
c
which different test methods were used to measure the
(that is, d’) from the corresponding row and column headings
difference,
of the table. Estimate the variance of d’ by referencing the
5.2.2 Comparing the relative sensitivities of different user
appropriate table for the test method. Find the value of B that
groups and consumer segments,
corresponds to the value of d’ obtained in the first step. The
5.2.3 Comparingtrainedpanelsthatusedifferentmeasuring
estimated variance of d’is S (d’) = B/n, where n is the sample
techniques,
size. Use the estimates d’ and S (d’) to construct confidence
5.2.4 Comparing the relative sensitivities of consumers
intervalsandtestsofhypothesesrelatedtotheobjectivesofthe
versus trained panels,
research.
5.2.5 Comparing different methods of consumer testing (for
4.3 For the A/Not A method, tally the observed choice
example, CLT versus HUT, preference versus hedonic scales,
proportions of “A” responses for the A sample and the “A”
etc.), and
responses for the Not-A sample. Read the value of d’ from
5.2.6 Comparing different discrimination test methods.
Table X1.9 in the column that corresponds to the observed
choice proportion of the “A” responses for the Not-A sample
6. Procedure
(p ) and the row that corresponds to the observed choice
na
6.1 Forced-Choice Methods—The relationship between δ
andtheexpectedchoiceproportion, P ,isdifferentfordifferent
c
Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
forced-choice methods because the decision rule used by the
4th Floor, New York, NY 10036.
assessors varies from one method to another (see Appendix
The variance of d’ is a complicated function of the true value of δ and the
decision rule when associated with the test method being used (see Appendix X3).
X3). As a result, different tables are required to estimate δ
However, regardless of the test method, the variance of d’ can always be expressed
depending on the method used. Tables for the four most
asS (d’)=B/n,wheretheparameterBcapturesalloftheinformationconcerningthe
commonlyusedmethodsarepresented.Theestimatedvalueof
test method, and n is the sample size. The values of B have been tabulated to make
the calculation of the variance of d’ a simple task. δ (that is, d’) is obtained as follows:
E2262 − 03 (2014)
6.1.1 Compute the observed choice proportion as p = x/n, on the physical scale used to collect the data. It is recognized
c
where x is the observed number of correct responses and n is that information detail is lost by collapsing the data into two
the sample size. categories. However, the estimates of d’ and its variance,
S (d’), obtained from the technique are accurate. The compu-
6.1.2 Obtain d’ by entering the table in Appendix X1 that
tational ease offsets the small loss of accuracy incurred.
correspondstothetestmethodused:triangletest(TableX1.1),
duo-trio (Table X1.3), 3-AFC (Table X1.5) or 2-AFC (Table 6.4.1 Tally the frequency distributions of category scale
X1.7).Findtheentryinthetablethatisclosesttotheobserved ratings for the two samples. Select the sample with the lower
value of p . The value of d’, accurate to one decimal place, is
median rating to be the Not-Asample. Select the sample with
c
the row-label of the table corresponding to the selected entry. the higher median rating to be the A sample.
Theseconddecimalplaceof d’isthecolumn-labelofthetable
6.4.2 Collapse the frequency data for each sample into two
corresponding to the selected entry.
categories as follows. Identify the category in which the
6.1.3 Obtain the estimated variance of d’ as follows. Enter
median of the Not-A sample occurs. Pool the number of
the appropriate table in Appendix X1: triangle test (Table responses from that category and all lower categories for each
X1.2), duo-trio (Table X1.4), 3-AFC (Table X1.6) or 2-AFC sample separately and record the totals in the 2-by-2 table
(Table X1.8). Find the value of B in the row and column that under “Low” (that is, the y and y tallies, below). Pool the
na a
correspond to the value of d’ obtained in 6.1.2. Compute the number of responses for the remaining, higher categories for
estimated variance of d’as S (d’) = B/n, where n is the sample eachsampleseparatelyandrecordthetotalsinthe2-by-2table
size. Use the estimates d’ and S (d’) to construct confidence under “High” (that is, the x and x tallies, below).
na a
intervalsandtestsofhypothesesrelatedtotheobjectivesofthe
Sample Low High
Not-A y x
research.
na na
A y x
a a
6.2 A/Not A Method—Compute the choice proportions of
6.4.3 Compute the choice proportions of the two samples,
the two samples, p = x /n and p = x /n, where x is the
a a na na a
p = x /n and p = x /n, where x and x are obtained from
a a na na a na
numberoftimesthe“A”sampleischosenasbeing“A,”, x is
na
the table above and n is the sample size, common to both
the number of times the “Not-A” sample is chosen as being
samples.
“A” and n is the sample size.
6.4.4 ApplythesametechniqueusedintheA/NotAmethod
NOTE 1—This practice only considers the case where the number of
(see 6.2). Read the value of d’ from Table X1.9 in Appendix
“A” samples equals the number of “Not-A” samples, n = n = n .
a na
X1 in the column that corresponds to the observed choice
6.2.1 Readthevalueof d’fromTableX1.9inAppendixX1 proportion of the Not-A sample (p ) and the row that
na
corresponds to the observed choice proportion of theAsample
in the column that corresponds to the observed choice propor-
tion of the “Not-A” sample (p ) and the row that corresponds (p ).
na a
to the observed choice proportion of the “A” sample (p ).
6.4.5 To obtain an estimate of the variance of d’, read the
a
6.2.2 To obtain an estimate of the variance of d’, read the value of B from Table X1.10 in Appendix X1 using the same
value of B from Table X1.10 in Appendix X1 using the same technique as in 6.4.4. The variance estimate is S (d’) = B/n,
technique as in 6.2.1. The variance estimate is S (d’) = B/n, where n is the sample size.
where n is the sample size.
6.5 Statistical Tests and Confidence Intervals—Often the
6.3 Same-Different Method—Compute the choice propor-
objective of a sensory discrimination test is to determine if the
tions for the matched (m) and unmatched (u) pairs of samples, samples in the test are perceptibly different. In other instances
p = x /n and p = x /n, where x is the number of
it is
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E2262 − 03 (Reapproved 2009) E2262 − 03 (Reapproved 2014)
Standard Practice for
Estimating Thurstonian Discriminal Distances
This standard is issued under the fixed designation E2262; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This practice describes procedures to estimate Thurstonian discriminal distances (that is, d’ values) from data obtained on
two samples. Procedures are presented for four forced-choice methods (that is, the triangle, the duo-trio, the 3-alternative-forced-
choice (or 3-AFC) and the 2-AFC (also called the directional difference test)), the A/Not-A method, the Same-Different method
and for data obtained from ordered category scales. Procedures for estimating the variance of d’ are also presented. Thus,
confidence intervals and statistical tests can be calculated for d’.
1.2 The procedures in this document pertain only to the unidimensional, equal-variance model. Other, more complicated
Thurstonian models, involving multiple dimensions and unequal variances exist but are not addressed in this standard. The
procedure for forced-choice methods is limited to dichotomous responses. The procedure for the A/Not-A method assumes equal
sample sizes for the two samples. The procedure for the Same-Different method assumes equal sample sizes for the matched and
unmatched pairs of samples. For all methods, only unreplicated tests are considered. (Tests in which each assessor performs
multiple (that is, replicated) evaluations require different analyses.)
1.3 Thurstonian scaling is a method for measuring the perceptual difference between two samples based on a probabilistic model
for categorical choice decision making. The magnitude of the perceived difference, δ, can be estimated from the assessors’
categorical choices using the methods described in this practice (See Appendix X3 for a more detailed description of Thurstonian
scaling).
1.4 In theory, the Thurstonian δ does not depend on the method used to measure the difference between two samples. As such,
δ provides a common scale of measure for comparing samples measured under a variety of test conditions. For example,
Thurstonian scaling can be used to compare products measured under different test conditions, to compare panels (trained,
consumer or both) that have evaluated the same samples (using the same or different test methods) and to compare test methods
on their ability to discriminate samples that exhibit a fixed sensory difference.
1.5 This standard may involve hazardous materials, operations and equipment. This standard does not purport to address all
of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate
safety and health practices and determine the applicability of regulatory limitations prior to use.
2. Referenced Documents
2.1 ASTM Standards:
E253 Terminology Relating to Sensory Evaluation of Materials and Products
E456 Terminology Relating to Quality and Statistics
E460 Practice for Determining Effect of Packaging on Food and Beverage Products During Storage
E679 Practice for Determination of Odor and Taste Thresholds By a Forced-Choice Ascending Concentration Series Method of
Limits
E1432 Practice for Defining and Calculating Individual and Group Sensory Thresholds from Forced-Choice Data Sets of
Intermediate Size
E1593 Guide for Assessing the Efficacy of Air Care Products in Reducing the Perception of Indoor Malodor
E1627 Practice for Sensory Evaluation of Edible Oils and Fats
E1697 Test Method for Unipolar Magnitude Estimation of Sensory Attributes
This practice is under the jurisdiction of ASTM Committee E18 on Sensory Evaluation and is the direct responsibility of Subcommittee E18.03 on Sensory Theory and
Statistics.
Current edition approved Sept. 1, 2009Sept. 1, 2014. Published March 2010September 2014. Originally approved in 2003. Last previous edition approved in 20032009
as E2262 – 03.E2262 – 03 (2009). DOI: 10.1520/E2262-03R09.10.1520/E2262-03R14.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2262 − 03 (2014)
E1810 Practice for Evaluating Effects of Contaminants on Odor and Taste of Exposed Fish
E1879 Guide for Sensory Evaluation of Beverages Containing Alcohol
E1885 Test Method for Sensory Analysis—Triangle Test
E1958 Guide for Sensory Claim Substantiation
E2049 Guide for Quantitative Attribute Evaluation of Fragrance/Odors for Shampoos and Hair Conditioners by Trained
Assessors
E2164 Test Method for Directional Difference Test
2.2 ASTM Publication:
Manual 26 Sensory Testing Methods, 2nd Edition
2.3 ISO Standard:
ISO 5495 Sensory Analysis—Methodology—Paired Comparison
3. Terminology
3.1 For definitions of terms relating to sensory analysis, see Terminology E253, and for terms relating to statistics, see
Terminology E456.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 δ—the Thurstonian discriminal distance is the distance between the means of the distributions of sensory magnitudes of
the two samples in the test (see Appendix X3).
3.2.2 d’—the statistic used to estimate δ based on the data obtained from the test.
3.2.3 choice proportion (P )—the expected proportion of responses from a forced-choice method (for example, if there is no
c
perceptible difference between the samples in a triangle test, P = 1/3. If there is a perceptible difference, P > 1/3).
c c
3.2.4 observed choice proportion (p ) —the statistic used to estimate choice proportion, P , where p = x/n, where x is the
c c c
observed number of correct responses and n is the sample size.
4. Summary of Practice
4.1 Determine the type of data collected on the two samples: data from a forced-choice test, an A/Not A test, a same-different
test or an ordered category scale.
4.2 For forced-choice tests, reference the table that corresponds to the test method (that is, triangle test—Tables X1.1 and X1.2;
duo-trio test—Tables X1.3 and X1.4; 3-AFC test—Tables X1.5 and X1.6; or 2-AFC test—Tables X1.7 and X1.8). Identify the
entry in the table closest to the observed choice proportion (p ) from the test. Read the estimated value of δ (that is, d’) from the
c
corresponding row and column headings of the table. Estimate the variance of d’ by referencing the appropriate table for the test
4 2
method. Find the value of B that corresponds to the value of d’ obtained in the first step. The estimated variance of d’ is S (d’)
= B/n, where n is the sample size. Use the estimates d’ and S (d’) to construct confidence intervals and tests of hypotheses related
to the objectives of the research.
4.3 For the A/Not A method, tally the observed choice proportions of “A” responses for the A sample and the “A” responses
for the Not-A sample. Read the value of d’ from Table X1.9 in the column that corresponds to the observed choice proportion of
the “A” responses for the Not-A sample (p ) and the row that corresponds to the observed choice proportion of the “A” responses
na
for the A sample (p ). The same method is used to estimate the variance of d’,S (d’), using Table X1.10.
a
4.4 For the Same-Different method, tally the proportion of “same” responses for the matched pairs of samples (that is, A/A or
B/B) and the proportion of “same” responses for the unmatched pairs of samples (that is, A/B or B/A). Read the value of d’ from
Table X1.11 in the column that corresponds to the observed proportion of “same” responses for the unmatched pairs (p / ) and the
s u
row that corresponds to the observed proportion of the “same” responses for the matched pairs (p / ). The same method is used
s m
to estimate the variance of d’, S (d’), using Table X1.12.
4.5 For ordered category scales, a rapid, table-look-up approach is used. For each sample, the category scale data are collapsed
into two categories. One sample is selected to be the “A” sample and the other sample is selected to be the “Not-A” sample. Choice
proportions are tallied for each sample and the values of d’ and its variance, S (d’), are obtained from Tables X1.9 and X1.10,
respectively, by the same techniques used in the A/Not A method.
5. Significance and Use
5.1 Under the assumptions of the model, the Thurstonian model approach to measuring the perceived difference between two
samples (whether overall or for a specific attribute) is independent of the sensory method used to collect the data. Converting
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036.
The variance of d’ is a complicated function of the true value of δ and the decision rule whenassociated when associated with the test method being used (see Appendix
X3). However, regardless of the test method, the variance of d’ can always be expressed as S (d’) = B/n, where the parameter B captures all of the information concerning
the test method, and n is the sample size. The values of B have been tabulated to make the calculation of the variance of d’ a simple task.
E2262 − 03 (2014)
results obtained from different test methods to d’ values permits the assessment of relative differences among samples without
requiring that the samples be compared to each other directly or that the same test methods be used for all pairs of samples.
5.2 Thurstonian scaling has been applied to:
5.2.1 Creating a historical database to track differences between production and reference samples over periods in which
different test methods were used to measure the difference,
5.2.2 Comparing the relative sensitivities of different user groups and consumer segments,
5.2.3 Comparing trained panels that use different measuring techniques,
5.2.4 Comparing the relative sensitivities of consumers versus trained panels,
5.2.5 Comparing different methods of consumer testing (for example, CLT versus HUT, preference versus hedonic scales, etc.),
and
5.2.6 Comparing different discrimination test methods.
6. Procedure
6.1 Forced-Choice Methods—The relationship between δ and the expected choice proportion, P , is different for different
c
forced-choice methods because the decision rule used by the assessors varies from one method to another (see Appendix X3). As
a result, different tables are required to estimate δ depending on the method used. Tables for the four most commonly used methods
are presented. The estimated value of δ (that is, d’) is obtained as follows:
6.1.1 Compute the observed choice proportion as p = x/n, where x is the observed number of correct responses and n is the
c
sample size.
6.1.2 Obtain d’ by entering the table in Appendix X1 that corresponds to the test method used: triangle test (Table X1.1),
duo-trio (Table X1.3), 3-AFC (Table X1.5) or 2-AFC (Table X1.7). Find the entry in the table that is closest to the observed value
of p . The value of d’, accurate to one decimal place, is the row-label of the table corresponding to the selected entry. The second
c
decimal place of d’ is the column-label of the table corresponding to the selected entry.
6.1.3 Obtain the estimated variance of d’ as follows. Enter the appropriate table in Appendix X1: triangle test (Table X1.2),
duo-trio (Table X1.4), 3-AFC (Table X1.6) or 2-AFC (Table X1.8). Find the value of B in the row and column that correspond
to the value of d’ obtained in 6.1.2. Compute the estimated variance of d’ as S (d’) = B/n, where n is the sample size. Use the
estimates d’ and S (d’) to construct confidence intervals and tests of hypotheses related to the objectives of the research.
6.2 A/Not A Method—Compute the choice proportions of the two samples, p = x /n and p = x /n, where x is the number
a a na na a
of times the “A” sample is chosen as being “A,”, x is the number of times the “Not-A” sample is chosen as being “A” and n
na
is the sample size.
NOTE 1—This practice only considers the case where the number of “A” samples equals the number of “Not-A” samples, n = n = n .
a na
6.2.1 Read the value of d’ from Table X1.9 in Appendix X1 in the column that corresponds to the observed choice proportion
of the “Not-A” sample (p ) and the row that corresponds to the observed choice proportion of the “A” sample (p ).
na a
6.2.2 To obtain an estimate of the variance of d’, read the value of B from Table X1.10 in Appendix X1 using the same technique
as in 6.2.1. The variance estimate is S (d’) = B/n, where n is the sample size.
6.3 Same-Different Method—Compute the choice proportions for the matched (m) and unmatched (u) pairs of samples, p =
s/m
x /n and p = x /n, where x is the number of “same” responses for the matched pairs (A/A or B/B) evaluated, x is the
s/m s/u s/u s/m s/u
number of “same” responses for the unmatched pair and n is the number of matched or unmatched pairs evaluated.
NOTE 2—This practice only considers the case where the number of matched pairs equals the number of unmatched pairs, n = n = n .
m u
6.3.1 Read the value of d’ from Table X1.11 in Appendix X1 in the column that corresponds to the observed proportion of
“same” responses for unmatched pair (p ) and the row that corresponds to the observed proportion of “same” responses for the
s/u
matched pair (p ).
s/m
6.3.2 To obtain an estimate of the variance of d’, read the value of B from Table X1.12 in Appendix X1 using the same technique
as in 6.3.1. The variance estimate is S (d’) = B/n, where n is the sample size.
6.4 Ordered Category Scales—A rapid, table-look-up method is described. The method collapses the category-scale data into
two categories, regardless of the number of categories on the physical scale used to collect the data. It is recognized that
information detail is lost by collapsing the data into two categories. However, the estimates of d’ and its variance, S (d’), obtained
from the technique are accurate. The computational ease offsets the small loss of accuracy incurred.
6.4.1 Tally the frequency distributions of category scale ratings for the two s
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