ASTM E2262-03(2009)
(Practice)Standard Practice for Estimating Thurstonian Discriminal Distances
Standard Practice for Estimating Thurstonian Discriminal Distances
SIGNIFICANCE AND USE
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.
Thurstonian scaling has been applied to:
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,
Comparing the relative sensitivities of different user groups and consumer segments,
Comparing trained panels that use different measuring techniques,
Comparing the relative sensitivities of consumers versus trained panels,
Comparing different methods of consumer testing (for example, CLT versus HUT, preference versus hedonic scales, etc.), and
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.
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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 2009)
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
require different analyses.) Group SensoryThresholds from Forced-Choice Data Sets
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 Sensorly Perceived Indoor Air Malodor
bilistic model for categorical choice decision making. The
Intensity
magnitude of the perceived difference, δ, can be estimated
E1627Practice for Sensory Evaluation of Edible Oils and
from the assessors’ categorical choices using the methods
Fats
describedinthispractice(SeeAppendixX3foramoredetailed
E1697Test Method for Unipolar Magnitude Estimation of
description of Thurstonian scaling).
Sensory Attributes
1.4 In theory, the Thurstonian δ does not depend on the
E1810Practice for Evaluating Effects of Contaminants on
method used to measure the difference between two samples.
Odor and Taste of Exposed Fish
Assuch, δprovidesacommonscaleofmeasureforcomparing
E1879Guide for Sensory Evaluation of Beverages Contain-
samples measured under a variety of test conditions. For
ing Alcohol
example,Thurstonian scaling can be used to compare products
E1885Test Method for Sensory Analysis—Triangle Test
measured under different test conditions, to compare panels
E1958Guide for Sensory Claim Substantiation
E2049 Guide for Quantitative Attribute Evaluation of
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, 2009. Published March 2010. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 2003. Last previous edition approved in 2003 as E2262–03. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E2262-03R09. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2262 − 03 (2009)
Fragrance/Odors for Shampoos and Hair Conditioners by choice proportion of the “A” responses for the Not-A sample
Trained Assessors (p ) and the row that corresponds to the observed choice
na
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
6. Procedure
Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
6.1 Forced-Choice Methods—The relationship between δ
4th Floor, New York, NY 10036.
andtheexpectedchoiceproportion, P ,isdifferentfordifferent
The variance of d’ is a complicated function of the true value of δ and the
c
decision rule whenassociated with the test method being used (see Appendix X3).
forced-choice methods because the decision rule used by the
However, regardless of the test method, the variance of d’ can always be expressed
assessors varies from one method to another (see Appendix
asS (d’)=B/n,wheretheparameterBcapturesalloftheinformationconcerningthe
X3). As a result, different tables are required to estimate δ
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. depending on the method used. Tables for the four most
E2262 − 03 (2009)
commonlyusedmethodsarepresented.Theestimatedvalueof dataintotwocategories,regardlessofthenumberofcategories
δ (that is, d’) is obtained as follows: on the physical scale used to collect the data. It is recognized
6.1.1 Compute the observed choice proportion as p = x/n, that information detail is lost by collapsing the data into two
c
where x is the observed number of correct responses and n is categories. However, the estimates of d’ and its variance,
the sample size. 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),
6.4.1 Tally the frequency distributions of category scale
duo-trio (Table X1.3), 3-AFC (Table X1.5) or 2-AFC (Table
ratings for the two samples. Select the sample with the lower
X1.7).Findtheentryinthetablethatisclosesttotheobserved
median rating to be the Not-Asample. Select the sample with
value of p . The value of d’, accurate to one decimal place, is
the higher median rating to be the A sample.
c
the row-label of the table corresponding to the selected entry.
6.4.2 Collapse the frequency data for each sample into two
Theseconddecimalplaceof d’isthecolumn-labelofthetable
categories as follows. Identify the category in which the
corresponding to the selected entry.
median of the Not-A sample occurs. Pool the number of
6.1.3 Obtain the estimated variance of d’ as follows. Enter
responses from that category and all lower categories for each
the appropriate table in Appendix X1: triangle test (Table
sample separately and record the totals in the 2-by-2 table
X1.2), duo-trio (Table X1.4), 3-AFC (Table X1.6) or 2-AFC
under “Low” (that is, the y and y tallies, below). Pool the
na a
(Table X1.8). Find the value of B in the row and column that
number of responses for the remaining, higher categories for
correspond to the value of d’ obtained in 6.1.2. Compute the
eachsampleseparatelyandrecordthetotalsinthe2-by-2table
estimated variance of d’as S (d’) = B/n, where n is the sample
under “High” (that is, the x and x tallies, below).
na a
size. Use the estimates d’ and S (d’) to construct confidence
Sample Low High
intervalsandtestsofhypothesesrelatedtotheobjectivesofthe
Not-A y x
na na
A y x
research. a a
6.4.3 Compute the choice proportions of the two samples,
6.2 A/Not A Method—Compute the choice proportions of
p = x /n and p = x /n, where x and x are obtained from
the two samples, p = x /n and p = x /n, where x is the a a na na a na
a a na na a
the table above and n is the sample size, common to both
numberoftimesthe“A”sampleischosenasbeing“A,”, x is
na
samples.
the number of times the “Not-A” sample is chosen as being
6.4.4 ApplythesametechniqueusedintheA/NotAmethod
“A” and n is the sample size.
(see 6.2). Read the value of d ’ from Table X1.9 in Appendix
NOTE 1—This practice only considers the case where the number of
X1 in the column that corresponds to the observed choice
“A” samples equals the number of “Not-A” samples, n = n = n .
a na
proportion of the Not-A sample (p ) and the row that
na
6.2.1 Readthevalueof d’fromTableX1.9inAppendixX1
corresponds to the observed choice proportion of theAsample
in the column that corresponds to the observed choice propor-
(p ).
a
tion of the “Not-A” sample (p ) and the row that corresponds
na
6.4.5 To obtain an estimate of the variance of d’, read the
to the observed choice proportion of the “A” sample (p ).
a
value of B from Table X1.10 in Appendix X1 using the same
6.2.2 To obtain an estimate of the variance of d’, read the
technique as in 6.4.4. The variance estimate is S (d’) = B/n,
value of B from Table X1.10 in Appendix X1 using the same
where n is the sample size.
technique as in 6.2.1. The variance estimate is S (d’) = B/n,
where n is the sample size. 6.5 Statistical Tests and Confidence Intervals—Often the
objective of a sensory discrimination test is to determine if the
6.3 Same-Different Method—Compute the choice propor-
samples in the test are perceptibly different. In other instances
tions for the matched (m) and unmatched (u) pairs of samp
...
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