Standard Practice for Estimating Thurstonian Discriminal Distances

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 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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Publication Date
09-Jul-2003
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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
Standard Practice for
1
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 compare test methods on their ability to discriminate samples
that exhibit a fixed sensory difference.
1.1 This practice describes procedures to estimate Thursto-
1.5 This standard may involve hazardous materials, opera-
nian discriminal distances (that is, d’ values) from data
tions and equipment. This standard does not purport to address
obtained on two samples. Procedures are presented for four
all of the safety concerns, if any, associated with its use. It is
forced-choice methods (that is, the triangle, the duo-trio, the
the responsibility of the user of this standard to establish
3-alternative-forced-choice (or 3-AFC) and the 2-AFC (also
appropriate safety and health practices and determine the
calledthedirectionaldifferencetest)),theA/Not-Amethod,the
applicability of regulatory limitations prior to use.
Same-Different method and for data obtained from ordered
category scales. Procedures for estimating the variance of d’
2. Referenced Documents
are also presented. Thus, confidence intervals and statistical
2
2.1 ASTM Standards:
tests can be calculated for d’.
E253 Terminology Relating to Sensory Evaluation of Ma-
1.2 The procedures in this document pertain only to the
terials and Products
unidimensional, equal-variance model. Other, more compli-
E456 Terminology Relating to Quality and Statistics
cated Thurstonian models, involving multiple dimensions and
E460 PracticeforDeterminingEffectofPackagingonFood
unequal variances exist but are not addressed in this standard.
and Beverage Products During Storage
Theprocedureforforced-choicemethodsislimitedtodichoto-
E679 Practice for Determination of Odor andTasteThresh-
mous responses. The procedure for the A/Not-A method
olds By a Forced-Choice Ascending Concentration Series
assumesequalsamplesizesforthetwosamples.Theprocedure
Method of Limits
for the Same-Different method assumes equal sample sizes for
E1432 Practice for Defining and Calculating Individual and
the matched and unmatched pairs of samples. For all methods,
Group Sensory Thresholds from Forced-Choice Data Sets
only unreplicated tests are considered. (Tests in which each
of Intermediate Size
assessor performs multiple (that is, replicated) evaluations
E1593 Guide for Assessing the Efficacy of Air Care Prod-
require different analyses.)
ucts in Reducing Sensorly Perceived Indoor Air Malodor
1.3 Thurstonian scaling is a method for measuring the
Intensity
perceptual difference between two samples based on a proba-
E1627 Practice for Sensory Evaluation of Edible Oils and
bilistic model for categorical choice decision making. The
Fats
magnitude of the perceived difference, d, can be estimated
E1697 Test Method for Unipolar Magnitude Estimation of
from the assessors’ categorical choices using the methods
Sensory Attributes
describedinthispractice(SeeAppendixX3foramoredetailed
E1810 Practice for Evaluating Effects of Contaminants on
description of Thurstonian scaling).
Odor and Taste of Exposed Fish
1.4 In theory, the Thurstonian d does not depend on the
E1879 GuideforSensoryEvaluationofBeveragesContain-
method used to measure the difference between two samples.
ing Alcohol
Assuch, dprovidesacommonscaleofmeasureforcomparing
E1885 Test Method for Sensory Analysis—Triangle Test
samples measured under a variety of test conditions. For
E1958 Guide for Sensory Claim Substantiation
example,Thurstonian scaling can be used to compare products
E2049 Guide for Quantitative Attribute Evaluation of
measured under different test conditions, to compare panels
Fragrance/Odors for Shampoos and Hair Conditioners by
(trained, consumer or both) that have evaluated the same
Trained Assessors
samples (using the same or different test methods) and to
E2164 Test Method for Directional Difference Test
2
2.2 ASTM Publication:
1
This practice is under the jurisdiction of ASTM Committee E18 on Sensory
2
Evaluation of Materials and Products and is the direct responsibility of Subcom- For referenced ASTM standards, visit the ASTM website, www.astm.org, or
mittee E18.03 on Sensory Theory and Statistics. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Current edition approved July 10, 2003. Published Aug. 2003. DOI: 10.1520/ Standards volume information, refer to the standard’s Document Summary page on
E2262-03. the ASTM website.
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