1、Designation: E2262 03 (Reapproved 2014)Standard Practice forEstimating Thurstonian Discriminal Distances1This standard is issued under the fixed designation E2262; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last re
2、vision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice describes procedures to estimate Thursto-nian discriminal distances (that is, d values) from dataobtained on tw
3、o samples. Procedures are presented for fourforced-choice methods (that is, the triangle, the duo-trio, the3-alternative-forced-choice (or 3-AFC) and the 2-AFC (alsocalled the directional difference test), theA/Not-Amethod, theSame-Different method and for data obtained from orderedcategory scales.
4、Procedures for estimating the variance of dare also presented. Thus, confidence intervals and statisticaltests can be calculated for d.1.2 The procedures in this document pertain only to theunidimensional, equal-variance model. Other, more compli-cated Thurstonian models, involving multiple dimensio
5、ns andunequal variances exist but are not addressed in this standard.The procedure for forced-choice methods is limited to dichoto-mous responses. The procedure for the A/Not-A methodassumes equal sample sizes for the two samples.The procedurefor the Same-Different method assumes equal sample sizes
6、forthe matched and unmatched pairs of samples. For all methods,only unreplicated tests are considered. (Tests in which eachassessor performs multiple (that is, replicated) evaluationsrequire different analyses.)1.3 Thurstonian scaling is a method for measuring theperceptual difference between two sa
7、mples based on a proba-bilistic model for categorical choice decision making. Themagnitude of the perceived difference, , can be estimatedfrom the assessors categorical choices using the methodsdescribed in this practice (See Appendix X3 for a more detaileddescription of Thurstonian scaling).1.4 In
8、theory, the Thurstonian does not depend on themethod used to measure the difference between two samples.As such, provides a common scale of measure for comparingsamples measured under a variety of test conditions. Forexample, Thurstonian scaling can be used to compare productsmeasured under differen
9、t test conditions, to compare panels(trained, consumer or both) that have evaluated the samesamples (using the same or different test methods) and tocompare test methods on their ability to discriminate samplesthat exhibit a fixed sensory difference.1.5 This standard may involve hazardous materials,
10、 opera-tions and equipment. This standard does not purport to addressall of the safety concerns, if any, associated with its use. It isthe responsibility of the user of this standard to establishappropriate safety and health practices and determine theapplicability of regulatory limitations prior to
11、 use.2. Referenced Documents2.1 ASTM Standards:2E253 Terminology Relating to Sensory Evaluation of Mate-rials and ProductsE456 Terminology Relating to Quality and StatisticsE460 Practice for Determining Effect of Packaging on Foodand Beverage Products During StorageE679 Practice for Determination of
12、 Odor and Taste Thresh-olds By a Forced-Choice Ascending Concentration SeriesMethod of LimitsE1432 Practice for Defining and Calculating Individual andGroup Sensory Thresholds from Forced-Choice Data Setsof Intermediate SizeE1593 Guide forAssessing the Efficacy ofAir Care Productsin Reducing the Per
13、ception of Indoor MalodorE1627 Practice for Sensory Evaluation of Edible Oils andFatsE1697 Test Method for Unipolar Magnitude Estimation ofSensory AttributesE1810 Practice for Evaluating Effects of Contaminants onOdor and Taste of Exposed FishE1879 Guide for Sensory Evaluation of Beverages Contain-i
14、ng AlcoholE1885 Test Method for Sensory AnalysisTriangle TestE1958 Guide for Sensory Claim SubstantiationE2049 Guide for Quantitative Attribute Evaluation ofFragrance/Odors for Shampoos and Hair Conditioners byTrained Assessors1This practice is under the jurisdiction of ASTM Committee E18 on Sensory
15、Evaluation and is the direct responsibility of Subcommittee E18.03 on SensoryTheory and Statistics.Current edition approved Sept. 1, 2014. Published September 2014. Originallyapproved in 2003. Last previous edition approved in 2009 as E2262 03 (2009).DOI: 10.1520/E2262-03R14.2For referenced ASTM sta
16、ndards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken,
17、PA 19428-2959. United States1E2164 Test Method for Directional Difference Test2.2 ASTM Publication:Manual 26 Sensory Testing Methods, 2nd Edition22.3 ISO Standard:ISO 5495 Sensory AnalysisMethodologyPaired Com-parison33. Terminology3.1 For definitions of terms relating to sensory analysis, seeTermin
18、ology E253, and for terms relating to statistics, seeTerminology E456.3.2 Definitions of Terms Specific to This Standard:3.2.1 the Thurstonian discriminal distance is the distancebetween the means of the distributions of sensory magnitudesof the two samples in the test (see Appendix X3).3.2.2 dthe s
19、tatistic used to estimate based on the dataobtained from the test.3.2.3 choice proportion (Pc)the expected proportion ofresponses from a forced-choice method (for example, if there isno perceptible difference between the samples in a triangle test,Pc= 1/3. If there is a perceptible difference, Pc 1/
20、3).3.2.4 observed choice proportion (pc)the statistic used toestimate choice proportion, Pc, where pc= x/n, where x is theobserved number of correct responses and n is the sample size.4. Summary of Practice4.1 Determine the type of data collected on the two samples:data from a forced-choice test, an
21、 A/Not A test, a same-different test or an ordered category scale.4.2 For forced-choice tests, reference the table that corre-sponds to the test method (that is, triangle testTables X1.1and X1.2; duo-trio testTables X1.3 and X1.4; 3-AFC testTables X1.5 and X1.6; or 2-AFC testTables X1.7 and X1.8).Id
22、entify the entry in the table closest to the observed choiceproportion (pc) from the test. Read the estimated value of (that is, d) from the corresponding row and column headingsof the table. Estimate the variance of d by referencing theappropriate table for the test method. Find the value of B that
23、corresponds to the value of d obtained in the first step.4Theestimated variance of disS2(d) = B/n, where n is the samplesize. Use the estimates d and S2(d) to construct confidenceintervals and tests of hypotheses related to the objectives of theresearch.4.3 For the A/Not A method, tally the observed
24、 choiceproportions of “A” responses for the A sample and the “A”responses for the Not-A sample. Read the value of d fromTable X1.9 in the column that corresponds to the observedchoice proportion of the “A” responses for the Not-A sample(pna) and the row that corresponds to the observed choiceproport
25、ion of the “A” responses for the A sample (pa). Thesame method is used to estimate the variance of d, S2(d),using Table X1.10.4.4 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 th
26、eunmatched pairs of samples (that is, A/B or B/A). Read thevalue of d from Table X1.11 in the column that corresponds tothe observed proportion of “same” responses for the un-matched pairs (ps/u) and the row that corresponds to theobserved proportion of the “same” responses for the matchedpairs (ps/
27、m). The same method is used to estimate the varianceof d, S2(d), using Table X1.12.4.5 For ordered category scales, a rapid, table-look-upapproach is used. For each sample, the category scale data arecollapsed into two categories. One sample is selected to be the“A” sample and the other sample is se
28、lected to be the “Not-A”sample. Choice proportions are tallied for each sample and thevalues of d and its variance, S2(d), are obtained from TablesX1.9 and X1.10, respectively, by the same techniques used inthe A/Not A method.5. Significance and Use5.1 Under the assumptions of the model, the Thursto
29、nianmodel approach to measuring the perceived difference betweentwo samples (whether overall or for a specific attribute) isindependent of the sensory method used to collect the data.Converting results obtained from different test methods to dvalues permits the assessment of relative differences amo
30、ngsamples without requiring that the samples be compared toeach other directly or that the same test methods be used for allpairs of samples.5.2 Thurstonian scaling has been applied to:5.2.1 Creating a historical database to track differencesbetween production and reference samples over periods inwh
31、ich different test methods were used to measure thedifference,5.2.2 Comparing the relative sensitivities of different usergroups and consumer segments,5.2.3 Comparing trained panels that use different measuringtechniques,5.2.4 Comparing the relative sensitivities of consumersversus trained panels,5.
32、2.5 Comparing different methods of consumer testing (forexample, CLT versus HUT, preference versus hedonic scales,etc.), and5.2.6 Comparing different discrimination test methods.6. Procedure6.1 Forced-Choice MethodsThe relationship between and the expected choice proportion, Pc, is different for dif
33、ferentforced-choice methods because the decision rule used by theassessors varies from one method to another (see AppendixX3). As a result, different tables are required to estimate depending on the method used. Tables for the four mostcommonly used methods are presented. The estimated value of (tha
34、t is, d) is obtained as follows:3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036.4The variance of d is a complicated function of the true value of and thedecision rule when associated with the test method being used (see Appendix X3).However,
35、 regardless of the test method, the variance of d can always be expressedas S2(d)=B/n, where the parameter B captures all of the information concerning thetest method, and n is the sample size. The values of B have been tabulated to makethe calculation of the variance of d a simple task.E2262 03 (20
36、14)26.1.1 Compute the observed choice proportion as pc= x/n,where x is the observed number of correct responses and n isthe sample size.6.1.2 Obtain d by entering the table in Appendix X1 thatcorresponds to the test method used: triangle test (Table X1.1),duo-trio (Table X1.3), 3-AFC (Table X1.5) or
37、 2-AFC (TableX1.7). Find the entry in the table that is closest to the observedvalue of pc. The value of d, accurate to one decimal place, isthe row-label of the table corresponding to the selected entry.The second decimal place of d is the column-label of the tablecorresponding to the selected entr
38、y.6.1.3 Obtain the estimated variance of d as follows. Enterthe appropriate table in Appendix X1: triangle test (TableX1.2), 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 thatcorrespond to the value of d obtained in 6.1.2. Compute theestima
39、ted variance of dasS2(d) = B/n, where n is the samplesize. Use the estimates d and S2(d) to construct confidenceintervals and tests of hypotheses related to the objectives of theresearch.6.2 A/Not A MethodCompute the choice proportions ofthe two samples, pa= xa/n and pna= xna/n, where xais thenumber
40、 of times the “A” sample is chosen as being “A,”, xnaisthe number of times the “Not-A” sample is chosen as being“A” and n is the sample size.NOTE 1This practice only considers the case where the number of“A” samples equals the number of “Not-A” samples, n = na= nna.6.2.1 Read the value of d from Tab
41、le X1.9 in Appendix X1in the column that corresponds to the observed choice propor-tion of the “Not-A” sample (pna) and the row that correspondsto the observed choice proportion of the “A” sample (pa).6.2.2 To obtain an estimate of the variance of d, read thevalue of B from Table X1.10 in Appendix X
42、1 using the sametechnique as in 6.2.1. The variance estimate is S2(d) = B/n,where n is the sample size.6.3 Same-Different MethodCompute the choice propor-tions for the matched (m) and unmatched (u) pairs of samples,ps/m= xs/m/n and ps/u= xs/u/n, where xs/mis the number of“same” responses for the mat
43、ched pairs (A/A or B/B)evaluated, xs/uis the number of “same” responses for theunmatched pair and n is the number of matched or unmatchedpairs evaluated.NOTE 2This practice only considers the case where the number ofmatched pairs equals the number of unmatched pairs, n = nm= nu.6.3.1 Read the value
44、of d from Table X1.11 in AppendixX1 in the column that corresponds to the observed proportionof “same” responses for unmatched pair (ps/u) and the row thatcorresponds to the observed proportion of “same” responsesfor the matched pair (ps/m).6.3.2 To obtain an estimate of the variance of d, read thev
45、alue of B from Table X1.12 in Appendix X1 using the sametechnique as in 6.3.1. The variance estimate is S2(d) = B/n,where n is the sample size.6.4 Ordered Category ScalesA rapid, table-look-upmethod is described. The method collapses the category-scaledata into two categories, regardless of the numb
46、er of categorieson the physical scale used to collect the data. It is recognizedthat information detail is lost by collapsing the data into twocategories. However, the estimates of d and its variance,S2(d), obtained from the technique are accurate. The compu-tational ease offsets the small loss of a
47、ccuracy incurred.6.4.1 Tally the frequency distributions of category scaleratings for the two samples. Select the sample with the lowermedian rating to be the Not-A sample. Select the sample withthe higher median rating to be the A sample.6.4.2 Collapse the frequency data for each sample into twocat
48、egories as follows. Identify the category in which themedian of the Not-A sample occurs. Pool the number ofresponses from that category and all lower categories for eachsample separately and record the totals in the 2-by-2 tableunder “Low” (that is, the ynaand yatallies, below). Pool thenumber of re
49、sponses for the remaining, higher categories foreach sample separately and record the totals in the 2-by-2 tableunder “High” (that is, the xnaand xatallies, below).Sample Low HighNot-A ynaxnaA yaxa6.4.3 Compute the choice proportions of the two samples,pa= xa/n and pna= xna/n, where xaand xnaare obtained fromthe table above and n is the sample size, common to bothsamples.6.4.4 Apply the same technique used in theA/NotAmethod(see 6.2). Read the value of d from Table X1.9 in AppendixX1 in the column that corre
