# ASTM E1432-04 (Reapproved 2011)

Designation: E1432 − 04 (Reapproved 2011)Standard Practice forDefining and Calculating Individual and Group SensoryThresholds from Forced-Choice Data Sets ofIntermediate Size1This standard is issued under the fixed designation E1432; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.INTRODUCTIONThe purpose of this practice is to determine individual sensory thresholds for odor, taste, and othermodalities and, when appropriate, calculate group thresholds. The practice takes as its starting pointany sensory threshold data set of more than 100 presentations, collected by a forced-choice procedure.The usual procedure is the Three-Alternative Forced-Choice (3-AFC) (see ISO 13301), as exemplifiedby Dynamic Triangle Olfactometry.Asimilar practice, Practice E679, utilizes limited-size data sets of50 to 100 3-AFC presentations, and is suitable as a rapid method to approximate group thresholds.Collection of the data is not a part of this practice. The data are assumed to be valid; for example,it is assumed that the stimulus is defined properly, that each subject has been fully trained to recognizethe stimulus and did indeed perceive it when it was present above his or her momentary threshold, andthat the quality of dilution medium did not vary.It is recognized that precise threshold values for a given substance do not exist in the same sensethat values of vapor pressure exist.Apanelist’s ability to detect a stimulus varies as a result of randomvariations in factors such as alertness, attention, fatigue, events at the molecular level, health status,etc., the effects of which can usually be described in terms of a probability function. At lowconcentrations of an odorant or tastant, the probability of detection by a given individual is typically0.0 and at high concentrations it is 1.0, and there is a range of concentrations in which the probabilityof detection is between these limits. By definition, the threshold is the concentration for which theprobability of detection of the stimulus is 0.5 (that is, 50 % above chance, by a given individual, underthe conditions of the test).Thresholds may be determined (1) for an individual (or for individuals one by one), and (2) for agroup (panel). While the determination of an individual threshold is a definable task, carefulconsideration of the composition of the group is necessary to ensure the determined thresholdrepresents the group of interest.There is a large degree of random error associated with estimating the probability of detection fromless than approximately 500 3-AFC presentations. The reliability of the results can be increasedgreatly by enlarging the panel and by replicating the tests.1. Scope1.1 The definitions and procedures of this practice apply tothe calculation of individual thresholds for any stimulus in anymedium, from data sets of intermediate size, that is, consistingof more than 20 to 40 3-AFC presentations per individual. Agroup threshold may be calculated using 5 to 15 individualthresholds.1.2 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.1This practice is under the jurisdiction of ASTM Committee E18 on SensoryEvaluation and is the direct responsibility of Subcommittee E18.04 on Fundamen-tals of Sensory.Current edition approved Aug. 1, 2011. Published August 2011. Originallyapproved in 1991. Last previous edition approved in 2004 as E1432–04 . DOI:10.1520/E1432-04R11.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States12. Principles2.1 The 3-AFC procedure is one of the set of n-AFCprocedures, any of which could be used, in principle, for themeasurement of sensory thresholds, as could the duo-trio, thetriangular, and the two-out-of-five procedures.2.2 For calculation of the threshold of one individual, thispractice requires data sets taken at five or more concentrationscale steps, typically six or seven steps, with each step differingfrom the previous step by a factor usually between 2 and 4,typically 3.0. The practice presupposes that the range ofconcentrations has been selected by pretesting, in order toensure that the individual’s threshold falls neither outside nornear the ends of the range, but well within it. At eachconcentration step, the individual must be tested several times,typically five or more times.2.3 Individual thresholds, as determined in 2.2, may be usedfor calculation of a group (or panel) threshold. The size andcomposition of the panel (usually 5 to 15 members, preferablymore) is determined according to the purpose for which thethreshold is required and the limitations of the testing situation(see 7.2).2.4 Pooling of the data sets from panel members to producea single step calculation of the panel threshold is not permitted.3. Referenced Documents3.1 ASTM Standards:2E122 Practice for Calculating Sample Size to Estimate, WithSpecified Precision, the Average for a Characteristic of aLot or ProcessE679 Practice for Determination of Odor and Taste Thresh-olds By a Forced-Choice Ascending Concentration SeriesMethod of Limits3.2 CEN Standard:3EN 13725 Air Quality—Determination of Odour Concentra-tion Using Dynamic Dilution Olfactometry3.3 ISO Standard:4ISO 13301 Sensory Analysis—Methodology—Generalguidance for Measuring Odour, Flavour, and Taste Detec-tion Thresholds by a Three Alternative Forced Choice(3-AFC) Procedure4. Terminology4.1 Definitions of Terms Specific to This Standard:4.1.1 Three-Alternative Forced-Choice (3-AFC) testprocedure—a test presentation used in many threshold tests.For example, in odor testing by Dynamic TriangleOlfactometry, the panelist is presented with three gas streams,only one of which contains the diluted odorant, while the othertwo contain odorless carrier gas. The panelist must indicate theone containing the added substance. (The 3-AFC procedure isdifferent from the classical Triangle test, in which either one ortwo of the three samples may contain the added substance.)4.1.2 model—an abstract or concrete analogy, usuallymathematical, which represents in a useful way the functionalelements of a system or process. In short, the experimenter’stheory of what is guiding the results observed.4.1.3 statistical model—a model assuming that the principalfactor causing the results to deviate from the true value is arandom error process. This can usually be described in terms ofa probability function, for example, a bell-shaped curve,symmetrical or skewed. Errors are binomially distributed in the3-AFC test procedure.4.1.4 threshold, detection—the intensity of the stimulus thathas a probability of 0.5 of being detected under the conditionsof the test. The probability of detection at any intensity is nota fixed attribute of the observer, but rather a value whichassumes that sensitivity varies as a result of random fluctuationin factors such as alertness, attention, fatigue, and events at themolecular level, the effects of which can be modeled by aprobability function.4.1.5 individual threshold—a threshold based on a series ofjudgments by a single panelist.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3Available from British Standards Institution (BSI), 389 Chiswick High Rd.,London W4 4AL, U.K., http://www.bsigroup.com.4Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http://www.ansi.org.NOTE 1—This probability graph shows 20 panelists sorted by rank asdescribed in 9.3.2. Data are adapted from French Standard X 43-101.Group threshold = T = 50 % point = log(Z50) = 2.32. Group standard de-viation from % and 84 % points = σ = (3.07 − 1.57) ⁄2 = 0.75 in log(Z)units. The 99 % point is off the graph but can be calculated as2.32 + (0.75 × 2.327) = 4.07, where 2.327 is the % point on the abscissa ofthe normal curve of error.FIG. 1 Group Threshold by Rank-Probability GraphE1432 − 04 (2011)24.1.6 group threshold—the average, median, geometricmean or other agreed measure (or an experimentally deter-mined measure) of central tendency of the individual thresh-olds of the members of a group (panel). The meaning andsignificance of the term depends on what the group is selectedto represent (see 7.2.2).4.1.7 scale step factor—for a scale of dilutions presented toa panel, the factor by which each step differs from adjacentsteps.4.1.8 dilution factor—the following applies to flow olfacto-metry: If F1represents the flow of odorless gas which serves todilute the flow of odorant, F2, the dilution factor, Z, is given by:Z 5F11F2F2(1)where Z is dimensionless. F1and F2may be expressed,both in units of mass, or (preferably) both in units of vol-ume; the report should state which. The term Z50representsthe dilution factor to threshold. Alternate terminology in useis as follows: dilution-to-threshold ratio (D/T or D-T); odorunit (OU); and effective dose (ED).5. Summary of Practice5.1 From a data set according to 2.2, calculate the thresholdfor one individual graphically or by linear regression accordingto 5.2, or by using a model fitting computer program accordingto 5.3.5.2 Obtain the threshold in 5.1 by first calculating theproportion correct above chance for each concentration step.This is accomplished by deducting, from the proportion ofcorrect choices, the proportion that would have been selectedby chance in the absence of the stimulus (see 8.1.2). Then, foreach individual calculate that concentration which has aprobability of 0.5 of being detected under the conditions of thetest. This is the individual threshold.5.3 Alternatively obtain the threshold in 5.1 directly fromthe proportion of correct choices by non-linear regression usinga computer program, as described in 8.2.2.5.4 Always report the individual thresholds of the panelists.Depending on the purpose for which a threshold is required(see 7.2), and on the distribution found, a group threshold maybe calculated as the arithmetic or geometric mean, the median,or another measure of central tendency, or it may be concludedthat no group threshold can be calculated (see 7.4).6. Significance and Use6.1 Sensory thresholds are used to determine the potential ofsubstances at low concentrations to impart odor, taste, skinfeel,etc. to some form of matter.6.2 Thresholds are used, for example, in setting limits in airpollution, in noise abatement, in water treatment, and in foodsystems.6.3 Thresholds are used to characterize and compare thesensitivity of individuals or groups to given stimuli, forexample, in medicine, ethnic studies, and the study of animalspecies.7. Panel Size and Composition Versus Purpose of Test7.1 Panel Size and Composition—Panel variables should bechosen as a function of the purpose for which the resultingthreshold is needed. The important panel variables are asfollows:7.1.1 Number of tests per panelist,7.1.2 Number of panelists,7.1.3 Selection of panelists to represent a given population,andFIG. 2 Symmetrical, Bell-Shaped DistributionFIG. 3 Skewed DistributionFIG. 4 Bi-Modal DistributionE1432 − 04 (2011)37.1.4 Degree of training.7.2 Purpose of Test—It is useful to distinguish the followingthree categories:7.2.1 Comparing an Individual’s Threshold With a Litera-ture Value—The test may be conducted, for example, todiagnose anosmia or ageusia, or to study sensitivity to pain,noise, or odor. This is the simplest category requiring aminimum of 20 to 40 3-AFC presentations to the individual inquestion (see 2.2). A number of training sessions may berequired to establish the range of concentrations that will beused and to make certain that the individual is fully familiarwith the stimulus to be detected as well as the mechanics of thetest.7.2.2 A Population Threshold is Required, for example, theodor threshold of a population exposed to a given pollutant, orthe flavor threshold of consumers of a beverage for a givencontaminant. In this case, recourse must be had to the rules ofsampling from a population (see Ref (1)5and Practice E122),which require the following:(1) That the population be accurately defined anddelimited,(2) That the sample drawn be truly random, that is, thatevery member of the population has a known chance of beingselected, and(3) That knowledge of the degree of variation occurringwithin the population exists or can be acquired in the course offormulating the plan of sampling.5The boldface numbers in parentheses refer to the list of references at the end ofthis standard.NOTE 1—The results (using Probits and linear regression) are as follows:Panelist No. 1 2 3 4 5 6Threshold, ppb 381 166 226 97 47 12Group standard deviation (six panelists), σ = 0.539 in log (ppb) units.FIG. 5 Graphic Estimation of Approximate Thresholds for the Six Panelists in 7.3E1432 − 04 (2011)4NOTE 1—The PROC NLIN fits nonlinear regression models by least squares. Following the regression expression, the operator selects one of fouriterative methods (here, DUD) and must specify an approximate value for the parameters B (the slope, here = −4) and T (the threshold, here = 2). TheNLIN procedure first prints out the starting values for B and T, then proceeds stepwise (here, ten steps) until the residual sum of squares no longerdecreases (“convergence criterion met”). The threshold (here, T = log(ppb) = 1.954) is found as the last value in the T column. The results for the sixpanelists are as follows:Panelist 1 2 3 4 5 6Method DUD DUD DUD DUD DUD MARQUARDTLog (ppb) 2.518 2.249 2.368 1.954 1.806 0.892Threshold, ppb 330 178 249 90 64 7.8Group standard deviation (six panelists),σ = 0.59 in log(ppb) units.FIG. 6 Output from SAS NLIN Program (6) with Details for Panelist No. 4E1432 − 04 (2011)57.2.2.1 In practice, the cost and availability of panelistsplaces serious limitations on the degree to which populationfactors affecting thresholds, for example, age groups, gender,ethnic origin, well versus ill, smoker versus nonsmoker, trainedversus casual observers, etc., can be covered. The experimenteris typically limited to panels of 5 to 15, with each receiving 20to 40 3-AFC presentations, for a total of 100 to 600 presenta-tions. If the resulting thresholds are to have validity for thepopulation, the experimenter should include the followingsteps:(1) Calculate and tabulate the thresholds for each indi-vidual;(2) Repeat the test for those individuals (outliers) fallingwell beyond the range of the rest of the panel;(3) For any ind