ASTM E1432-19

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Designation: E1432 − 04 (Reapproved 2011) E1432 − 19
Standard Practice for
Defining and Calculating Individual and Group Sensory
Thresholds from Forced-Choice Data Sets of
Intermediate Size
This standard is issued under the fixed designation E1432; 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.
INTRODUCTION
The purpose of this practice is to determine individual sensory thresholds for odor, taste, and other
modalities and, when appropriate, calculate group thresholds. The practice takes as its starting point
any 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 exemplified
by Dynamic Triangle Olfactometry. A similar practice, Practice E679, utilizes limited-size data sets of
50 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 recognize
the stimulus and did indeed perceive it when it was present above his or her momentary threshold, and
that 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 sense
that values of vapor pressure exist. A panelist’sAn assessor’s ability to detect a stimulus varies as a
result of random variations 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
low concentrations of an odorant or tastant, the probability of detection by a given individual is
typically 0.0 and at high concentrations it is 1.0, and there is a range of concentrations in which the
probability of detection is between these limits. By definition, the threshold is the concentration for
which the probability of detection of the stimulus is 0.5 (that is, 50 % above chance, by a given
individual, under the conditions of the test).
Thresholds may be determined (1) for an individual (or for individuals one by one), and (2) for a
group (panel). While the determination of an individual threshold is a definable task, careful
consideration of the composition of the group is necessary to ensure the determined threshold
represents the group of interest.
There is a large degree of random error associated with estimating the probability of detection from
less than approximately 500 3-AFC presentations. The reliability of the results can be increased
greatly by enlarging the panel and by replicating the tests.
1. Scope
1.1 The definitions and procedures of this practice apply to the calculation of individual thresholds for any stimulus in any
medium, from data sets of intermediate size, that is, consisting of more than 20 to 40 3-AFC presentations per individual. A group
threshold may be calculated using 5 to 15 individual thresholds.
1.2 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 safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
This practice is under the jurisdiction of ASTM Committee E18 on Sensory Evaluation and is the direct responsibility of Subcommittee E18.04 on Fundamentals of
Sensory.
Current edition approved Aug. 1, 2011Aug. 1, 2019. Published August 2011September 2019. Originally approved in 1991. Last previous edition approved in 20042011
as E1432E1432 – 04–04 . DOI: 10.1520/E1432-04R11. (Reapproved 2011) . DOI: 10.1520/E1432-19.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1432 − 19
1.3 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Principles
2.1 The 3-AFC procedure is one of the set of n-AFC procedures, any of which could be used, in principle, for the measurement
of sensory thresholds, as could the duo-trio, the triangular, and the two-out-of-five procedures.other discrimination tests.
2.2 For calculation of the threshold of one individual, this practice requires data sets taken at five or more concentration scale
steps, typically six or seven steps, with each step differing from the previous step by a factor usually between 2 and 4, typically
3.0. The practice presupposes that the range of concentrations has been selected by pretesting, in order to ensure that the
individual’s threshold falls neither outside nor near the ends of the range, but well within it. At each concentration step, the
individual must be tested several times, typically five or more times.
2.3 Individual thresholds, as determined in 2.2, may be used for calculation of a group (or panel) threshold. The size and
composition of the panel (usually 5 to 15 members, preferably more) is determined according to the purpose for which the
threshold is required and the limitations of the testing situation (see 7.2).
2.4 Pooling of the data sets from panel members to produce a single step calculation of the panel threshold is not permitted.
3. Referenced Documents
3.1 ASTM Standards:
E122 Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or
Process
E679 Practice for Determination of Odor and Taste Thresholds By a Forced-Choice Ascending Concentration Series Method of
Limits
3.2 CEN Standard:
EN 13725 Air Quality—Determination of Odour Concentration Using Dynamic Dilution Olfactometry
3.3 ISO Standard:
ISO 13301 Sensory Analysis—Methodology—General guidance for Measuring Odour, Flavour, and Taste Detection Thresholds
by a Three Alternative Forced Choice (3-AFC) Procedure
4. Terminology
4.1 Definitions of Terms Specific to This Standard:
4.1.1 Three-Alternative Forced-Choice (3-AFC) test procedure—a test presentation used in many threshold tests. For example,
in odor testing by Dynamic Triangle Olfactometry, the panelist is presented with three gas streams, only one of which contains the
diluted odorant, while the other two contain odorless carrier gas. The panelist must indicate the one containing the added substance.
(The 3-AFC procedure is different from the classical Triangle test, in which either one or two of the three samples may contain
the added substance.)
4.1.1 model—an abstract or concrete analogy, usually mathematical, which represents in a useful way the functional elements
of a system or process. In short, the experimenter’s theory of what is guiding the results observed.
4.1.2 statistical model—a model assuming that the principal factor causing the results to deviate from the true value is a random
error process. This can usually be described in terms of a probability function, for example, a bell-shaped curve, symmetrical or
skewed. Errors are binomially distributed in the 3-AFC test procedure.
4.1.3 threshold, detection—the intensity of the stimulus that has a probability of 0.5 of being detected under the conditions of
the test. The probability of detection at any intensity is not a fixed attribute of the observer, but rather a value which assumes that
sensitivity varies as a result of random fluctuation in factors such as alertness, attention, fatigue, and events at the molecular level,
the effects of which can be modeled by a probability function.
4.1.4 individual threshold—a threshold based on a series of judgments by a single panelist.assessor.
4.1.5 group threshold—the average, median, geometric mean or other agreed measure (or an experimentally determined
measure) of central tendency of the individual thresholds of the members of a group (panel). The meaning and significance of the
term depends on what the group is selected to represent (see 7.2.2).
4.1.6 scale step factor—for a scale of dilutions presented to a panel, the factor by which each step differs from adjacent steps.
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NOTE 1—This probability graph shows 20 panelistsassessors sorted by rank as described in 9.3.2. Data are adapted from French Standard X 43-101.
Group threshold = T = 50 % point = log(Z ) = 2.32. Group standard deviation 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 as 2.32 + (0.75 × 2.327) = 4.07, where 2.327 is the % point on the abscissa of the normal curve of error.
FIG. 1 Group Threshold by Rank-Probability Graph
FIG. 2 Symmetrical, Bell-Shaped Distribution
4.1.7 dilution factor—the following applies to flow olfactometry: If F represents the flow of odorless gas which serves to dilute
the flow of odorant, F , the dilution factor, Z, is given by:
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FIG. 3 Skewed Distribution
FIG. 4 Bi-Modal Distribution
F 1F
1 2
Z 5 (1)
F
where Z is dimensionless. F and F may be expressed, both in units of mass, or (preferably) both in units of volume; the
1 2
report should state which. The term Z represents the dilution factor to threshold. Alternate terminology in use is as follows:
dilution-to-threshold ratio (D/T or D-T); odor unit (OU); and effective dose (ED).
5. Summary of Practice
5.1 From a data set according to 2.2, calculate the threshold for one individual graphically or by linear regression according to
5.2, or by using a model fitting computer program according to 5.3.
5.2 Obtain the threshold in 5.1 by first calculating the proportion correct above chance for each concentration step. This is
accomplished by deducting, from the proportion of correct choices, the proportion that would have been selected by chance in the
absence of the stimulus (see 8.1.2). Then, for each individual calculate that concentration which has a probability of 0.5 of being
detected under the conditions of the test. This is the individual threshold.
5.3 Alternatively obtain the threshold in 5.1 directly from the proportion of correct choices by non-linear regression using a
computer program, as described in 8.2.2.
5.4 Always report the individual thresholds of the panelists.assessors. Depending on the purpose for which a threshold is
required (see 7.2), and on the distribution found, a group threshold may be calculated as the arithmetic or geometric mean, the
median, or another measure of central tendency, or it may be concluded that no group threshold can be calculated (see 7.4).
6. Significance and Use
6.1 Sensory thresholds are used to determine the potential of substances at low concentrations to impart odor, taste, skinfeel,
etc. to some form of matter.
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NOTE 1—The results (using Probits and linear regression) are as follows:
Panelist No. 1 2 3 4 5 6
Assessor No. 1 2 3 4 5 6
Threshold, ppb 381 166 226 97 47 12
Group standard deviation (six panelists), σ = 0.539 in log (ppb) units.
Group standard deviation (six assessors), σ = 0.539 in log (ppb) units.
FIG. 5 Graphic Estimation of Approximate Thresholds for the Six PanelistsAssessors in 7.3
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** PURPOSE: Fit logistic models P = (1/3 + EXP[K])/(1 + EXP[K]),
** where:
** K = B(T - LOG[X]),
** P = proportion of correct identifications,
** B = slope,
** X = concentration (ppb) of Substance X in purified water, and
** T = threshold value in log(ppb).
*;
PROC NLIN METHOD=GAUSS DATA=INPUT;
BY ASSESSOR;
PARMS B = -4 T = 2;
K = B*(T-LOG10(X));
E = EXP(K);
N = (1/3+E);
D = D = (1+E);
MODEL P=N/D;
TITLE2 ‘Logistic Regression Models’;
RUN;
OUTPUT FOR ASSESSOR 4:
Dependent Variable P
Method: Gauss-Newton
Iterative Phase
Sum of
Iter B T Squares
0 -4.0000 2.0000 0.0258
1 -5.8644 1.9598 0.0107
2 -6.3222 1.9568 0.0104
3 -6.2451 1.9537 0.0104
4 -6.2933 1.9541 0.0104
5 -6.2769 1.9538 0.0104
6 -6.2841 1.9539 0.0104
7 -6.2813 1.9539 0.0104
8 -6.2824 1.9539 0.0104
9 -6.2821 1.9539 0.0104
10 -6.2821 1.9539 0.0104
NOTE: Convergence criterion met.
Approx
Sum of Mean F
Source DF Squares Square Value Pr > F
Model 2 2.3508 1.1754 340.37 0.0003
Error 3 0.0104
Uncorrected Total 5 2.3611
Approx Std
Parameter Estimate error 95 % Confidence Limits
B -6.2821 1.6732 -11.6068 -0.9574
T 1.9539 0.0471 1.8039 2.1038
NOTE 1—The PROC NLIN fits nonlinear regression models by least squares. Following the regression expression, the operator selects one of four
iterative methods (here, DUD)GAUSS) and must specify an approximate value for the parameters B (the slope, here = −4)here = -4) and T (the threshold,
here = 2). The NLIN procedure first prints out the starting values for B and T, then proceeds stepwise (here, ten steps) until the residual sum of squares
no longer decreases (“convergence criterion met”). The threshold (here, TT = log(ppb) = 1.954) = log(ppb) = 1.954) is found as the last value in the T
column. The results for the six panelistsassessors are as follows:
Panelist 1 2 3 4 5 6
Method DUD DUD DUD DUD DUD MARQUARDT
Log (ppb) 2.518 2.249 2.368 1.954 1.806 0.892
Threshold, ppb 330 178 249 90 64 7.8
Group standard deviation (six panelists),σ = 0.59 in log(ppb) units.
Assessor 1 2 3 4 5 6
Log (ppb) 2.519 2.249 2.356 1.954 1.807 0.904
Threshold, ppb 330 178 227 90 64 8
Group standard deviation (six assessors), σ = 0.58 in log (ppb) units.
FIG. 6 Output from SAS NLIN Program (6) with Details for PanelistAssessor No. 4
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6.2 Thresholds are used, for example, in setting limits in air pollution, in noise abatement, in water treatment, and in food
systems.
6.3 Thresholds are used to characterize and compare the sensitivity of individuals or groups to given stimuli, for example, in
medicine, ethnic studies, and the study of animal species.
7. Panel Size and Composition Versus Purpose of Test
7.1 Panel Size and Composition—Panel variables should be chosen as a function of the purpose for which the resulting threshold
is needed. The important panel variables are as follows:
7.1.1 Number of tests per panelist,assessor,
7.1.2 Number of panelists,assessors,
7.1.3 Selection of panelistsassessors to represent a given population, and
7.1.4 Degree of training.
7.2 Purpose of Test—It is useful to distinguish the following three categories:
7.2.1 Comparing an Individual’s Threshold With a Literature Value—The test may be conducted, for example, to diagnose
anosmia or ageusia, or to study sensitivity to pain, noise, or odor. This is the simplest category requiring a minimum of 20 to 40
3-AFC presentations to the individual in question (see 2.2). A number of training sessions may be required to establish the range
of concentrations that will be used and to make certain that the individual is fully familiar with the stimulus to be detected as well
as the mechanics of the test.
7.2.2 A Population Threshold is Required, for example, the odor threshold of a population exposed to a given pollutant, or the
flavor threshold of consumer
...