ASTM E1885-18

Standard Test Method for Sensory Analysis—Triangle Test

SIGNIFICANCE AND USE
5.1 This test method is effective for the following test objectives:  
5.1.1 To determine whether a perceivable difference results or a perceivable difference does not result, for example, when a change is made in ingredients, processing, packaging, handling or storage; or  
5.1.2 To select, train and monitor assessors.  
5.2 This test method itself does not change whether the purpose of the triangle test is to determine that two products are perceivably different versus that the products are not perceivably different. Only the selected values of pd, α, and β change. If the objective of the test is to determine if there is a perceivable difference between two products, then the value selected for α is typically smaller than the value selected for β. If the objective is to determine if the two products are sufficiently similar to be used interchangeably, then the value selected for β is typically smaller than the value selected for α and the value of pd is selected to define “sufficiently similar.”
SCOPE
1.1 This test method covers a procedure for determining whether a perceptible sensory difference exists between samples of two products.  
1.2 This test method applies whether a difference may exist in a single sensory attribute or in several.  
1.3 This test method is applicable when the nature of the difference between the samples is unknown. It does not determine the size or the direction of the difference. The attribute(s) responsible for the difference are not identified.  
1.4 Compared to the duo-trio test, the triangle test can achieve an equivalent level of statistical significance with fewer assessors. For details on how the triangle test compares to other three-sample tests, see Refs (1) , (2), (3) and (4).2  
1.5 This test method is applicable only if the products are homogeneous. If two samples of the same product can often be distinguished, then another method, for example, descriptive analysis, may be more appropriate.  
1.6 This test method is applicable only when the products do not cause excessive sensory fatigue, carryover or adaptation.  
1.7 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.8 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.

General Information

• Status: Published
• Publication Date: 14-Aug-2018
• ICS: 67.240 - Sensory analysis
• Technical Committee: E18 - Sensory Evaluation
• Drafting Committee: E18.04 - Test Methods

Relations

• Replaces: ASTM E1885-04(2011) - Standard Test Method for Sensory Analysis<char: emdash>Triangle Test
• Effective Date: 15-Aug-2018
• Refers: ASTM E456-13a(2022)e1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Apr-2022
• Refers: ASTM E253-19 - Standard Terminology Relating to Sensory Evaluation of Materials and Products
• Effective Date: 15-Oct-2019
• Refers: ASTM E253-18a - Standard Terminology Relating to Sensory Evaluation of Materials and Products
• Effective Date: 01-Oct-2018
• Refers: ASTM E253-18 - Standard Terminology Relating to Sensory Evaluation of Materials and Products
• Effective Date: 15-Jun-2018
• Refers: ASTM E456-13A(2017)e3 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Oct-2017
• Refers: ASTM E456-13A(2017)e1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Oct-2017
• Refers: ASTM E1871-17 - Standard Guide for Serving Protocol for Sensory Evaluation of Foods and Beverages
• Effective Date: 01-Sep-2017
• Refers: ASTM E253-17 - Standard Terminology Relating to Sensory Evaluation of Materials and Products
• Effective Date: 01-May-2017
• Refers: ASTM E253-16 - Standard Terminology Relating to Sensory Evaluation of Materials and Products
• Effective Date: 01-Jun-2016
• Refers: ASTM E253-15b - Standard Terminology Relating to Sensory Evaluation of Materials and Products
• Effective Date: 01-Dec-2015
• Refers: ASTM E253-15a - Standard Terminology Relating to Sensory Evaluation of Materials and Products
• Effective Date: 01-Jun-2015
• Refers: ASTM E253-15 - Standard Terminology Relating to Sensory Evaluation of Materials and Products
• Effective Date: 15-Jan-2015
• Refers: ASTM E456-13ae1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Nov-2013
• Refers: ASTM E456-13ae3 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Nov-2013

Overview

ASTM E1885-18: Standard Test Method for Sensory Analysis-Triangle Test is a key standard developed by ASTM International. This sensory analysis standard outlines a scientifically rigorous method-the triangle test-for determining whether a perceivable sensory difference exists between two product samples. The triangle test is widely used in food and beverage industries, as well as in materials evaluation, for difference testing and similarity testing. The method offers robust statistical power with fewer assessors compared to other difference test formats.

Key Topics

• Triangle Test Principles:
  In the triangle test, each assessor receives three coded samples: two are identical and one is different. Assessors are required to identify the “odd” sample, even if by guesswork. This forced-choice procedure ensures objectivity in sensory discrimination.

• Test Objectives:

  • Determining if a sensory difference exists (e.g., after changes in formulation, processing, or packaging)
  • Assessing similarity for interchangeability of products
  • Selecting, training, and monitoring sensory panel assessors

• Applicable Conditions:

  • Suitable where the nature or direction of the difference is unknown
  • Best for homogeneous products
  • Not appropriate if products may cause sensory fatigue or adaptation

• Statistical Sensitivity:
  Sensitivity and reliability are achieved by carefully selecting values for α (type I error), β (type II error), and the proportion of discriminators (pd).

  • Lower α prioritizes confidence in declaring a difference
  • Lower β prioritizes confidence in declaring similarity
    Tables within the standard specify minimum numbers of assessors and correct responses needed for statistical significance.

• Panel Design and Data Analysis:

  • Requires balanced presentation sequences to avoid order bias
  • Only one “odd” sample per triad; responses are tallied for significance
  • Statistical analysis determines if a perceivable difference exists

Applications

The ASTM E1885-18 triangle test method is practical and flexible for:

• Product Development:
  Assess whether changes in ingredients, processing, packaging, or storage affect sensory perception.

• Quality Control:
  Verify product consistency and detect inadvertent changes during production.

• Packaging Evaluation:
  Determine if alternative packaging materials impact sensory attributes after shelf life studies.

• Panelist Management:
  Select and monitor sensory assessors for acuity and training effectiveness.

• Process Optimization:
  Inform decision-making for cost-saving formulations, ensuring that new processes do not affect perceived product quality.

Example Use Cases:

• A brewery evaluating whether a new process changes the flavor profile of non-alcoholic beer.
• A confectionery company testing if a new wrapper alters candy bar taste after storage.
• Food manufacturers comparing batches for sensory equivalence.

Related Standards

Professionals using ASTM E1885-18 may also reference:

• ASTM E253: Terminology Relating to Sensory Evaluation of Materials and Products
• ASTM E456: Terminology Relating to Quality and Statistics
• ASTM E1871: Guide for Serving Protocol for Sensory Evaluation of Foods and Beverages
• ASTM E2262: Practice for Estimating Thurstonian Discriminal Distances
• ISO 4120: Sensory Analysis – Methodology – Triangular Test

These related standards provide additional definitions, terminology, and best practices for sensory evaluation and statistical analysis.

---

Keywords: ASTM E1885-18, triangle test, sensory analysis, difference testing, similarity testing, sensory evaluation, quality control, food testing, statistical significance, sensory panel, product development, packaging evaluation.

Standards Content (Sample)

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.
Designation: E1885 − 18
Standard Test Method for
Sensory Analysis—Triangle Test
This standard is issued under the fixed designation E1885; 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.
1. Scope 2. Referenced Documents
2.1 ASTM Standards:
1.1 This test method covers a procedure for determining
E253 Terminology Relating to Sensory Evaluation of Mate-
whether a perceptible sensory difference exists between
rials and Products
samples of two products.
E456 Terminology Relating to Quality and Statistics
1.2 This test method applies whether a difference may exist
E1871 Guide for Serving Protocol for Sensory Evaluation of
in a single sensory attribute or in several.
Foods and Beverages
E2262 Practice for Estimating Thurstonian Discriminal Dis-
1.3 This test method is applicable when the nature of the
tances
difference between the samples is unknown. It does not
determine the size or the direction of the difference. The 2.2 ISO Standard:
attribute(s) responsible for the difference are not identified. ISO 4120 Sensory Analysis – Methodology – Triangular
Test
1.4 Compared to the duo-trio test, the triangle test can
achieve an equivalent level of statistical significance with
3. Terminology
fewer assessors. For details on how the triangle test compares
3.1 Definitions–For definition of terms relating to sensory
to other three-sample tests, see Refs (1), (2), (3) and (4).
analysis, see Terminology E253, and for terms relating to
1.5 This test method is applicable only if the products are
statistics, see Terminology E456.
homogeneous. If two samples of the same product can often be
3.2 Definitions of Terms Specific to This Standard:
distinguished, then another method, for example, descriptive
3.2.1 α (alpha) risk—probability of concluding that a per-
analysis, may be more appropriate.
ceptible difference exists when, in reality, one does not. (Also
1.6 This test method is applicable only when the products
known as Type I Error or significance level.)
do not cause excessive sensory fatigue, carryover or adapta-
3.2.2 β (beta) risk—probability of concluding that no per-
tion.
ceptible difference exists when, in reality, one does. (Also
1.7 This standard does not purport to address all of the known as Type II Error.)
safety concerns, if any, associated with its use. It is the
3.2.3 p —probability of a correct response.
c
responsibility of the user of this standard to establish appro-
3.2.4 p (proportion of discriminators)—proportion of the
d
priate safety, health, and environmental practices and deter-
population represented by the assessors that can distinguish
mine the applicability of regulatory limitations prior to use.
between the two products.
1.8 This international standard was developed in accor-
3.2.5 product—material to be evaluated.
dance with internationally recognized principles on standard-
3.2.6 sample—unit of product prepared, presented, and
ization established in the Decision on Principles for the
evaluated in the test.
Development of International Standards, Guides and Recom-
mendations issued by the World Trade Organization Technical
3.2.7 sensitivity—general term used to summarize the per-
Barriers to Trade (TBT) Committee.
formance characteristics of the test. The sensitivity of the test
is rigorously defined, in statistical terms, by the values selected
for α, β, and p .
d
This test method is under the jurisdiction ofASTM Committee E18 on Sensory
Evaluation and is the direct responsibility of Subcommittee E18.04 on Fundamen-
tals of Sensory. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Aug. 15, 2018. Published August 2018. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1997. Last previous edition approved in 2011 as E1885 – 04 (2011). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/E1885-18. the ASTM website.
2 4
The boldface numbers given in parentheses refer to a list of references at the Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
end of the text. 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1885 − 18
3.2.8 δ—Thurstonian measure of sensory difference (effect therefore increase the likelihood of finding a significant differ-
size) relative to perceptual noise (standard deviation) (see ence. Monitoring the performance of assessors over time may
Practice E2262). be useful for increased sensitivity.
3.2.9 triad—three uniquely coded samples given to an
7.2 Chooseassessorsinaccordancewithtestobjectives.For
assessor in the triangle test; two samples are alike (that is, of
example, to project results to a general consumer population,
one product) and one is different (that is, of the other product).
assessors with unknown sensitivity might be selected. To
increase protection of product quality, assessors with demon-
4. Summary of Test Method
strated acuity should be selected.
4.1 Clearly define the test objective in writing.
7.3 Thedecisiontousetrainedoruntrainedassessorsshould
be addressed prior to testing. Training may include a prelimi-
4.2 Choose the number of assessors based on the level of
nary presentation on the nature of the samples and the problem
sensitivity desired for the test. The sensitivity of the test is, in
concerned. If the test concerns the detection of particular taint,
part, a function of two competing risks: the risk of declaring
consider the inclusion of samples during training that demon-
the samples different when they are not (that is, α-risk) and the
strate its presence and absence. Such demonstration will
risk of not declaring the samples different when they are (that
increase the panel’s acuity for the taint but may detract from
is, β-risk).Acceptable values of α and β vary depending on the
other differences. See STP 758 for details (8). Allow adequate
test objective and should be determined before the test (see
time between the exposure to the training samples and the
Appendix X3).
actual triangle test to avoid carryover.
4.3 Assessors receive a triad and are informed that two of
7.4 During the test sessions, avoid giving information about
the samples are alike and that one is different. The assessors
product identity, expected treatment effects, or individual
report which they believe to be the different, or “odd,” sample,
performance until all testing is complete.
even if the selection is based only on a guess.
7.5 Pooling multiple evaluations by the same assessor is not
4.4 Results are tallied and significance determined by ref-
recommended because results are less representative of the
erence to a statistical table.
population and the risk of incorrect conclusion is greater.
5. Significance and Use
8. Number of Assessors
5.1 This test method is effective for the following test
8.1 Choose the number of assessors to yield the level of
objectives:
sensitivity called for by the test objectives. The sensitivity of
5.1.1 To determine whether a perceivable difference results
the test is a function of three values: the α-risk, and the β-risk,
or a perceivable difference does not result, for example, when
and the maximum allowable proportion of distinguishers, p .
a change is made in ingredients, processing, packaging, han-
d
dling or storage; or
8.2 Priortoconductingthetest,selectvaluesforα,βand p .
d
5.1.2 To select, train and monitor assessors.
The following can be considered as general guidelines.
8.2.1 For α-risk: A statistically significant result at:
5.2 This test method itself does not change whether the
8.2.1.1 10 to 5 % (0.10 to 0.05) indicates “slight” evidence
purposeofthetriangletestistodeterminethattwoproductsare
that a difference was apparent;
perceivably different versus that the products are not perceiv-
8.2.1.2 5 to 1 % (0.05 to 0.01) indicates “moderate” evi-
ably different. Only the selected values of p , α, and β change.
d
dence that a difference was apparent;
If the objective of the test is to determine if there is a
8.2.1.3 1 to 0.1 % (0.01 to 0.001) indicates “strong” evi-
perceivable difference between two products, then the value
dence that a difference was apparent; and
selected for α is typically smaller than the value selected for β.
8.2.1.4 Below 0.1 % (<0.001) indicates “very strong” evi-
If the objective is to determine if the two products are
dence that a difference was apparent.
sufficiently similar to be used interchangeably, then the value
8.2.2 For β–risk: The strength of the evidence that a
selected for β is typically smaller than the value selected for α
difference was not apparent is assessed using the same criteria
and the value of p is selected to define “sufficiently similar.”
d
as above (substituting “was not apparent” for “was apparent”).
6. Apparatus
8.2.3 For p : the maximum allowable proportion of
d
distinguishers, p , falls into three ranges:
d
6.1 Carry out the test under conditions that prevent contact
8.2.3.1 p < 25 % represent small values;
d
between assessors until the evaluations have been completed
8.2.3.2 25 % < p < 35 % represent medium sized values;
d
for example, booths that comply with STP 913 (5).
and
6.2 Sample preparation and serving sizes should comply
8.2.3.3 p > 35 % represent large values.
d
with Practice E1871. See Refs (6) or (7).
7. Assessors
In this test method, the probability of a correct response, p is modeled as p =
d c
α/β α/β
1 p + (1/3) (1-p ), where p is the proportion of the entire population of
7.1 All assessors must be familiar with the mechanics of the d d d
assessors who can distinguish between the two products. It is a strictly statistical
triangle test (the format, the task, and the procedure of
“guessing model” of the assessor’s behavior. It is not a psychometric model of the
evaluation). Experience and familiarity with the product and
assessor’s decision process, such as the Thurstone-Ura model that could also be
testmethodmayincreasethesensitivityofanassessorandmay applied in discrimination testing.
E1885 − 18
8.3 Having defined the required level of sensitivity for the tions of the test require the prevention of repeat evaluations for
test using 8.2, use Table A1.1 to determine the number of example, if samples are bulky, leave an aftertaste, or show
assessors necessary. Enter Table A1.1 in the section corre- slight differences in appearance that cannot be masked, present
sponding to the selected value of p and the column corre- thesamplessequentiallyanddonotallowrepeatedevaluations.
d
sponding to the selected value of β. The minimum required
9.5 Each scoresheet should provide for a single triad of
number of assessors is found in the row corresponding to the
samples. If a different set of products is to be evaluated by an
selected value of α. Alternatively, Table A1.1 can be used to
assessor in a single session, the completed scoresheet and any
develop a set of values for p , α and β that provide acceptable
d
remaining product should be returned to the test administrator
sensitivity while maintaining the number of assessors within
prior to receiving the subsequent triad. The assessor cannot go
practical limits. The approach is presented in detail in Ref (9).
back to any of the previous samples or change the verdict on
8.4 If one wishes to use Thurstonian δ as a measure of
any previous test.
sensory effect size, use Tables A2.1 and A2.2 to convert
9.6 Do not ask questions about preference, acceptance, or
between p and δ. See Ref (10) for further discussion on the
d
degree of difference after the initial selection of the odd
relationship between Thurstonian δ and p .
d
sample. The selection the assessor has just made may bias the
8.5 Often in practice, the number of assessors is determined
reply to any additional questions. Responses to such questions
by material conditions (for example, duration of the
may be obtained through separate tests for preference,
experiment, number of available assessors, quantity of prod-
acceptance, degree of difference, etc. (see Manual 26) (11).A
uct). However, increasing the number of assessors increases
comment section asking why the choice was made may be
the likelihood of detecting small proportions of distinguishers.
included for the assessor’s remarks.
Thus, one should expect to use larger numbers of assessors
9.7 The triangle test is a forced-choice procedure; assessors
when trying to demonstrate that products are similar compared
are not allowed the option of reporting “no difference.” An
towhenoneistryingtoprovetheyaredifferent.Often18to36
assessor who detects no difference between the samples should
assessors are used when testing for a difference. For compa-
beinstructedtorandomlyselectoneofthesamplesasbeingthe
rable sensitivity when testing for similarity, 42 to 78 assessors
odd one and can indicate that the selection was only a guess in
are needed.
the comments section of the scoresheet.
9. Procedure
10. Analysis and Interpretation of Results
9.1 Prepareworksheetsandscoresheets(seeAppendixX1–
10.1 Use Table A1.2 to analyze the data obtained from a
Appendix X3) in advance of the test so as to utilize an equal
triangletest.Theactualnumberofassessorscanbegreaterthan
numberofthesixpossiblesequencesoftwoproducts,AandB.
the minimum value given in Table A1.1. If the number of
Distribute these at random in groups of six among the
correct responses is greater than or equal to the number given
panelists. The six sequences are:
in Table A1.2, conclude that a perceptible difference exists
ABB AAB ABA
between the samples. If the number of correct responses is less
BAA BBA BAB
thanthenumbergiveninTableA1.2,concludethatthesamples
9.2 Sometimes the final number of assessors does not end
are sufficiently similar.Again, the conclusions are based on the
up as a multiple of six. For example, if a test was planned for
risks accepted when the level of sensitivity (that is, p , α, and
d
36 assessors and only 34 actually participated, there would be
β) was selected in determining the number of assessors.
five complete series of the six sequences and one incomplete
10.2 If desired, calculate a confidence interval on the
set of four in which two of the six triads were randomly
dropped. proportion of the population that can distinguish the samples.
This method is described in Appendix X4.
9.3 It is critical to the validity of the test that assessors
cannot identify the samples from the way in which they are
11. Report
presented. For example, in a test evaluating flavor differences,
one should avoid any subtle differences in temperature or
11.1 Report the test objective, the results, and the conclu-
appearance caused by factors such as the time sequence of
sions. The following additional information is recommended:
preparation. It may be possible to mask color differences using
11.1.1 The purpose of the test and the nature of the
light filters, subdued illumination, or colored serving contain-
treatment studied;
ers. Code the serving containers containing the samples in a
11.1.2 Full Identification of the Samples—Origin, method
uniform manner, preferably using three-digit numbers, chosen
of preparation, quantity, shape, storage prior to testing, serving
at random for each test. Prepare samples out of sight and in an
size, temperature. (Sample information should communicate
identicalmanner:sameapparatus,sameservingcontainers,and
that all storage handling, and preparation was done in such a
same quantities of products (see ASTM Serving Protocols).
way as to yield samples that differ only due to the variable of
interest, if at all);
9.4 Present each triad simultaneously if possible, following
11.1.3 The number of assessors, the number of correct
the same spatial arrangement for each assessor (on a line to be
selections, and the result of the statistical evaluation;
sampled always from left to right, in a triangular array, etc.)
Within the triad, assessors are typically allowed to make 11.1.4 Assessors—Age, gender, experience in sensory
repeated evaluations of each sample as desired. If the condi- testing, with the product, with the samples in the test;
E1885 − 18
11.1.5 Any information and any specific instructions given the precision of results that is applicable to all populations of
the assessor in connection with the test; assessors cannot be made. However, adherence to the recom-
11.1.6 The test environment: use of booths, simultaneous or
mendations stated in this standard should increase the repro-
sequential presentation, light conditions, whether the identity
ducibility of results and minimize bias.
of the samples was disclosed after the test and the manner in
which it was done; and
13. Keywords
11.1.7 The location and date of the test and the name of the
13.1 difference testing; discrimination test; sensory analy-
panel leader.
sis; similarity testing; triangle test
12. Precision and Bias
12.1 Because results of sensory difference tests are func-
tions of
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E1885 − 04 (Reapproved 2011) E1885 − 18
Standard Test Method for
Sensory Analysis—Triangle Test
This standard is issued under the fixed designation E1885; 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.
1. Scope
1.1 This test method covers a procedure for determining whether a perceptible sensory difference exists between samples of two
products.
1.2 This test method applies whether a difference may exist in a single sensory attribute or in several.
1.3 This test method is applicable when the nature of the difference between the samples is unknown. It does not determine the
size or the direction of the difference. The attribute(s) responsible for the difference are not identified.
1.4 Compared to the duo-trio test, the triangle test can achieve an equivalent level of statistical significance with fewer assessors.
For details on how the triangle test compares to other three-sample tests, see Refs (1),(2),(3) and (4).
1.5 This test method is applicable only if the products are homogeneous. If two samples of the same product can often be
distinguished, then another method, for example, descriptive analysis, may be more appropriate.
1.6 This test method is applicable only when the products do not cause excessive sensory fatigue, carryover or adaptation.
1.7 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.
1.8 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. Referenced Documents
2.1 ASTM Standards:
E253 Terminology Relating to Sensory Evaluation of Materials and Products
E456 Terminology Relating to Quality and Statistics
E1871 Guide for Serving Protocol for Sensory Evaluation of Foods and Beverages
E2262 Practice for Estimating Thurstonian Discriminal Distances
2.2 ISO Standard:
ISO 4120 Sensory Analysis – Methodology – Triangular Test
3. Terminology
3.1 Definitions–For definition of terms relating to sensory analysis, see Terminology E253, and for terms relating to statistics,
see Terminology E456.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 α (alpha) risk—probability of concluding that a perceptible difference exists when, in reality, one does not. (Also known
as Type I Error or significance level.)
This test method 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. 15, 2018. Published August 2011August 2018. Originally approved in 1997. Last previous edition approved in 20042011 as
E1885 – 04. 04 (2011). DOI: 10.1520/E1885-04R11.10.1520/E1885-18.
The boldface numbers given in parentheses refer to a list of references at the end of the text.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1885 − 18
3.2.2 β (beta) risk—probability of concluding that no perceptible difference exists when, in reality, one does. (Also known as
Type II Error.)
3.2.3 p —probability of a correct response.
c
3.2.4 p (proportion of discriminators)—proportion of the population represented by the assessors that can distinguish between
d
the two products.
3.2.5 product—material to be evaluated.
3.2.6 sample—unit of product prepared, presented, and evaluated in the test.
3.2.7 sensitivity—general term used to summarize the performance characteristics of the test. The sensitivity of the test is
rigorously defined, in statistical terms, by the values selected for α, β, and p .
d
3.2.8 δ—Thurstonian measure of sensory difference (effect size) relative to perceptual noise (standard deviation) (see Practice
E2262).
3.2.9 triad—three uniquely coded samples given to an assessor in the triangle test; two samples are alike (that is, of one product)
and one is different (that is, of the other product).
3.3 triad—three uniquely coded samples given to an assessor in the triangle test; two samples are alike (that is, of one product)
and one is different (that is, of the other product).
4. Summary of Test Method
4.1 Clearly define the test objective in writing.
4.2 Choose the number of assessors based on the level of sensitivity desired for the test. The sensitivity of the test is, in part,
a function of two competing risks: the risk of declaring the samples different when they are not (that is, α-risk) and the risk of not
declaring the samples different when they are (that is, β-risk). Acceptable values of α and β vary depending on the test objective
and should be determined before the test (see Appendix X3).
4.3 Assessors receive a triad and are informed that two of the samples are alike and that one is different. The assessors report
which they believe to be the different, or “odd,” sample, even if the selection is based only on a guess.
4.4 Results are tallied and significance determined by reference to a statistical table.
5. Significance and Use
5.1 This test method is effective for the following test objectives:
5.1.1 To determine whether a perceivable difference results or a perceivable difference does not result, for example, when a
change is made in ingredients, processing, packaging, handling or storage; or
5.1.2 To select, train and monitor assessors.
5.2 This test method itself does not change whether the purpose of the triangle test is to determine that two products are
perceivably different versus that the products are not perceivably different. Only the selected values of p , α, and β change. If the
d
objective of the test is to determine if there is a perceivable difference between two products, then the value selected for α is
typically smaller than the value selected for β. If the objective is to determine if the two products are sufficiently similar to be used
interchangeably, then the value selected for β is typically smaller than the value selected for α and the value of p is selected to
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define “sufficiently similar.”
6. Apparatus
6.1 Carry out the test under conditions that prevent contact between assessors until the evaluations have been completed for
example, booths that comply with STP 913 (5).
6.2 Sample preparation and serving sizes should comply with Practice E1871. See Refs (6) or (7).
7. Assessors
7.1 All assessors must be familiar with the mechanics of the triangle test (the format, the task, and the procedure of evaluation).
Experience and familiarity with the product and test method may increase the sensitivity of an assessor and may therefore increase
the likelihood of finding a significant difference. Monitoring the performance of assessors over time may be useful for increased
sensitivity.
7.2 Choose assessors in accordance with test objectives. For example, to project results to a general consumer population,
assessors with unknown sensitivity might be selected. To increase protection of product quality, assessors with demonstrated acuity
should be selected.
7.3 The decision to use trained or untrained assessors should be addressed prior to testing. Training may include a preliminary
presentation on the nature of the samples and the problem concerned. If the test concerns the detection of particular taint, consider
the inclusion of samples during training that demonstrate its presence and absence. Such demonstration will increase the panel’s
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acuity for the taint but may detract from other differences. See STP 758 for details (8). Allow adequate time between the exposure
to the training samples and the actual triangle test to avoid carryover.
7.4 During the test sessions, avoid giving information about product identity, expected treatment effects, or individual
performance until all testing is complete.
7.5 Pooling multiple evaluations by the same assessor is not recommended because results are less representative of the
population and the risk of incorrect conclusion is greater.
8. Number of Assessors
8.1 Choose the number of assessors to yield the level of sensitivity called for by the test objectives. The sensitivity of the test
is a function of three values: the α-risk, and the β-risk, and the maximum allowable proportion of distinguishers, p .
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8.2 Prior to conducting the test, select values for α, β and p . The following can be considered as general guidelines.
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8.2.1 For α-risk: A statistically significant result at:
8.2.1.1 10 to 5 % (0.10 to 0.05) indicates “slight” evidence that a difference was apparent;
8.2.1.2 5 to 1 % (0.05 to 0.01) indicates “moderate” evidence that a difference was apparent;
8.2.1.3 1 to 0.1 % (0.01 to 0.001) indicates “strong” evidence that a difference was apparent; and
8.2.1.4 Below 0.1 % (<0.001) indicates “very strong” evidence that a difference was apparent.
8.2.2 For β–risk: The strength of the evidence that a difference was not apparent is assessed using the same criteria as above
(substituting “was not apparent” for “was apparent”).
8.2.3 For p : the maximum allowable proportion of distinguishers, p , falls into three ranges:
d d
8.2.3.1 p < 25 % represent small values;
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8.2.3.2 25 % < p < 35 % represent medium sized values; and
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8.2.3.3 p > 35 % represent large values.
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8.3 Having defined the required level of sensitivity for the test using 8.2, use TableTable A1.1 A1.1 to determine the number
of assessors necessary. Enter TableTable A1.1 A1.1 in the section corresponding to the selected value of p and the column
d
corresponding to the selected value of β. The minimum required number of assessors is found in the row corresponding to the
selected value of α. Alternatively, TableTable A1.1 A1.1 can be used to develop a set of values for p , α and β that provide
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acceptable sensitivity while maintaining the number of assessors within practical limits. The approach is presented in detail in Ref
(9).
8.4 If one wishes to use Thurstonian δ as a measure of sensory effect size, use Tables A2.1 and A2.2 to convert between p and
d
δ. See Ref (10) for further discussion on the relationship between Thurstonian δ and p .
d
8.5 Often in practice, the number of assessors is determined by material conditions (for example, duration of the experiment,
number of available assessors, quantity of product). However, increasing the number of assessors increases the likelihood of
detecting small proportions of distinguishers. Thus, one should expect to use larger numbers of assessors when trying to
demonstrate that products are similar compared to when one is trying to prove they are different. Often 18 to 36 assessors are used
when testing for a difference. For comparable sensitivity when testing for similarity, 42 to 78 assessors are needed.
9. Procedure
9.1 Prepare worksheets and scoresheets (see Appendix X1 – Appendix X3) in advance of the test so as to utilize an equal
number of the six possible sequences of two products, A and B. Distribute these at random in groups of six among the panelists.
The six sequences are:
ABB AAB ABA
BAA BBA BAB
9.2 Sometimes the final number of assessors does not end up as a multiple of six. For example, if a test was planned for 36
assessors and only 34 actually participated, there would be five complete series of the six sequences and one incomplete set of four
in which two of the six triads were randomly dropped.
9.3 It is critical to the validity of the test that assessors cannot identify the samples from the way in which they are presented.
For example, in a test evaluating flavor differences, one should avoid any subtle differences in temperature or appearance caused
by factors such as the time sequence of preparation. It may be possible to mask color differences using light filters, subdued
illumination, or colored serving containers. Code the serving containers containing the samples in a uniform manner, preferably
using three-digit numbers, chosen at random for each test. Prepare samples out of sight and in an identical manner: same apparatus,
same serving containers, and same quantities of products (see ASTM Serving Protocols).
α/β α/β
In this test method, the probability of a correct response, p is modeled as p = 1 p + (1/3) (1-p ), where p is the proportion of the entire population of assessors
d c d d d
who can distinguish between the two products. It is a strictly statistical “guessing model” of the assessor’s behavior. It is not a psychometric model of the assessor’s decision
process, such as the Thurstone-Ura model that could also be applied in discrimination testing.
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9.4 Present each triad simultaneously if possible, following the same spatial arrangement for each assessor (on a line to be
sampled always from left to right, in a triangular array, etc.) Within the triad, assessors are typically allowed to make repeated
evaluations of each sample as desired. If the conditions of the test require the prevention of repeat evaluations for example, if
samples are bulky, leave an aftertaste, or show slight differences in appearance that cannot be masked, present the samples
sequentially and do not allow repeated evaluations.
9.5 Each scoresheet should provide for a single triad of samples. If a different set of products is to be evaluated by an assessor
in a single session, the completed scoresheet and any remaining product should be returned to the test administrator prior to
receiving the subsequent triad. The assessor cannot go back to any of the previous samples or change the verdict on any previous
test.
9.6 Do not ask questions about preference, acceptance, or degree of difference after the initial selection of the odd sample. The
selection the assessor has just made may bias the reply to any additional questions. Responses to such questions may be obtained
through separate tests for preference, acceptance, degree of difference, etc. (see Manual 26) (1011). A comment section asking why
the choice was made may be included for the assessor’s remarks.
9.7 The triangle test is a forced-choice procedure; assessors are not allowed the option of reporting “no difference.” An assessor
who detects no difference between the samples should be instructed to randomly select one of the samples as being the odd one
and can indicate that the selection was only a guess in the comments section of the scoresheet.
10. Analysis and Interpretation of Results
10.1 Use TableTable A1.2 A1.2 to analyze the data obtained from a triangle test. The actual number of assessors can be greater
than the minimum value given in Table A1.1Table A1.1. . If the number of correct responses is greater than or equal to the number
given in Table A1.2Table A1.2, , conclude that a perceptible difference exists between the samples. If the number of correct
responses is less than the number given in Table A1.2Table A1.2, , conclude that the samples are sufficiently similar. Again, the
conclusions are based on the risks accepted when the level of sensitivity (that is, p , α, and β) was selected in determining the
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number of assessors.
10.2 If desired, calculate a confidence interval on the proportion of the population that can distinguish the samples. This method
is described in Appendix X4.
11. Report
11.1 Report the test objective, the results, and the conclusions. The following additional information is recommended:
11.1.1 The purpose of the test and the nature of the treatment studied;
11.1.2 Full Identification of the Samples—Origin, method of preparation, quantity, shape, storage prior to testing, serving size,
temperature. (Sample information should communicate that all storage handling, and preparation was done in such a way as to
yield samples that differ only due to the variable of interest, if at all);
11.1.3 The number of assessors, the number of correct selections, and the result of the statistical evaluation;
11.1.4 Assessors—Age, gender, experience in sensory testing, with the product, with the samples in the test;
11.1.5 Any information and any specific instructions given the assessor in connection with the test;
11.1.6 The test environment: use of booths, simultaneous or sequential presentation, light conditions, whether the identity of the
samples was disclosed after the test and the manner in which it was done; and
11.1.7 The location and date of the test and the name of the panel leader.
12. Precision and Bias
12.1 Because results of sensory difference tests are functions of individual sensitivities, a general statement regarding the
precision of results that is applicable to all populations of assessors cannot be made. However, adherence to the recommendations
stated in this standard should increase the reproducibility of results and minimize bias.
13. Keywords
13.1 difference testing; discrimination test; sensory analysis; similarity testing; triangle test
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ANNEXANNEXES
(Mandatory Information)
A1. NUMBER OF ASSESSORS AND CORRECT RESPONSES NEEDED FOR A TRIANGLE TEST
TABLE A1.1 Number of Assessors Needed for a Triangle Test (9)
NOTE 1—Entri
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