ASTM E2139-05(2018)

Standard Test Method for Same-Different Test

SIGNIFICANCE AND USE
5.1 This overall difference test method is used when the test objective is to determine whether a sensory difference exists or does not exist between two samples. It is also known as the simple difference test.  
5.2 The test is appropriate in situations where samples have extreme intensities, give rapid sensory fatigue, have long lingering flavors, or cannot be consumed in large quantities, or a combination thereof.  
5.3 The test is also appropriate for situations where the stimulus sites are limited to two (for example, two hands, each side of the face, two ears).  
5.4 The test provides a measure of the bias where judges perceive two same products to be different.  
5.5 The test has the advantage of being a simple and intuitive task.
SCOPE
1.1 This test method describes a procedure for comparing two products.  
1.2 This test method does not describe the Thurstonian modeling approach to this test.  
1.3 This test method is sometimes referred to as the simple-difference test.  
1.4 A same-different test determines whether two products are perceived to be the same or different overall.  
1.5 The procedure of the test described in this test method consists of presenting a single pair of samples to each assessor. The presentation of multiple pairs would require different statistical treatment and it is outside of the scope of this test method.  
1.6 This test method is not attribute-specific, unlike the directional difference test.  
1.7 This test method is not intended to determine the magnitude of the difference; however, statistical methods may be used to estimate the size of the difference.  
1.8 This test method may be chosen over the triangle or duo-trio tests where sensory fatigue or carry-over are a concern, or where a simpler task is needed.  
1.9 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.10 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: 31-Jul-2018
• ICS: 03.100.50 - Production. Production management
• Technical Committee: E18 - Sensory Evaluation
• Drafting Committee: E18.04 - Test Methods

Relations

• Replaces: ASTM E2139-05(2011) - Standard Test Method for Same-Different Test
• Effective Date: 01-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 E2139-05(2018): Standard Test Method for Same-Different Test is an internationally recognized sensory evaluation standard issued by ASTM International. This method, sometimes referred to as the "simple-difference test," is designed to determine whether a perceptible sensory difference exists between two products. It is particularly valuable when assessing products that present challenges such as extreme intensities, rapid sensory fatigue, lingering flavors, or limited quantities for testing.

The Same-Different Test is a practical, versatile tool in sensory science, supporting industries that require reliable detection of sensory differences or confirmation that two samples are sensorially similar. The method is in compliance with international standardization principles established by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

Key Topics

• Purpose and Application: The method is used to detect the presence or absence of a sensory difference between two samples, not to quantify the degree or source of that difference.
• Test Procedure: Each assessor receives a single pair of samples and is asked to evaluate whether the samples are the same or different, making the task simple and intuitive.
• Appropriate Use Cases:
  • Useful where samples cause sensory fatigue or carry-over effects
  • Suitable when product consumption must be limited
  • Effective in situations with only two stimulus sites (e.g., hands, sides of the face)
• Statistical Considerations: The test assesses overall difference, not attribute-specific characteristics. Statistical analysis (often Fisher’s Exact Test) is used to determine whether the number of "different" responses between sample pairs is significant.
• Advantages:
  • Straightforward protocol increases compliance and reliability among assessors
  • Reduces sensory fatigue compared to other difference tests (e.g., triangle or duo-trio tests)
  • Allows for estimation of test sensitivity and sample size to achieve desired risk levels (Type I and II errors)
• Practical Details: Assessors do not require in-depth product attribute training but should be familiar with test mechanics. The test can be conducted efficiently with appropriate precautions for eliminating sample bias and ensuring unbiased, representative populations.

Applications

The ASTM E2139 Same-Different Test is widely used in:

• Food and Beverage Quality Control: Identifying whether product reformulations or ingredient substitutions result in perceptible differences.
• Personal Care and Consumer Goods: Comparing sensory attributes of lotions, fragrances, or cleaning products for equivalency or differentiation.
• Pharmaceuticals: Ensuring consistency in flavor, odor, or texture between production batches.
• Product Development: Determining the impact of new formulations or process changes before proceeding to consumer preference testing.
• Sensory Panel Qualification: Verifying the capacity to detect differences for quality assurance or regulatory compliance.

This test method is especially preferred when sensory fatigue could limit the reliability of more complex difference testing approaches, or when sample quantities are limited.

Related Standards

Several standards and guidelines complement or reference ASTM E2139, including:

• 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
• ISO 5495: Sensory Analysis – Methodology – Paired Comparison
• ASTM Manual 26: Sensory Testing Methods
• STP 758: Guidelines for the Selection and Training of Sensory Panel Members
• STP 913: Guidelines for Physical Requirements for Sensory Evaluation Laboratories

These standards provide additional methodological guidance, definitions, and protocols for conducting robust sensory testing and data analysis.

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Keywords: sensory difference test, ASTM E2139, same-different test, simple-difference test, sensory evaluation standard, food testing, product comparison, Fisher’s Exact Test, sensory panel, product development, sensory fatigue, quality control.

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: E2139 − 05 (Reapproved 2018)
Standard Test Method for
Same-Different Test
This standard is issued under the fixed designation E2139; 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 2. Referenced Documents
1.1 This test method describes a procedure for comparing 2.1 ASTM Standards:
two products. E253Terminology Relating to Sensory Evaluation of Mate-
rials and Products
1.2 This test method does not describe the Thurstonian
E456Terminology Relating to Quality and Statistics
modeling approach to this test.
E1871GuideforServingProtocolforSensoryEvaluationof
1.3 This test method is sometimes referred to as the simple-
Foods and Beverages
difference test. 2
2.2 ASTM Publications:
1.4 A same-different test determines whether two products
Manual 26Sensory Testing Methods, 2nd Edition
are perceived to be the same or different overall. STP 758Guidelines for the Selection and Training of Sen-
sory Panel Members
1.5 The procedure of the test described in this test method
STP 913Guidelines for Physical Requirements for Sensory
consistsofpresentingasinglepairofsamplestoeachassessor.
Evaluation Laboratories
The presentation of multiple pairs would require different
2.3 ISO Standard:
statistical treatment and it is outside of the scope of this test
ISO 5495Sensory Analysis—Methodology—Paired Com-
method.
parison
1.6 This test method is not attribute-specific, unlike the
directional difference test.
3. Terminology
1.7 This test method is not intended to determine the
3.1 For definition of terms relating to sensory analysis, see
magnitude of the difference; however, statistical methods may
Terminology E253, and for terms relating to statistics, see
be used to estimate the size of the difference.
Terminology E456.
1.8 This test method may be chosen over the triangle or
3.2 Definitions of Terms Specific to This Standard:
duo-trio tests where sensory fatigue or carry-over are a
3.2.1 α (alpha) risk—probability of concluding that a per-
concern, or where a simpler task is needed.
ceptible difference exists when, in reality, one does not (also
1.9 This standard may involve hazardous materials, known as Type I Error or significance level).
operations, and equipment. This standard does not purport to
3.2.2 β (beta) risk—probability of concluding that no per-
address all of the safety concerns, if any, associated with its
ceptible difference exists when, in reality, one does (also
use. It is the responsibility of the user of this standard to
known as Type II Error).
establish appropriate safety, health, and environmental prac-
3.2.3 chi-square test—statistical test used to test hypotheses
tices and determine the applicability of regulatory limitations
on frequency counts and proportions.
prior to use.
3.2.4 ∆ (delta)—test sensitivity parameter established prior
1.10 This international standard was developed in accor-
to testing and used along with the selected values of α, β, and
dance with internationally recognized principles on standard-
an estimated value of p to determine the number of assessors
ization established in the Decision on Principles for the
needed in a study. Delta (∆) is the minimum difference in
Development of International Standards, Guides and Recom-
proportions that the researcher wants to detect, where the
mendations issued by the World Trade Organization Technical
difference is ∆ = p − p . ∆ is not a standard measure of
2 1
Barriers to Trade (TBT) Committee.
1 2
ThistestmethodisunderthejurisdictionofASTMCommitteeE18onSensory For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Evaluation and is the direct responsibility of Subcommittee E18.04 on Fundamen- contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
tals of Sensory. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved Aug. 1, 2018. Published August 2018. Originally the ASTM website.
approved in 2005. Last previous edition approved in 2011 as E2139–05 (2011). Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
DOI: 10.1520/E2139-05R18. 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
E2139 − 05 (2018)
sensory difference. The same value of ∆ may correspond to 5.3 The test is also appropriate for situations where the
different sensory differences for different values of p (see 9.5 stimulussitesarelimitedtotwo(forexample,twohands,each
for an example). side of the face, two ears).
3.2.5 Fisher’s Exact Test (FET)—statisticaltestoftheequal-
5.4 The test provides a measure of the bias where judges
ity of two independent binomial proportions. perceive two same products to be different.
3.2.6 p —proportion of assessors in the population who
5.5 The test has the advantage of being a simple and
would respond different to the matched sample pair. Based on intuitive task.
experiencewithusingthesame-differenttestandpossiblywith
the same type of products, the user may have a priori 6. Apparatus
knowledge about the value of p .
6.1 Carry out the test under conditions that prevent contact
3.2.7 p —proportion of assessors in the population who
between assessors until the evaluations have been completed,
would respond different to the unmatched sample pair. for example, booths that comply with STP 913.
3.2.8 power 1-β (beta) risk—probability of concluding that
6.2 For food and beverage tests, sample preparation and
a perceptible difference exists when, in reality, one of size ∆
serving sizes should comply with Practice E1871, or see Refs
does.
(1) or (2).
3.2.9 product—material to be evaluated.
7. Definition of Hypotheses
3.2.10 sample—unit of product prepared, presented, and
7.1 This test can be characterized by a two-by-two table of
evaluated in the test.
probabilities according to the sample pair that the assessors in
3.2.11 sensitivity—termusedtosummarizetheperformance
the population would receive and their responses, as follows:
characteristics of this test. The sensitivity of the test is defined
Assessor Would Receive
by the four values selected for α, β, p , and ∆.
Matched Pair Unmatched Pair
(AA or BB) (AB or BA)
Assessor’s Same: 1 − p 1− p
1 2
4. Summary of Test Method
Response
Different: p p =(= p + ∆)
1 2 1
Total: 1 1
4.1 Clearly define the test objective in writing.
where p and p are the probabilities of responding different
1 2
4.2 Choosethenumberofassessorsbasedonthesensitivity
for those who would receive the matched pairs and the
desired for the test. The sensitivity of the test is in part related
unmatched pairs, respectively.
to two competing risks: the risk of declaring a difference when
7.2 To determine whether the samples are perceptibly dif-
there is none (that is, α-risk), and the risk of not declaring a
ferent with a given sensitivity, the following one-sided statis-
differencewhenthereisone(thatis, β-risk).Acceptablevalues
tical hypothesis is tested:
of α and β vary depending on the test objective. The values
should be agreed upon by all parties affected by the results of
H : p = p
o 1 2
H : p < p
the test. a 1 2
7.3 The hypothesis test can be expressed in terms of the
4.3 The two products of interest (A and B) are selected.
minimumdetectabledifference ∆(H : ∆=0versus H : ∆>0).
o a
Assessors are presented with one of four possible pairs of
Delta (∆) will equal 0 and p will equal p if there is no
1 2
samples: A/A, B/B, A/B, and B/A. The total number of same
detectable difference between the samples. This test addresses
pairs(A/AandB/B)usuallyequalsthetotalnumberofdifferent
whether or not ∆ is greater than 0. Thus, the hypothesis is
pairs (A/B and B/A). The assessor’s task is to categorize the
one-sided because it is not of interest in this test to consider
given pair of samples as same or different.
that responding different to the matched pair could be more
4.4 The data are summarized in a two-by-two table where
likely than responding different to the unmatched pair.
the columns show the type of pair received (same or different)
and the rows show the assessor’s response (same or different).
8. Assessors
A Fisher’s Exact Test (FET) is used to determine whether the
8.1 Allassessorsmustbefamiliarwiththemechanicsofthe
samplesareperceptiblydifferent.Otherstatisticalmethodsthat
same-different test (the format, the task, and the procedure of
approximate the FET can sometimes be used.
evaluation).Greatertestsensitivity,ifneeded,maybeachieved
through selection of assessors who demonstrate above average
5. Significance and Use
individual sensitivity (see STP 758).
5.1 Thisoveralldifferencetestmethodisusedwhenthetest
8.2 In order to perform this test, assessors do not require
objectiveistodeterminewhetherasensorydifferenceexistsor
special sensory training on the samples in question. For
does not exist between two samples. It is also known as the
example, they do not need to be able to recognize any specific
simple difference test.
attribute.
5.2 The test is appropriate in situations where samples have
extreme intensities, give rapid sensory fatigue, have long
lingering flavors, or cannot be consumed in large quantities, or
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
a combination thereof. this standard.
E2139 − 05 (2018)
8.3 The assessors must be sampled from a homogeneous 0.70−0.50=0.20and β=0.10or90%power.Thenumberof
populationthatiswell-defined.Thepopulationmustbechosen assessors needed in this case is 224 (Table A1.1).
onthebasisofthetestobjective.Definingcharacteristicsofthe
population can be, for example, training level, gender, experi- 10. Procedure
ence with the product, and so forth.
10.1 Determine the number of assessors needed for the test
as well as the population that they should represent (for
9. Number of Assessors
example, assessors selected for a specific sensory sensitivity).
9.1 Choose all the sensitivity parameters that are needed to
10.2 It is critical to the validity of the test that assessors
choose the number of assessors for the test. Choose the α-risk
cannot identify the samples from the way in which they are
andthe β-risk.Basedonexperience,choosetheexpectedvalue
presented.Oneshouldavoidanysubtledifferencesintempera-
for p . Choose ∆, p − p , the minimum difference in propor-
1 2 1
ture or appearance, especially color, caused by factors such as
tions that the researcher wants to detect. The most commonly
the time sequence of preparation. It may be possible to mask
used values for α-risk, β-risk, p and ∆ are α = 0.05, β = 0.20,
color differences using light filters, subdued illumination or
p = 0.3, and ∆ = 0.3. These values can be adjusted on a
colored vessels. Prepare samples out of sight and in an
case-by-case basis to reflect the sensitivity desired versus the
identical manner: same apparatus, same vessels, same quanti-
number of assessors.
ties of product (see Practice E1871). The samples may be
9.2 Having defined the required sensitivity (α-risk, β-risk,
prepared in advance; however, this may not be possible for all
p , and ∆), determine the corresponding sample size from
types of products. It is essential that the samples cannot be
Table A1.1 (see Ref (3)). This is done by first finding the
recognized from the way they are presented.
section of the table with a p value corresponding to the
10.3 Prepare serving order worksheet and ballot in advance
proportion of assessors in the population who would respond
ofthetesttoensureabalancedorderofsamplepresentationof
different to the matched sample pair. Second, locate the total
the two products, A and B. One of four possible pairs (A/A,
sample size from the intersection of the desired α, p (or ∆),
B/B,A/B,andB/A)isassignedtoeachassessor.Makesurethis
and β values. In the case of the most commonly used values
assignment is done randomly. Design the test so that the
listedin9.1,TableA1.1indicatesthat84assessorsareneeded.
numberof samepairsequalsthenumberof differentpairs.The
Thesamplesize nisbasedonthenumberofsameanddifferent
presentation order of the different pairs should be balanced as
samples being equal. The sample sizes listed are the total
much as possible. Serving order worksheets should also
sample size rounded up to the nearest number evenly divisible
include the identification of the samples for each set.
by4sincetherearefourpossiblecombinationsofthesamples.
Todeterminethenumberofsameanddifferentpairstoprepare,
10.4 Prepare the response ballots in a way consistent with
divide n by two.
the product you are evaluating. For example, in a taste test,
give the following instructions: (1) you will receive two
9.3 If the user has no prior experience with the same-
samples. They may be the same or different; (2) evaluate the
differenttestandhasnospecificexpectationforthevalueof p ,
samples from left to right; and (3) determine whether they are
thentwooptionsareavailable.Eitheruse p =0.3andproceed
the same or different.
as indicated in 9.2, or use the last section of Table A1.1. This
10.4.1 Theresearchercanchoosetoaddaninstructiontothe
sectiongivessamplesizesthatarethelargestrequired,given α,
ballot indicating whether the assessor may re-evaluate the
β, and ∆, regardless of p .
samples or not.
9.4 Ofteninpractice,thenumberofassessorsisdetermined
10.4.2 The ballot should also identify the assessor and date
by practical conditions (for example, duration of the
of test, as well as a ballot number that must be related to the
experiment,numberofavailableassessors,quantityofproduct,
sample set identification on the worksheet.
and so forth). However, increasing the number of assessors
10.4.3 A section soliciting comments may be included
increases the likelihood of detecting small differences. Thus,
following the initial forced-choice question.
one should expect to use larger numbers of assessors when
10.4.4 The example of a ballot is provided in Fig. X2.2.
trying to demonstrate that products are similar compared to
when one is trying to demonstrate that they are different.
10.5 When possible, present both samples at the same time,
9.4.1 When the number of assessors is fixed, the power of
along with the response ballot. In some instances, the samples
the test (1-β) may be calculated by establishing a value for p ,
may be presented sequentially if required by the type of
defining the required sensitivity for α-risk and the ∆, locating
productorthewaytheyneedtobepresented,orboth.Thismay
the number of assessors nearest the fixed amount, and then
be the case, for example, for the evaluation of a fragrance in a
following up the column to the listed β-risk.
room where the assessor must change rooms to evaluate the
9.5 If a researcher wants to be 90% certain of detecting second sample.
response proportions of p = 60 % versus the expected
10.6 Collect all ballots and tabulate results for analysis.
p =40% with an α-risk of 5%, then ∆ = 0.60 − 0.40 = 0.20
and β = 0.10 or 90% power. The number of assessors needed
11. Analysis and Interpretation of Results
in this case is 232 (Table A1.1). If a researcher wants to be
90% certain of detecting response proportions of p =70% 11.1 The data from the test is summarized in a two-by-two
versus the expected p =50% with an α-risk of 5%, then ∆ = table, as illustrated in the table below.
E2139 − 05 (2018)
TABLE 1 Critical Values for a One Sided, 1 Degree of Freedom χ
Assessor Received
Test
Matched Pair Unmatched
(AA or BB) Pair Total
A
Critical Value (one sided 1df
α Level
(AB or BA)
χ )
Assessor’s Same: 17 9 26
0.01 5.41
Response Different: 13 21 34
0.05 2.71
Total: 30 30 60
0.1 1.64
11.1.1 Before computing any test statistic, determine if the 0.2 0.708
0.3 0.275
number of different responses from those who received the
0.4 0.0642
unmatched pair is less than or equal to the number of different
A 2
A one sided value is obtained by using the χ value corresponding to twice the
responses from those who received the matched pair. If this is
desired a level.
the case, conclude that the hypothesis of no difference cannot
be rejected. If this is not the case, the computation of a test
statistic is needed to determine whether the samples are
perceptibly different or not.
12.1.1 The purpose of the test and the nature of the
11.2 Analyze the data using a Fisher’s Exact Test (4, 5, 6).
treatment studied;
TheFETiswidelyavailableinindustrystandardsoftware.See
12.1.2 Full identification of the samples: origin, method of
computation examples in X1.5.2 and X2.5.2.
preparation, quantity, shape, storage prior to testing, serving
11.3 Other statistical tests can also be used as an approxi-
size, and temperature. (Sample information should communi-
mation to the FET, provided the data table is not sparse. A
cate that all storage, handling, and preparation was done in
sparse table is defined as one that has at least one expected
suchawayastoyieldsamplesthatdifferedonlyinthevariable
frequency less than 5. The expected frequency in row i and
of interest);
column j is computed as:
12.1.3 Thenumberofassessors,thenumberofselectionsof
~Row i Total!~Column j Total!
each sample, and the result of the statistical analysis;
E 5 (1)
ij
GrandTotal
~ !
12.1.4 Relevant assessor information such as age, gender,
experience in sensory testing, and experience with the product
11.3.1 For example, the expected frequency for Row 1:
andtestsamples.Providealldetailsnecessarytoclearlydefine
Column 1 (that is, same response on a matched pair) is:
the population represented by the assessors;
26 30
~ !~ !
12.1.5 Anyinformationorinstructionsgiventotheassessor
E 5 513 (2)
in connection with the test;
11.4 Available tests that approximate the FET include the
12.1.6 Thetestenvironment:useofbooths,simultaneousor
one-tailed continuity corrected Chi-square (χ ) (7), the one-
sequential presentation, environmental conditions, whether the
tailed non-continuity corrected Chi-square (χ ) (8) and the
identity of samples was disclosed after the test and the manner
z-test (9).
in which this was done; and
11.4.1 In the case of either Chi-square test, compare the
12.1.7 The location and date of the test and name of the
calculated statistic to the critical value of a χ distribution with
panel leader.
onedegreeoffreedomandan αleveloftwicethedesiredlevel.
The critical values for a number of α levels are given in Table
13. Precision and Bias
1. For example, the critical value for a 5% α level is 2.71.
13.1 Because results of this test are a function of individual
11.4.2 Computation examples of the one-tailed continuity,
sensitivities, a general statement regarding the precision of
corrected Chi-square are given in X1.5.3 and X2.5.3.
results that is applicable to all populations of assessors cannot
11.4.3 Inthecaseofa z-test,comparethecalculatedstatistic
be made. However, adherence to the recommendations in this
to the one-tailed critical value of the z distribution for the
test method should increase the reproducibility of results and
chosen α level.
minimize bias.
12. Report
14. Keywords
12.1 Report the test objective, the results, the conclusions,
and the population to which they can be generalized. The 14.1 differencetest;minimizecarry-over;minimizesensory
following additional information is recommended: fatigue; sensory test for difference; two-sample sensory test
E2139 − 05 (2018)
ANNEX
(Mandatory Information)
A1. NUMBER OF ASSESSORS REQUIRED FOR THE SAME-DIFFERENT TEST
A1.1 See Table A1.1.
E2139 − 05 (2018)
TABLE A1.1 Number of Assessors Required for Same-Different Test Based on Fishers Exact Test (One-Tailed) (see Ref 3)
NOTE 1—Please note that this table is divided into sections based upon the value of p . The sample size specified for ∆ in the table will apply only
to that p;if p changes, a different sample size may be needed even if the value of ∆ remains the same.
1 1
NOTE 2—First, select the appropriate value for p and then find the section of the table that corresponds to it. If you do not know your actual p it is
1 1
proposed that a value of p =0.3 is a reasonable generic starting point.Alternatively, you can use the last section of this table which gives sample sizes
that are the largest required given α, β, and ∆.
NOTE 3—The values recorded in this table have been rounded to the nearest whole number evenly divisible by four to allow for equal presentation
of all possible paired combinations of the same and different samples.
NOTE 4—The values in this table were determined by calculating the appropriate N divisible by 4 that is at least equal to the power (1-β) listed.
p =0.1 β
α p ∆ 0.5 0.4 0.3 0.2 0.1 0.05 0.01
0.4 0.2 0.1 32 44 60 88 168 224 364
0.40.3 0.2 162028365268 124
0.40.4 0.3 121616243240 60
0.4 0.5 0.4 8 12 12 16 20 28 40
0.40.6 0.5 8 812121620 28
0.4 0.7 0.6 8888 12 16 20
0.4 0.8 0.7 4888 12 12 16
0.4 0.9 0.8 448888 12
0.3 0.2 0.1 52 68 88 136 200 276 436
0.30.3 0.2 162440486888 144
0.30.4 0.3 121620284048 72
0.3 0.5 0.4 8 12 12 16 28 32 48
0.30.6 0.5 8 812122024 36
0.3 0.7 0.6 8888 12 20 24
0.3 0.8 0.7 4888 12 12 20
0.3 0.9 0.8 448888 12
0.2 0.2 0.1 72 96 132 180 260 348 536
0.20.3 0.2 2840486088 112 172
0.20.4 0.3 202028324860 92
0.20.5 0.4 161620243240 56
0.20.6 0.5 121216162028 40
0.20.7 0.6 121212121620 28
0.20.8 0.7 4 812121216 20
0.2 0.9 0.8 4488 12 12 16
0.1 0.2 0.1 116 156 200 264 368 464 684
0.1 0.3 0.2 44 52 68 88 116 152 216
0.10.4 0.3 243240486476 112
0.10.5 0.4 162024324048 68
0.10.6 0.5 121620243236 48
0.10.7 0.6 121216162028 36
0.10.8 0.7 8 812161620 28
0.1 0.9 0.8 8888 12 16 20
0.05 0.2 0.1 176 216 272 348 464 576 820
0.05 0.3 0.2 64 76 92 112 148 184 256
0.05 0.4 0.3 36 40 48 60 80 96 132
0.05 0.5 0.4 24 28 32 40 52 60 84
0.05 0.6 0.5 20 20 24 28 36 40 56
0.05 0.7 0.6 12 16 20 20 24 32 40
0.05 0.8 0.7 12 12 12 16 20 24 32
0.05 0.9 0.8 12 12 12 12 16 20 24
0.01 0.2 0.1 312 372 444 540 688 824 1116
0.01 0.3 0.2 104 120 144 172 216 260 344
0.01 0.4 0.3 56 68 76 92 112 136 176
0.01 0.5 0.4 36 40 48 60 72 84 112
0.01 0.6 0.5 28 28 36 40 48 60 76
0.01 0.7 0.6 20 24 28 32 36 44 56
0.01 0.8 0.7 16 20 20 24 28 32 40
0.01 0.9 0.8 12 12 16 20 20 24 32
p =0.2 β
α p ∆ 0.5 0.4 0.3 0.2 0.1 0.05 0.01
0.
...