SIST EN ISO 10399:2010
(Main)Sensory analysis - Methodology - Duo-trio test (ISO 10399:2004)
Sensory analysis - Methodology - Duo-trio test (ISO 10399:2004)
This International Standard describes a procedure for determining whether a perceptible sensory difference or similarity exists between samples of two products. The method is a forced-choice procedure. The method is applicable whether a difference exists in a single sensory attribute or in several attributes. The method is statistically less efficient than the triangle test (described in ISO 4120) but is easier to perform by the assessors. The method is applicable even when the nature of the difference is unknown [i.e. it determines neither the size nor the direction of difference between samples, nor is there any indication of the attribute(s) responsible for he difference]. The method is applicable only if the products are fairly homogeneous. he method is effective for
a) determining that
- ther a perceptible difference results (duo-trio testing for difference), or
- a perceptible difference does not result (duo-trio testing for similarity) when, for example, a change is made in ingredients, processing, packaging, handling or storage;
b) or for selecting, training and monitoring assessors.
Two forms of the method are described:
- the constant-reference technique, used when one product is familiar to the assessors (e.g. a sample from regular production), and
- the balanced-reference technique, used when one product is not more familiar than the other.
Sensorische Analyse - Prüfverfahren - Duo-Trio-Prüfung (ISO 10399:2004)
Diese Internationale Norm beschreibt ein Verfahren zur Feststellung, ob zwischen den Proben von zwei Prüfmaterialien ein wahrnehmbarer sensorischer Unterschied oder Ähnlichkeit vorhanden ist. Bei dem Verfahren wird nach dem „Forced-Choice“-Prinzip vorgegangen. Das Verfahren ist unabhängig davon anwendbar, ob der Unterschied nur bei einem einzelnen sensorischen Merkmal oder auch bei mehreren Merkmalen vorliegt.
Das Verfahren ist statistisch weniger aussagekräftig als die (in ISO 4120 beschriebene) Dreiecksprüfung, jedoch von den Prüfpersonen leichter durchzuführen.
Das Verfahren ist auch anwendbar, wenn die Art des Unterschiedes unbekannt ist [das heißt, es bestimmt weder Größe noch Richtung eines Unterschiedes zwischen den Proben, noch liefert es Hinweise auf Merkmale, die für den Unterschied verantwortlich sind]. Das Verfahren ist nur anwendbar, wenn die Prüfmaterialien homogen sind.
Das Verfahren eignet sich besonders für:
a) die Untersuchung daraufhin:
ob ein wahrnehmbarer Unterschied (Duo-Trio-Prüfung auf Unterschied) resultiert, oder
ob kein wahrnehmbarer Unterschied (Duo-Trio-Prüfung auf Ähnlichkeit) resultiert, wenn zum Beispiel eine Änderung von Zutaten, Verarbeitung, Verpackung, Behandlung oder Lagerung vorgenommen wurde;
b) oder für die Auswahl, Schulung und Leistungsüberprüfung von Prüfpersonen.
Zwei Formen des Verfahrens werden beschrieben:
das Verfahren mit konstanter Referenz, das angewendet wird, wenn den Prüfpersonen eines der Prüfmateriale bekannt ist (z. B. eine Probe aus der normalen Produktion), und
das Verfahren mit balancierter Referenz, das angewendet wird, wenn keines der beiden Prüfmaterialien bekannter als das andere ist.
Analyse sensorielle - Méthodologie - Essai duo-trio (ISO 10399:2004)
L'ISO 10399:2004 décrit un mode opératoire permettant de déterminer s'il existe une différence sensorielle perceptible ou une similitude entre les échantillons de deux produits. La méthode est une procédure à choix forcé. Elle s'applique s'il existe une différence pour une seule propriété sensorielle ou pour plusieurs.
La méthode est statistiquement moins efficace que l'essai triangulaire, mais elle est plus facile à réaliser par les sujets.
La méthode est applicable même lorsque la nature de la différence est inconnue, ce qui signifie qu'elle ne détermine ni la taille ni le sens de la différence entre des échantillons et qu'elle ne donne pas non plus d'indications sur la ou les propriétés à l'origine de cette différence. La présente méthode n'est applicable que si les produits sont relativement homogènes.
La méthode est efficace pour a) déterminer qu'il existe une différence perceptible (essai duo-trio de différence), ou qu'il n'existe pas de différence perceptible (essai duo-trio de similitude), quand, par exemple, des modifications sont apportées aux ingrédients, à la transformation, à l'emballage, aux opérations de manutention ou de stockage; ou b) pour sélectionner, entraîner et contrôler les sujets.
Deux formes de cette méthode sont décrites: la technique de la référence constante, utilisée lorsque les sujets connaissent bien un produit (un échantillon de fabrication courante par exemple), et la technique de la référence équilibrée, utilisée quand aucun des produits n'est pas plus connu que l'autre.
Senzorična analiza - Metodologija - Preskus "duo-trio" (ISO 10399:2004)
Ta mednarodni standard določa postopek za določevanje ali obstaja zaznavna senzorična razlika oziroma podobnost med vzorci dveh proizvodov. Ta metoda je postopek prisiljenega odločanja. Metoda velja, če obstoja razlika v eni senzorični lastnosti ali več lastnosti. Metoda je statistično manj učinkovita kot trikotniški preskus (opisan v ISO 4120), vendar ga ocenjevalci lažje izvedejo. Metoda velja tudi takrat, kadar je značilnost razlike neznana [t.j. ne določi niti velikosti niti ne smeri razlike med vzorci, niti ni noben atribut, odgovoren za nastale razlike, nakazan]. Metoda velja samo, če so proizvodi precej homogeni. Metoda je učinkovita kadar
a) se določa
- da obstajajo zaznavne razlike v rezultatih (duo-trio preskušanje za razlike) ali
- da ne pride do zaznavnih razlik (duo-trio preskušanje za podobnosti) kadar, na primer, se spremenijo sestavine, predelava, pakiranje, ravnanje ali skladiščenje;
b) se izbira, usposablja in nadzoruje ocenjevalce.
Opisani sta dve obliki metode:
- tehnika konstantne reference, ki se uporablja kadar je en proizvod že poznan ocenjevalcem (npr. vzorec iz običajne proizvodnje), in
- tehnika uravnotežene reference, ki se uporablja, kadar en proizvod ni bolj poznan kot drugi.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN ISO 10399:2010
01-september-2010
6HQ]RULþQDDQDOL]D0HWRGRORJLMD3UHVNXVGXRWULR ,62
Sensory analysis - Methodology - Duo-trio test (ISO 10399:2004)
Sensorische Analyse - Prüfverfahren - Duo-Trio-Prüfung (ISO 10399:2004)
Analyse sensorielle - Méthodologie - Essai duo-trio (ISO 10399:2004)
Ta slovenski standard je istoveten z: EN ISO 10399:2010
ICS:
67.240 6HQ]RULþQDDQDOL]D Sensory analysis
SIST EN ISO 10399:2010 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST EN ISO 10399:2010
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SIST EN ISO 10399:2010
EUROPEAN STANDARD
EN ISO 10399
NORME EUROPÉENNE
EUROPÄISCHE NORM
February 2010
ICS 67.240
English Version
Sensory analysis - Methodology - Duo-trio test (ISO
10399:2004)
Analyse sensorielle - Méthodologie - Essai duo-trio (ISO Sensorische Analyse - Prüfverfahren - Duo-Trio-Prüfung
10399:2004) (ISO 10399:2004)
This European Standard was approved by CEN on 31 January 2010.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the
official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2010 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 10399:2010: E
worldwide for CEN national Members.
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SIST EN ISO 10399:2010
EN ISO 10399:2010 (E)
Contents Page
Foreword .3
2
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SIST EN ISO 10399:2010
EN ISO 10399:2010 (E)
Foreword
The text of ISO 10399:2004 has been prepared by Technical Committee ISO/TC 34 “Food products” of the
International Organization for Standardization (ISO) and has been taken over as EN ISO 10399:2010.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by August 2010, and conflicting national standards shall be withdrawn at
the latest by August 2010.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.
Endorsement notice
The text of ISO 10399:2004 has been approved by CEN as a EN ISO 10399:2010 without any modification.
3
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SIST EN ISO 10399:2010
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SIST EN ISO 10399:2010
INTERNATIONAL ISO
STANDARD 10399
Second edition
2004-06-15
Sensory analysis — Methodology —
Duo-trio test
Analyse sensorielle — Méthodologie — Essai duo-trio
Reference number
ISO 10399:2004(E)
©
ISO 2004
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SIST EN ISO 10399:2010
ISO 10399:2004(E)
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ii © ISO 2004 – All rights reserved
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SIST EN ISO 10399:2010
ISO 10399:2004(E)
Contents Page
Foreword. iv
1 Scope. 1
2 Normative references . 1
3 Terms and definitions. 2
4 Principle . 2
5 General test conditions and requirements. 3
6 Assessors . 3
6.1 Qualification . 3
6.2 Number of assessors. 4
7 Procedure. 4
8 Analysis and interpretation of results . 5
8.1 When testing for a difference . 5
8.2 When testing for similarity. 5
9 Test report. 6
10 Precision and bias . 6
Annex A (normative) Tables. 7
Annex B (informative) Examples. 12
Bibliography . 19
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SIST EN ISO 10399:2010
ISO 10399:2004(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 10399 was prepared by Technical Committee ISO/TC 34, Food products, Subcommittee SC 12, Sensory
analysis.
This second edition cancels and replaces the first edition (ISO 10399:1991), which has been technically
revised.
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SIST EN ISO 10399:2010
INTERNATIONAL STANDARD ISO 10399:2004(E)
Sensory analysis — Methodology — Duo-trio test
1 Scope
This International Standard describes a procedure for determining whether a perceptible sensory difference or
similarity exists between samples of two products. The method is a forced-choice procedure. The method is
applicable whether a difference exists in a single sensory attribute or in several attributes.
The method is statistically less efficient than the triangle test (described in ISO 4120) but is easier to perform
by the assessors.
The method is applicable even when the nature of the difference is unknown [i.e. it determines neither the size
nor the direction of difference between samples, nor is there any indication of the attribute(s) responsible for
the difference]. The method is applicable only if the products are fairly homogeneous.
The method is effective for
a) determining that
either a perceptible difference results (duo-trio testing for difference), or
a perceptible difference does not result (duo-trio testing for similarity) when, for example, a change is
made in ingredients, processing, packaging, handling or storage;
b) or for selecting, training and monitoring assessors.
Two forms of the method are described:
the constant-reference technique, used when one product is familiar to the assessors (e.g. a sample from
regular production), and
the balanced-reference technique, used when one product is not more familiar than the other.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 5492:1992, Sensory analysis — Vocabulary
ISO 8589:1988, Sensory analysis — General guidance for the design of test rooms
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SIST EN ISO 10399:2010
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3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 5492 and the following apply.
3.1
alpha-risk
αααα-risk
probability of concluding that a perceptible difference exists when one does not
NOTE This is also known as Type I error, significance level or false positive rate.
3.2
beta-risk
ββββ-risk
probability of concluding that no perceptible difference exists when one does
NOTE This is also known as Type II error or false negative rate.
3.3
difference
situation in which samples can be distinguished based on their sensory properties
NOTE The proportion of assessments in which a perceptible difference is detected between the two products is given
the symbol p .
d
3.4
product
material to be evaluated
3.5
sample
unit of product prepared, presented and evaluated in the test
3.6
sensitivity
general term used to summarize the performance characteristics of the test
NOTE In statistical terms, the sensitivity of the test is defined by the values of α, β and p .
d
3.7
similarity
situation in which any perceptible differences between the samples are so small that the products can be used
interchangeably
3.8
triad
those three samples given to an assessor in the duo-trio test
NOTE In the duo-trio test, one sample is labelled as the reference, the other two are marked with different codes.
One of the coded samples is the same product as the reference; the other coded sample is the other product in the test.
4 Principle
The number of assessors is chosen based on the sensitivity desired for the test. (See 6.2 and the discussion
in A.3.)
Assessors receive a set of three samples (i.e. a triad), one sample of which is labelled as a reference and the
other two samples have different codes. The assessors are informed that one of the coded samples is the
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SIST EN ISO 10399:2010
ISO 10399:2004(E)
same as the reference and that one is different. Based on their training and the instructions given prior to the
test, the assessors report either which of the coded samples they believe to be same as the reference, or
which of the coded samples they believe to be different from the reference.
The number of correct responses is counted and the significance is determined by reference to a statistical
table.
5 General test conditions and requirements
5.1 Clearly define the test objective in writing.
5.2 Carry out the test under conditions that prevent communication among assessors until all the
evaluations have been completed using facilities and booths that comply with ISO 8589.
5.3 Prepare the samples out of sight of the assessors and in an identical manner (i.e. same apparatus,
same vessels, same quantity of product).
5.4 Assessors shall not be able to identify the samples from the way in which they are presented. For
example, in a taste test, avoid any differences in appearance. Mask any irrelevant colour differences using
light filters and/or subdued illumination.
5.5 Code the vessels containing the samples in a uniform manner, preferably using three-digit numbers,
chosen at random for each test. Each triad is composed of three samples, one labelled as the reference and
two labelled with different codes. Preferably, different codes should be used for each assessor during a
session. However, the same two codes may be used for all assessors within a test, provided that each code is
used only once per assessor during a test session (e.g., if several duo-trio tests on different products are
being conducted in the same session).
5.6 The quantity or volume served shall be identical for the three samples in each triad, just as that of all
the other samples in a series of tests on a given type of product. The quantity or volume to be evaluated may
be imposed. If it is not, the assessors should be told to take quantities or volumes that are always similar
whatever the sample.
5.7 The temperature of the three samples in each triad shall be identical, just as that of all the other
samples in a series of tests on a given type of product. It is preferable to present the samples at the
temperature at which the product is generally consumed.
5.8 The assessors shall be told whether or not they are to swallow the samples or whether they are free to
do as they please. In this latter case, they shall be requested to proceed in the same manner for all samples.
5.9 During the test sessions, avoid giving information about product identity, expected treatment effects, or
individual performance until all testing is completed.
6 Assessors
6.1 Qualification
All assessors should possess the same level of qualification, this level being chosen on the basis of the test
objective (see ISO 8586-1 and ISO 8586-2 for guidance). Experience and familiarity with the product may
improve the performance of an assessor and, therefore, may increase the likelihood of finding a significant
difference. Monitoring the performance of assessors over time may be useful for increased sensitivity.
All assessors shall be familiar with the mechanics of the duo-trio test (i.e. the format, task and evaluation
procedure).
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6.2 Number of assessors
Choose the number of assessors so as to obtain the sensitivity required for the test (see discussion in A.3).
Using large numbers of assessors increases the likelihood of detecting small differences between the
products. However, in practice, the number of assessors often is determined by material conditions (e.g.
duration of the experiment, number of available assessors, quantity of product). When testing for a difference,
typical numbers of assessors are between 32 and 36. When testing for no meaningful difference (i.e.
similarity), twice as many assessors (i.e. approximately 72) are needed for equivalent sensitivity.
Avoid replicate evaluations by the same assessor whenever possible. However, if replicate evaluations are
needed to produce a sufficient number of total evaluations, every effort should be made to have each
assessor perform the same number of replicate evaluations. For example, if only twelve assessors are
available, have each assessor evaluate three triads to obtain a total of 36 evaluations.
NOTE Treating three evaluations performed by twelve assessors as 36 independent evaluations is not valid when
testing for similarity using Table A.2. However, the test for difference using Table A.1 is valid even when replicate
evaluations are performed (see [9] and [10]). Recent publications (see [7] and [8]) on replicated discrimination tests
suggest alternative approaches for analysing replicated evaluations in discrimination tests.
7 Procedure
7.1 If the product is familiar to the assessors (e.g. a control sample from the production line), use the
constant reference technique. If neither product is more familiar than the other, use the balanced-reference
technique
a) Constant-reference technique: Prepare worksheets and scoresheets (see B.2) in advance of the test so
as to utilize an equal number of the two possible sequences of two products, A and B:
A-REF AB A-REF BA
Distribute these at random in groups of two among the assessors (i.e. use each sequence once among
the first two assessors; use each sequence once again among the next two assessors, etc.) This will
minimize the imbalance that results if the total number of assessors is not an even number.
b) Balanced-reference technique: Prepare worksheets and scoresheets (see B.1) in advance of the test
so as to utilize an equal number of the four possible sequences of two products, A and B:
A-REF AB A-REF BA
B-REF AB B-REF BA
where the first two triads contain product A as the reference (i.e. A-REF) and the last two triads contain
product B as the reference (i.e. B-REF). Distribute these at random in groups of four among the
assessors (i.e. use each sequence once among the first group of four assessors; use each sequence
once again among the next group of four assessors, etc.). This will minimize the imbalance that results if
the total number of assessors is not a multiple of four.
7.2 Present the three samples of each triad simultaneously if possible, following the same spatial
arrangement for each assessor (e.g. on a line to be sampled always from left to right, in a triangular array).
Within the triad, assessors are generally allowed to make repeated evaluations of each sample as desired (if,
of course, the nature of the product allows for repeated evaluations).
7.3 Instruct the assessors to evaluate the reference sample first, then evaluate the two coded samples in
the order in which they were presented. Inform the assessors that one of the coded samples is the same as
the reference and that one is different from the reference. Instruct the assessors to indicate either which of the
two coded samples is the same as the reference, or which of the two coded samples is different from the
reference.
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NOTE When deciding whether to instruct the assessors to select the sample that is the same as the reference or to
select the sample that is different from the reference, consideration should be given to whether or not the panel routinely
uses other discrimination test methods. Many discrimination test methods like the triangle test, for example, focus on
identifying the “odd” or “different” sample in the test. Instructing the assessors to identify the “different” sample in one
method and to identify the “same” sample in another method may cause confusion and lead to higher levels of incorrect
responses.
7.4 Each scoresheet should provide for a single triad of samples. If an assessor is to carry out more than
one test in a session, collect the completed scoresheet and unused samples prior to serving the subsequent
triad. The assessor shall not go back to any of the previous samples or change the verdict on any previous
test.
7.5 Do not ask questions about preference, acceptance or degree of difference after the assessor has
made a selection. 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 ISO 6658. A comment section asking why the choice was made may be included for the
assessor’s remarks.
7.6 The duo-trio 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 and to indicate that the selection was only a guess in the comments section of the
scoresheet.
8 Analysis and interpretation of results
8.1 When testing for a difference
Use Table A.1 to analyse the data obtained from a duo-trio test. If the number of correct responses is greater
than or equal to the number given in Table A.1 (corresponding to the number of assessors and the α-risk level
chosen for the test), conclude that a perceptible difference exists between the samples (see B.1).
If desired, calculate a confidence interval on the proportion of the population that can distinguish the samples.
The method is described in B.3.
1)
8.2 When testing for similarity
Use Table A.2 to analyse the data obtained from a duo-trio test. If the number of correct responses is less
than or equal to the number given in Table A.2 (corresponding to the number of assessors, the β-risk level
and the value of p chosen for the test), conclude that no meaningful difference exists between the samples
d
(see B.2). If results will be compared from one test to another, then the same value of p should be chosen for
d
all tests.
If desired, calculate a confidence interval on the proportion of the population that can distinguish the samples.
The method is described in B.3.
1) In this International Standard, “similar” does not mean “identical”. Rather, “similar” means that the two products are
sufficiently alike to be used interchangeably. It is not possible to prove that two products are identical. However, it can be
demonstrated that any difference that does exist between two products is so small as to have no practical significance.
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9 Test report
Report the test objective, the results and the conclusions. The following additional information is
recommended:
the purpose of the test and the nature of the treatment studied;
full identification of the samples (i.e. 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;
the number of assessors, the number of correct responses and the result of the statistical evaluation
(including the values of α, β and p used for the test);
d
assessors: experience (in sensory testing, with the product, with the samples in the test), age and gender
(see ISO 8586-1 and ISO 8586-2 for guidance);
any information and any specific recommendations given to the assessors in connection with the test;
the test environment (i.e test facility used, simultaneous or sequential presentation, if the identity of
samples was disclosed after the test, if so, in what manner);
the location, date of the test and name of the panel leader.
10 Precision and bias
Because results of sensory discrimination tests are functions of individual sensitivities, a general statement
regarding the reproducibility of results that is applicable to all populations of assessors cannot be made.
Precision regarding a particular population of assessors increases as the size of the panel increases and also
with training and with exposure to the product.
As a forced-choice procedure is used, results obtained by this method are bias-free, provided that the
precautions in Clause 7 are fully observed.
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Annex A
(normative)
Tables
A.1 Values given in Table A.1 are the minimum number of correct responses required for significance at the
stated α level (i.e. column) for the corresponding number of assessors, n (i.e. row). Reject the assumption of
“no difference” if the number of correct responses is greater than or equal to the value in Table A.1.
Table A.1 — Minimum number of correct responses needed to conclude that a perceptible
difference exists based a duo-trio test
α α
n n
0,20 0,10 0,05 0,01 0,001 0,20 0,10 0,05 0,01 0,001
6 5 6 6 — — 26 16 17 18 20 22
7 6 6 7 7 — 27 17 18 19 20 22
8 6 7 7 8 — 28 17 18 19 21 23
9 7 7 8 9 — 29 18 19 20 22 24
10 7 8 9 10 10 30 18 20 20 22 24
11 8 9 9 10 11 32 19 21 22 24 26
12 8 9 10 11 12 36 22 23 24 26 28
13 9 10 10 12 13 40 24 25 26 28 31
14 10 10 11 12 13 44 26 27 28 31 33
15 10 11 12 13 14 48 28 29 31 33 36
16 11 12 12 14 15 52 30 32 33 35 38
17 11 12 13 14 16 56 32 34 35 38 40
18 12 13 13 15 16 60 34 36 37 40 43
19 12 13 14 15 17 64 36 38 40 42 45
20 13 14 15 16 18 68 38 40 42 45 48
21 13 14 15 17 18 72 41 42 44 47 50
22 13 14 15 17 19 76 43 45 46 49 52
23 15 16 16 18 20 80 45 47 48 51 55
24 15 16 17 19 20 84 47 49 51 54 57
25 16 17 18 19 21 88 49 51 53 56 59
NOTE 1 Values in the table are exact because they are based on the binomial distribution. For values of n not in the table, compute
approximate values for the missing entries based on the normal approximation to the binomial as follows:
minimum number of responses (x) = nearest whole number greater than
x = (nz/2) + n/4
where z varies with the significance level as follows: 0,84 for α = 0,20; 1,28 for α = 0,10; 1,64 for α = 0,05; 2,33 for α = 0,01; 3,09
for α = 0,001.
NOTE 2 Values of n < 24 are usually not recommended for a duo-trio test for a difference.
NOTE 3 Adapted from Reference [11].
A.2 Values given in Table A.2 are the maximum number of correct responses required for “similarity” at the
chosen levels of p , β and n. Accept the assumption of “no difference” at the 100(1–β) % level of confidence if
d
the number of correct responses is less than or equal to the value in Table A.2.
© ISO 2004 – All rights reserved 7
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SIST EN ISO 10399:2010
ISO 10399:2004(E)
Table A.2 — Maximum number of correct responses needed to conclude
that two samples are similar, based on a duo-trio test
p p
d d
n β n β
10 % 20 % 30 % 40 % 50 % 10 % 20 % 30 % 40 % 50 %
20
...
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