SIST EN ISO 4120:2007
(Main)Sensory analysis - Methodology - Triangle test (ISO 4120:2004)
Sensory analysis - Methodology - Triangle test (ISO 4120:2004)
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 more efficient than the duo-trio test (described in ISO 10399), but has limited use with products that exhibit strong carryover and/or lingering flavours. 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 (triangle testing for difference), or - a perceptible difference does not result (triangle 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.
Sensorische Analyse - Prüfverfahren - Dreiecksprüfung (ISO 4120:2004)
Diese Internationale Norm beschreibt ein Verfahren zur Feststellung, ob zwischen den Proben von zwei Prüf¬materialien ein wahrnehmbarer sensorischer Unterschied oder Ähnlichkeit vorhanden ist. Bei dem Verfahren wird nach dem Forced-Choice-Prinzip vorgegangen. Das Verfahren ist anwendbar, wenn der Unterschied nur bei einem einzelnen sensorischen Merkmal oder auch bei mehreren Merkmalen vorliegen kann.
Das Verfahren ist statistisch aussagekräftiger als die Duo-Trio-Prüfung, hat aber eine begrenzte Anwendung bei Prüfmaterialien, die starke überdeckende und/oder nachwirkende olfaktorische/gustatorische Eindrücke hinterlassen.
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 Merk¬male, 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 (Dreiecksprüfung auf Unterschied) resultiert, oder
ob kein wahrnehmbarer Unterschied (Dreiecksprüfung 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.
Analyse sensorielle - Méthodologie - Essai triangulaire (ISO 4120:2004)
L'ISO 4120:2004 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 plus efficace que l'essai duo-trio, mais est d'une utilisation limitée pour les produits présentant une forte rémanence et/ou des arômes persistants.
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 triangulaire de différence), ou qu'il n'existe pas de différence perceptible (essai triangulaire de similitude) quand, par exemple, des modifications sont apportées aux ingrédients, à la transformation, à l'emballage, aux opérations de manutention ou de stockage; b) ou pour sélectionner, entraîner et contrôler les sujets.
Senzorična analiza - Metodologija - Preskus "triangel" (ISO 4120:2004)
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN ISO 4120:2007
01-november-2007
6HQ]RULþQDDQDOL]D0HWRGRORJLMD3UHVNXVWULDQJHO ,62
Sensory analysis - Methodology - Triangle test (ISO 4120:2004)
Sensorische Analyse - Prüfverfahren - Dreiecksprüfung (ISO 4120:2004)
Analyse sensorielle - Méthodologie - Essai triangulaire (ISO 4120:2004)
Ta slovenski standard je istoveten z: EN ISO 4120:2007
ICS:
67.240 6HQ]RULþQDDQDOL]D Sensory analysis
SIST EN ISO 4120:2007 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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EUROPEAN STANDARD
EN ISO 4120
NORME EUROPÉENNE
EUROPÄISCHE NORM
July 2007
ICS 67.240
English Version
Sensory analysis - Methodology - Triangle test (ISO 4120:2004)
Analyse sensorielle - Méthodologie - Essai triangulaire (ISO Sensorische Analyse - Prüfverfahren - Dreiecksprüfung
4120:2004) (ISO 4120:2004)
This European Standard was approved by CEN on 12 July 2007.
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, 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: rue de Stassart, 36 B-1050 Brussels
© 2007 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 4120:2007: E
worldwide for CEN national Members.
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EN ISO 4120:2007 (E)
Foreword
The text of ISO 4120:2004 has been prepared by Technical Committee ISO/TC 34 "Agricultural
food products” of the International Organization for Standardization (ISO) and has been taken
over as EN ISO 4120:2007 by Technical Committee CEN/SS C01 "Food Products", the
secretariat of which is held by CMC.
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 January 2008, and conflicting national
standards shall be withdrawn at the latest by January 2008.
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, 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.
Endorsement notice
The text of ISO 4120:2004 has been approved by CEN as EN ISO 4120:2007 without any
modifications.
2
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INTERNATIONAL ISO
STANDARD 4120
Second edition
2004-06-15
Sensory analysis — Methodology —
Triangle test
Analyse sensorielle — Méthodologie — Essai triangulaire
Reference number
ISO 4120:2004(E)
©
ISO 2004
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ISO 4120:2004(E)
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ii © ISO 2004 – All rights reserved
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ISO 4120:2004(E)
Contents Page
Foreword. iv
1 Scope. 1
2 Normative references . 1
3 Terms and definitions. 1
4 Principle . 2
5 General test conditions and requirements. 3
6 Assessors . 3
6.1 Qualification . 3
6.2 Number of assessors. 3
7 Procedure. 4
8 Analysis and interpretation of results . 4
8.1 When testing for a difference . 4
8.2 When testing for similarity. 5
9 Test report. 5
10 Precision and bias . 5
Annex A (normative) Tables. 6
Annex B (informative) Examples. 10
Bibliography . 15
© ISO 2004 – All rights reserved iii
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ISO 4120:2004(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 4120 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 4120:1983), which has been technically revised.
iv © ISO 2004 – All rights reserved
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INTERNATIONAL STANDARD ISO 4120:2004(E)
Sensory analysis — Methodology — Triangle 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 more efficient than the duo-trio test (described in ISO 10399), but has limited use
with products that exhibit strong carryover and/or lingering flavours.
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 (triangle testing for difference), or
a perceptible difference does not result (triangle 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.
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
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
αα-risk
αα
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.
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ISO 4120:2004(E)
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 triangle test
NOTE In the triangle test, each sample is marked with a different code. Two of the samples are alike (i.e. from one
product) and one is different (i.e. from the other product).
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) and are informed that two of the samples are alike and
that one is different. The assessors report which sample they believe to be different, even if the selection is
based only on a guess.
The number of correct responses is counted and the significance is determined by reference to a statistical
table.
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ISO 4120:2004(E)
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 quantities 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, each with a different code.
Preferably, different codes should be used for each assessor during a session. However, the same three
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 triangle 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 the
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 triangle test (i.e. format, task and evaluation
procedure).
6.2 Number of assessors
Choose the number of assessors so as to obtain the sensitivity required for the test (see the 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 is often 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 24 and 30. When testing for no meaningful difference (i.e.
similarity), twice as many assessors (i.e. approximately 60) are needed for equivalent sensitivity.
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ISO 4120:2004(E)
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 ten assessors are available,
have each assessor evaluate three triads to obtain a total of 30 evaluations.
NOTE Treating three evaluations performed by ten assessors as 30 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 [6] and [7]) on replicated discrimination tests
suggest alternative approaches for analysing replicated evaluations in discrimination tests.
7 Procedure
7.1 Prepare worksheets and scoresheets (see B.1 and B.2) in advance of the test so as to utilize an equal
number of the six possible sequences of two products, A and B:
ABB AAB ABA
BAA BBA BAB
Distribute these at random in groups of six among the assessors (i.e. use each sequence once among the first
group of six assessors; use each sequence once again among the next group of six assessors, etc.). This will
minimize the imbalance that results if the total number of assessors is not a multiple of six.
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 triangle 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 samples in the order in which they were presented. Inform the
assessors that two of the samples are the same and that one is different. Each assessor should then indicate
which one of the three samples is different from the other two.
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 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 ISO 6658 for guidance.) A comment section asking why the choice was made may be
included for the assessor’s remarks.
7.6 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 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 triangle 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).
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ISO 4120:2004(E)
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 triangle 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 are to be compared from one test to another, then the same value of p should be chosen
d
for 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.
No conclusion should be drawn for maximum numbers of correct responses below n/3.
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 disclosed after the test and, 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 a function 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 their training and with exposure to the product.
Since a forced-choice procedure is used, results obtained by this method are bias-free, provided that the
precautions in Clause 7 are fully observed.
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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ISO 4120:2004(E)
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-risk 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 on a triangle 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 4 5 5 6 — 27 12 13 14 16 18
7 4 5 5 6 7 28 12 14 15 16 18
8 5 5 6 7 8 29 13 14 15 17 19
9 5 6 6 7 8 30 13 14 15 17 19
10 6 6 7 8 9
31 14 15 16 18 20
11 6 7 7 8 10 32 14 15 16 18 20
12 6 7 8 9 10 33 14 15 17 18 21
13 7 8 8 9 11 34 15 16 17 19 21
14 7 8 9 10 11 35 15 16 17 19 22
15 8 8 9 10 12
36 15 17 18 20 22
16 8 9 9 11 12 42 18 19 20 22 25
17 8 9 10 11 13 48 20 21 22 25 27
18 9 10 10 12 13 54 22 23 25 27 30
19 9 10 11 12 14 60 24 26 27 30 33
20 9 10 11 13 14 66 26 28 29 32 35
21 10 11 12 13 15 72 28 30 32 34 38
22 10 11 12 14 15 78 30 32 34 37 40
23 11 12 12 14 16 84 33 35 36 39 43
24 11 12 13 15 16 90 35 37 38 42 45
25 11 12 13 15 17 96 37 39 41 44 48
26 12 13 14 15 17 102 39 41 43 46 50
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=+(3n/ ) z 2n / 9
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 < 18 are usually not recommended for a triangle 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.
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ISO 4120:2004(E)
Table A.2 — Maximum number of correct responses needed to conclude that two samples
are similar, based on a triangle test
p p
d d
n β n β
10 % 20 % 30 % 40 % 50 % 10 % 20 % 30 % 40 % 50 %
18 0,001 0 1 2 3 5 66 0,001 14 18 22 26 31
0,01 2 3 4 5 6 0,01 16 20 25 29 34
0,05 3 4 5 6 8 0,05 19 23 28 32 37
0,10 4 5 6 7 8 0,10 20 25 29 33 38
0,20 4 6 7 8 9 0,20 22 26 31 35 40
24 0,001 2 3 4 6 8 72 0,001 15 20 24 29 34
0,01 3 5 6 8 9 0,01 18 23 28 32 38
0,05 5 6 8 9 11 0,05 21 26 30 35 40
0,10 6 7 9 10 12 0,10 22 27 32 37 42
0,20 7 8 10 11 13 0,20 24 29 34 39 44
30 0,001 3 5 7 9 11 78 0,001 17 22 27 32 38
0,01 5 7 9 11 13 0,01 20 25 30 36 41
0,05 7 9 11 13 15 0,05 23 28 33 39 44
0,10 8 10 11 14 16 0,10 25 30 35 40 46
0,20 9 11 13 15 17 0,20 27 32 37 42 48
36 0,001 5 7 9 11 14 84 0,001 19 24 30 35 41
0,01 7 9 11 14 16 0,01 22 28 33 39 45
0,05 9 11 13 16 18 0,05 25 31 36 42 48
0,10 10 12 14 17 19 0,10 27 32 38 44 49
0,20 11 13 16 18 21 0,20 29 34 40 46 51
42 0,001 6 9 11 14 17 90 0,001 21 27 32 38 45
0,01 9 11 14 17 20 0,01 24 30 36 42 48
0,05 11 13 16 19 22 0,05 27 33 39 45 52
0,10 12 14 17 20 23 0,10 29 35 41 47 53
0,20 13 16 19 22 24 0,20 31 37 43 49 55
48 0,001 8 11 14 17 21 96 0,001 23 29 35 42 48
0,01 11 13 17 20 23 0,01 26 33 39 45 52
0,05 13 16 19 22 26 0,05 30 36 42 49 55
0,10 14 17 20 23 27 0,10 31 38 44 50 57
0,20 15 18 22 25 28 0,20 33 40 46 53 59
54 0,001 10 13 17 20 24 102 0,001 25 31 38 45 52
0,01 12 16 19 23 27 0,01 28 35 42 49 56
0,05 15 18 22 25 29 0,05 32 38 45 52 59
0,10 16 20 23 27 31 0,10 33 40 47 54 61
0,20 18 21 25 28 32 0,20 36 42 49 56 63
60 0,001 12 15 19 23 27 108 0,001 27 34 41 48 55
0,01 14 18 22 26 30 0,01 31 37 45 52 59
0,05 17 21 25 29 33 0,05 34 41 48 55 63
0,10 18 22 26 30 34 0,10 36 43 50 57 65
0,20 20 24 28 32 36 0,20 38 45 52 60 67
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
the 100(1–β) % upper confidence limit for p based on the normal approximation to the binomial as:
d
23
1, 5(x /nz)−+0, 5 1, 5 (nx−x ) /n
β
where
x is the number of correct answers; n is the number of assessors; z varies as follows: 0,84 for β = 0,20; 1,28 for β = 0,10;
β
1,64 for β = 0,05; 2,33 for β = 0,01; 3,09 for β = 0,001.
If the computed value is less than the selected limit for p , then declare the samples similar at the β level of significance.
d
NOTE 2 Values of n < 30 are usually not recommended for a triangle test for similarity.
NOTE 3 Adapted from Reference [11].
© ISO 2004 – All rights reserved 7
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ISO 4120:2004(E)
A.3 Table A.3 shows a statistical approach for determining the number of assessors. The statistical
sensitivity of the test is a function of three values: the α-risk, the β-risk and the maximum allowable proportion
2)
of distinguishers, p . Prior to conducting the test, select values for α, β and p using the following guidelines.
d d
As a rule of thumb, a statistically significant result at
an α-risk of 10 % to 5 % (0,10 to 0,05) indicates slight evidence that a difference was apparent,
an α-risk of 5 % to 1 % (0,05 to 0,01) indicates moderate evidence that a difference was apparent,
an α-risk of 1 % to 0,1 % (0,01 to 0,001) indi
...
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