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International
Standard
ISO 29842
Second edition
Sensory analysis — Methodology —
2024-06
Balanced incomplete block designs
Analyse sensorielle — Méthodologie — Plans de présentation en
blocs incomplets équilibrés
Reference number
© ISO 2024
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ii
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Specification of balanced incomplete block designs . 1
5 Data analysis . 2
5.1 General .2
5.2 Analysis of variance for rating data .3
5.3 Friedman's sum rank analysis for rank data .5
6 Application in sensory evaluation. 6
Annex A (informative) Catalogue of incomplete block designs . 7
Annex B (informative) Example of balanced incomplete block design with ratings data .15
Annex C (informative) Example of balanced incomplete block design with rank data . 17
Bibliography . 19
iii
Foreword
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This document 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 29842:2011), of which it constitutes a minor
revision. It also incorporates the Amendment ISO 29842:2011/Amd.1:2015.
The changes are as follows:
— the corrections of the amendment have been included;
— in Table 2, the formulae in the column “Mean square” have been corrected.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
iv
International Standard ISO 29842:2024(en)
Sensory analysis — Methodology — Balanced incomplete
block designs
1 Scope
This document specifies a method for the application of balanced incomplete block designs to sensory
descriptive and hedonic tests.
This document is applicable when the number of test samples exceeds the number of evaluations that an
assessor can perform reliably in a single session.
This document also specifies the fundamental characteristics of balanced incomplete block designs and
establishes guidelines for their application in sensory evaluation.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements 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 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 5492, Sensory analysis — Vocabulary
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 5492 and the
following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
block design
multi-sample serving protocol in which an assessor evaluates all or a subset of the
samples in a study
3.2
repetition
one occurrence of an experimental design
4 Specification of balanced incomplete block designs
Balanced incomplete block (BIB) designs apply to sensory tests in which the total number of samples
is greater than the number that can be evaluated before sensory and psychological fatigue set in. In BIB
designs, each assessor evaluates only a subset of the total number of samples in a single session.
An example of a BIB design is shown in Table 1.
Table 1 — A BIB design with five samples and 10 block/assessors
Test sample
Block
(assessor)
1 2 3 4 5
1 × × × — —
2 × × — × —
3 × × — — ×
4 × — × × —
5 × — × — ×
6 × — — × ×
7 — × × × —
8 — × × — ×
9 — × — × ×
10 — — × × ×
In a BIB design each assessor evaluates a subset, k, of the total number of samples, t, where k < t. The subset of
samples that an assessor evaluates is selected so that, in a single repetition of the BIB design, every sample is
evaluated an equal number of times and all possible pairs of two samples are evaluated by an equal number
of assessors.
The notation most commonly used in a BIB design is as follows:
— t number of test samples;
— k number of samples evaluated by an assessor in a single session (k < t);
— b total number of blocks (typically, assessors) in one repetition of the BIB design;
— r number of times each test sample is evaluated in one repetition of the BIB design;
— λ number of times each pair of samples is evaluated by the same assessor;
— p number of times the basic BIB design is repeated.
Notationally, each assessor evaluates k of the t samples (k < t). The subset of k samples that an assessor
evaluates is selected so that in a single repetition of the BIB design every sample is evaluated an equal
number of times and all possible pairs of samples are evaluated by an equal number of assessors. The number
of blocks (assessors) required to complete a single repetition of the BIB design is denoted by b. The number
of times each sample is evaluated in a single repetition of the BIB design is denoted by r and the number of
times every pair of two samples is evaluated together is denoted by λ.
The entire BIB design may need to be repeated several times in order to achieve an adequate level of precision
for the study. The number of repetitions of the basic BIB design is denoted by p. The total number of blocks
(typically assessors) is then p*b and the total of evaluations per sample is then p*r. The total number of times
each pair of samples is seen together is p*λ.
The constant values of r and λ for all samples in the BIB design imparts important statistical properties to
data collected from the design. The constant value of r ensures that the mean values of all of the samples are
estimated with equal precision. The constant value of λ ensures that all pair-wise comparisons between any
two samples are equally sensitive.
5 Data analysis
5.1 General
Two types of data can be collected using balanced incomplete block designs. Ratings data, or scores, are
obtained when assessors use a scale to report the perceived intensities of the attributes or impressions they
are evaluating. Rank data are obtained when assessors order the samples from lowest to highest (or vice
versa) relative to the attribute they are evaluating. Different data analysis methods are used for ratings and
rank data.
5.2 Analysis of variance for rating data
Analysis of variance (ANOVA) is used to analyse ratings data obtained from the BIB design. The sources
of variability accounted for in the ANOVA model for the BIB design are the same as those accounted for in
a randomized (complete) block design. In both cases, the total variability is partitioned into the separate
effects of blocks (typically assessors), treatments (typically samples) and errors. Because each assessor
evaluates only a subset of the total number of test samples, more complicated formulae are required to
calculate the ANOVA sum-of-squares for the BIB design than for the randomized (complete) block design.
The sensory analyst shall ensure that the program used to perform the analysis is capable of handling BIB
designs. In many statistical computer packages, the ANOVA procedure applies only to complete designs,
i.e. studies in which every assessor evaluates all of the test samples. For incomplete designs, such as BIB
designs, the general linear model (GLM) procedure or a mixed model procedure is required.
The form of the ANOVA used to analyse BIB data depends on how the design is administered.
Where the experiment is of the form of the example in Table 1, with a single repetition of the design, the
ANOVA table is as shown in Table 2.
Table 2 — ANOVA table for balanced incomplete block design (single repetition)
Source of variation Degrees of freedom Sum of squares Mean square F
(DF) (SS) (MS)
Total ν = t*r – 1 S
T T
Assessors ν = b – 1 S
B B
Samples (adjusted for assessors) ν = t – 1 S MS = S /ν MS /MS
S S S S S S E
Error ν = t*r – t – b + 1 S MS = S /ν
E E E E E
If the F-statistic in Table 2 exceeds the upper-α critical value of an F with the corresponding degrees of
freedom, then the null hypothesis assumption of equivalent mean ratings is rejected. If the F-statistic is
significant, a multiple comparison procedure, such as Fisher's LSD (least significant difference), L, shall be
applied to determine which samples are significantly different from one another. The equation for Fisher's
LSD, L, appropriate for a single repetition of this BIB design is:
2MS
kt()−1
E
Lt=
αν/,2
E
r ()kt−1
where
t, k and r are as defined in Clause 4;
MS is the mean square for error from the ANOVA table;
E
ν is the number of degrees of freedom for error from the ANOVA table;
E
t
is the upper α/2 critical value of Student's t-distribution with ν degrees of freedom.
αν/,2
E
E
The same value of α shall be used for assessing the significance of the F-statistic and in Fisher's LSD, L.
The BIB design shall be repeated p times to achieve an adequate level of precision from the study. If the
total number of blocks is too large for each assessor to evaluate all of them, each of the p*b assessors shall
evaluate only one block of k samples. Within each block, the order in which the k samples are evaluated shall
be done at random. Th
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