1、April 2013 Translation by DIN-Sprachendienst.English price group 13No part of this translation may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).ICS
2、67.240!$E“1973404www.din.deDDIN ISO 29842Sensory analysis Methodology Balanced incomplete block designs (ISO 29842:2011),English translation of DIN ISO 29842:2013-04Sensorische Analyse Prfverfahren Balancierte unvollstndige Blockplne (ISO 29842:2011),Englische bersetzung von DIN ISO 29842:2013-04Ana
3、lyse sensorielle Mthodologie Plans de prsentation en blocs incomplets quilibrs (ISO 29842:2011),Traduction anglaise de DIN ISO 29842:2013-04www.beuth.deDocument comprises pagesIn case of doubt, the German-language original shall be considered authoritative.2303.13A comma is used as the decimal marke
4、r. Contents Page National foreword 3 National Annex NA (informative) Bibliography . 4 1 Scope . 5 2 Normative references . 5 3 Terms and definitions 5 4 Specification of balanced incomplete block designs . 5 5 Data analysis . 7 5.1 General . 7 5.2 Analysis of variance for rating data 7 5.3 Friedmans
5、 sum rank analysis for rank data . 9 6 Application in sensory evaluation 10 Annex A (informative) Catalogue of incomplete block designs 11 Annex B (informative) Example of balanced incomplete block design with ratings data 19 Annex C (informative) Example of balanced incomplete block design with ran
6、k data . 21 Bibliography . 23 2 DIN ISO 29842:2013-04 National foreword This document (ISO 29842:2011) has been prepared by Technical Committee ISO/TC 34 “Food products” (Secretariat: AFNOR, France), Subcommittee SC 12 “Sensory analysis” (Secretariat: IRAM, Argentina). The responsible German body in
7、volved in its preparation was the Normenausschuss Lebensmittel und landwirtschaftliche Produkte (Food and Agricultural Products Standards Committee), Working Committee modification. The DIN Standards corresponding to the International Standards referred to in this document are as follows: ISO 3534-1
8、 DIN ISO 3534-1 ISO 5492 DIN EN ISO 5492 ISO 6658 DIN 10950 ISO 8586-1 DIN 10961 ISO 8586-2 DIN EN ISO 8586-2 ISO 8587 DIN EN ISO 8587 ISO 13299 DIN EN ISO 13299 3 DIN ISO 29842:2013-04 NA 057-01-01 AA Sensorik. The text of ISO 29842:2011 has been adopted in this standard without any National Annex
9、NA (informative) Bibliography DIN 10950, Sensory analysis Basic principles DIN 10961, Training of assessors for sensory analysis DIN ISO 3534-1, 4 DIN ISO 29842:2013-04 Statistics Vocabulary and symbols Part 1: General statistical terms and terms used in probability DIN EN ISO 5492, Sensory analysis
10、 Vocabulary DIN EN ISO 8586-2, Sensory analysis General guidance for the selection, training and monitoring of assessors Part 2: Expert sensory assessors DIN ISO 8587, Sensory analysis Methodology Ranking DIN EN ISO 13299, Sensory analysis Methodology General guidance for establishing a sensory prof
11、ile Sensory analysis Methodology Balanced incomplete block designs 1 Scope This International Standard specifies a method for the application of balanced incomplete block designs to sensory descriptive and hedonic tests. This International Standard applies when the number of test samples exceeds the
12、 number of evaluations that an assessor can perform reliably in a single session. This International Standard also specifies the fundamental characteristics of balanced incomplete block designs and establishes guidelines for their application in sensory evaluation. 2 Normative references The followi
13、ng 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 3534-1, Statistics Vocabulary and symbols Part 1: Genera
14、l 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 5492, ISO 3534-1, and the following apply. 3.1 block design sensory analysis multi-sample serving protocol in whic
15、h 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 numbe
16、r 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. 5 DIN ISO 29842:2013-04 Table 1 A BIB design with five samples and 10 blo
17、ck/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
18、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 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 (t
19、ypically, assessors) in one repetition of the BIB design r number of times each test sample is evaluated in one repetition of the BIB design 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
20、 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 (assesso
21、rs) 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 . The entire BIB design may need
22、 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 tim
23、es each pair of samples is seen together is p*. The constant values of r and 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. Th
24、e constant value of ensures that all pair-wise comparisons between any two samples are equally sensitive. 6 DIN ISO 29842:2013-04 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 t
25、o 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
26、.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
27、, 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
28、 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 e
29、very 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
30、 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 (DF) Sum of squares (SS) Mean square (MS) F Total T= t*r 1 STAssessors B= b
31、1 SBSamples (adjusted for assessors) S= t 1 SSMSSSS/SMSS/MSEError E= t*r t b + 1 SEMSESE/EIf the F-statistic in Table 2 exceeds the upper- 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
32、is significant, a multiple comparison procedure, such as Fishers LSD (least significant diffference), L, shall be applied to determine which samples are significantly different from one another. The equation for Fishers LSD, L, appropriate for a single repetition of this BIB design is: EE/2,2 (1)(1)
33、MS ktLtrkt=where t, k and r are as defined in Clause 4; MSEis the mean square for error from the ANOVA table; Eis the number of degrees of freedom for error from the ANOVA table; E/2,tis the upper /2 critical value of Students t-distribution with Edegrees of freedom. 7 DIN ISO 29842:2013-04 The same
34、 value of shall be used for assessing the significance of the F-statistic and in Fishers 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 as
35、sessors 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. The ANOVA table for this design is presented in Table 3. Table 3 ANOVA table for balanced incomplete block design (p repetitions performed by p*b assessors e
36、ach evaluating a single block of k samples) Source of variation Degrees of freedom (DF) Sum of squares (SS) Mean square (MS) F Total T= t*p*r 1 STBlocks (assessors) B= p*b 1 SBSamples (adjusted for assessors) S= t 1 SSMSS= SS/SMSS/MSEError E= t*p*r t p*b + 1 SEMSE= SE/EIf the F-statistic in Table 3
37、exceeds the 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 Fishers LSD, L, shall be applied to determine which samples are signif
38、icantly different from one another. The equation for Fishers LSD, L, appropriate for a BIB design is: EE/2,2 (1)(1)MS ktLtprkt=where t, k, p and r are as defined in Clause 4; MSEis the mean square for error from the ANOVA table; Eis the number of degrees of freedom for error from the ANOVA table; E/
39、2,tis the upper /2 critical value of Students t-distribution with Edegrees of freedom. The same value of shall be used for assessing the significance of the F-statistic and in Fishers LSD, L. If each assessor evaluates all b blocks in the BIB design, then the “assessor effect” and the “assessor-by-s
40、ample” interaction can be partitioned out of the total variability (see Table 4). This approach is especially applicable when the total number of blocks in one repetition of the BIB design is small (e.g. b 6). The order in which the blocks are presented to the assessor shall be done at random. Withi
41、n each block, the order in which the samples are evaluated shall be done at random. In either approach, the variability that arises from the assessors is accounted for and the interaction between assessors and samples replaces the error term that was used in Tables 2 and 3. 8 DIN ISO 29842:2013-04 T
42、able 4 ANOVA table for balanced incomplete block design (p repetitions performed by p assessors each evaluating b blocks of k samples) Source of variation Degrees of freedom (DF) Sum of squares (SS) Mean square (MS) F Total T= t*p*r 1 STAssessor P= p 1 SPBlocks (within assessor) B(P)= p*(b 1) SB(P)S
43、amples (adjusted for assessor) S= t 1 SSMSS= SS/SMSS/MSA*SAssessor*samples A*S= (p 1)(t 1) SA*SMSA*S= SA*S/A*SResidual E= p*(t*r t b + 1) SEMSE= SE/EIf the F-statistic in Table 4 exceeds the critical value of an F with the corresponding degrees of freedom, then the null hypothesis assumption of equi
44、valent mean ratings is rejected. If the F-statistic is significant, a multiple comparison procedure, such as Fishers LSD, L, shall be applied to determine which samples are significantly different from one another. The equation for Fishers LSD, L, appropriate for a BIB design is: A*SA*S/2,2 (1)(1)MS
45、 ktLtprkt=where t, k, p and r are as defined in Clause 4; MSA*Sis the mean square for the assessor*sample interaction from the ANOVA table; A*Sis the number of degrees of freedom for the assessor*sample interaction from the ANOVA table; A*S/2,tis the upper /2 critical value of Students t-distributio
46、n with A*Sdegrees of freedom. The same value of shall be used for assessing the significance of the F-statistic and in Fishers LSD, L. 5.3 Friedmans sum rank analysis for rank data1)A Friedman-type statistic shall be applied to rank data arising from a BIB design. Friedmans test statistic, Ftest, is
47、 given by: 22test112 3( 1)(1)tjjkprFRptk=+=+where t, k, r, and p are as defined above and Rjis the rank sum of the jth sample (Reference 8). Tables of critical values of Ftestare available for selected combinations of t = 3 6, k = 2 5, and p = 1 7 (Reference 9). However, in most sensory studies, the
48、 total number of blocks exceeds the values in the tables. For these situations, the test procedure is to reject the assumption of equivalency among the samples if the value of Ftestexceeds the upper critical value of a 2-statistic with (t 1) degrees of freedom. 1) There are several statistical methods for analysing rank data that are obtained from a BIB design. Interested readers are encouraged to review the statistical literature on the topic. Friedmans method has been chosen for detailed discussion because it is statistically powerful and computationally convenient
