SIST-TP CEN/TR 10345:2008
(Main)Guideline for statistical data treatment of inter laboratory tests for validation of analytical methods
Guideline for statistical data treatment of inter laboratory tests for validation of analytical methods
Revision of ECISS Information Circular No 5.This document is a guideline to carry out the statistical evaluation of data from an inter laboratory test for method validation. Its purpose is to detail the methodology of ISO 5725-1, -2 and -3:1994 standards for the treatment of registered data in the conditions used within the ECISS/TC 20 working groups.
Richtlinien für statistische Verfahren der Probenahme und Analyse von Eisen, Stahl und anderen Eisenmetallen
Guide pour le traitement statistique des données de validation de méthodes d'analyse, issues d'essais interlaboratoire
Ce document est un guide pour le traitement statistique des données de validation de méthodes, issues
d'essais interlaboratoire.
Son but est de préciser dans le détail la méthodologie des normes ISO 5725-1, -2 et -3:1994 pour le
traitement de données obtenues dans les conditions mises en oeuvre au sein des groupes de travail de
l'ECISS/TC 20.
NOTE Le présent document n'est pas une simplification de la norme ISO 5725, qui est le seul document de
référence.
Smernice za statistične postopke vzorčenja in analize železa, jekla in drugih kovinskih materialov na osnovi železa
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST-TP CEN/TR 10345:2008
01-september-2008
6PHUQLFH]DVWDWLVWLþQHSRVWRSNHY]RUþHQMDLQDQDOL]HåHOH]DMHNODLQGUXJLK
NRYLQVNLKPDWHULDORYQDRVQRYLåHOH]D
Guideline for statistical data treatment of inter laboratory tests for validation of analytical
methods
Richtlinien für statistische Verfahren der Probenahme und Analyse von Eisen, Stahl und
anderen Eisenmetallen
Guide pour le traitement statistique des données de validation de méthodes d'analyse,
issues d'essais interlaboratoire
Ta slovenski standard je istoveten z: CEN/TR 10345:2008
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
77.080.01 Železne kovine na splošno Ferrous metals in general
SIST-TP CEN/TR 10345:2008 en,fr
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST-TP CEN/TR 10345:2008
TECHNICAL REPORT
CEN/TR 10345
RAPPORT TECHNIQUE
TECHNISCHER BERICHT
June 2008
ICS 03.120.30; 17.020
English Version
Guideline for statistical data treatment of inter laboratory tests
for validation of analytical methods
Guide pour le traitement statistique des données de Richtlinien für statistische Verfahren der Probenahme und
validation de méthodes d'analyse, issues d'essais Analyse von Eisen, Stahl und anderen Eisenmetallen
interlaboratoire
This Technical Report was approved by CEN on 22 October 2007. It has been drawn up by the Technical Committee ECISS/TC 20.
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
© 2008 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TR 10345:2008: E
worldwide for CEN national Members.
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Contents Page
Foreword.3
1 Scope .4
2 Normative references .4
3 Principle.4
4 Preliminary rules.4
4.1 First rule (‘to be clear’) .4
4.2 Second rule (‘to be modest’) .5
4.3 Minimal characteristics of data population.5
5 Procedure .6
5.1 Bases .6
5.2 Raw data examination .6
5.3 Intra laboratory repeatability variance (Cochran’s test).6
5.4 Intra laboratory reproducibility variance (Grubbs’ test).6
5.5 Inter laboratory reproducibility variance (Grubbs’ test).7
5.6 Retained data examination .8
5.7 Calculation of the variances associated to the tested method.8
5.8 Treatment for unexpected calculated variances .8
5.9 Estimation of a function linking variance and level.8
6 Report .9
7 General remarks.9
Annex A Steps for the validation of a Draft Standard.10
Annex B Synoptic of the operations described in Annex A.12
Annex C Examples.17
Bibliography .46
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Foreword
This document CEN/TR 10345:2008 has been prepared by Technical Committee ECISS/TC 20 “Methods of
chemical analysis of ferrous products”, the secretariat of which is held by SIS.
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1 Scope
This document is a guideline to carry out the statistical evaluation of data from an inter laboratory test for
method validation.
Its purpose is to detail the methodology of ISO 5725-1, -2 and -3:1994 standards for the treatment of
registered data in the conditions used within the ECISS/TC 20 working groups.
NOTE The present document is not a simplification of ISO 5725 standard, which is the only reference document
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 5725-1:1994, Accuracy (trueness and precision) of measurement methods and results — Part 1: General
principles and definitions
ISO 5725-2:1994, Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic
method for the determination of repeatability and reproducibility of a standard measurement method
ISO 5725-3:1994, Accuracy (trueness and precision) of measurement methods and results — Part 3:
Intermediate measures of the precision of a standard measurement method
3 Principle
An inter laboratory test for method validation is organised at each stage of the development of a standard draft.
Changing economical conditions have lead to the optimisation of the work of the participating laboratories.
The principle retained by the ECISS/TC 20 is to have three values by participant laboratory: two values
obtained in repeatability conditions (day 1) and a third obtained in intra laboratory reproducibility conditions
(day 2). The data evaluation requires a complex statistical analysis, which may be very confusing for a non-
specialist, even if it is widely detailed in the ISO 5725:1994 standard. Consequently, it seems useful to clarify
the methodology of this standard for the above purpose and to underline that difficulties found should be
discussed and solved with statisticians.
Values that are identified as statistically abnormal at 99 % (outliers) using numerical Cochran’s and Grubbs’
tests lead to the elimination of the laboratory that produced them, at the stage at which they are detected: this
principle is adopted even though we risk to wrongly eliminating one result in one hundred. Nevertheless, it is
essential to investigate with the laboratory that produced the involved results the reasons for this elimination
and to pay particular attention to all of the values produced by this laboratory.
Also, in the case of a laboratory which produces values that are determined as statistically significant at 95 %
(stragglers) by numerical Cochran’s and Grubbs’ tests a particular attention should be paid to all the other
values produced by this laboratory.
4 Preliminary rules
4.1 First rule (‘to be clear’)
The inter laboratory test should be adapted in order to meet the following requirements:
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to estimate the variances linked to the tested method (repeatability, intra laboratory reproducibility, inter
laboratories reproducibility);
to check that inter laboratories variance is compatible with defined criteria for referee or routine methods
(Aim CVR or Max CVR) for their full range of application.
The following must be imposed on the working groups:
a) minimal number of participating laboratories (8 / 10 / 15… - see ISO 5725-1, Annex B);
b) rigorous implementation of the working programme;
c) appropriate number of significant figures to be given for each transmitted value, in order to allow an
optimal statistical data evaluation.
4.2 Second rule (‘to be modest’)
The statistical treatment must be performed by application of the ISO 5725:1994 standard, and by following
the here after described procedure. In order to solve the statistical problems encountered, the help of an
expert should be sought. It should be noted that the ISO 5725-2 et 5725-3:1994 standards don’t give an
exhaustive description of all situations and that they clearly indicate that statistical data treatment should be
performed by a person experienced in work planning and in statistical analysis (ISO 5725-2 § 6.2). Various
situations may arise in practice, which require the application of the variance analysis general modes
(ANOVA), these ISO 5725 standards specifying only simplified procedures.
4.3 Minimal characteristics of data population
The number of samples to be tested should be at least two for each range of values to be determined, (for
example between 0,010 and 0,099 we must have two samples, between 0,10 and 0,99 we must have two
samples and so on), and should never be less than 5 for the full range of values. It is useful, when possible,
that the inter laboratory test be performed using CRMs representing at least 50 % of the total number of
samples to be tested. The remaining samples can be internal reference materials provided by laboratories on
condition that their homogeneity has been tested and found to be compatible with inter laboratory test
requirements. These points are not the subject of the present document.
In the present economical situation, an inter laboratory test should be planed with at least 8 laboratories from
at least 5 different countries.
The values provided by the participating laboratories should have a sufficient number of significant figures in
order to enable correct statistical data treatment; although the number of significant figures does not influence
the precision of the result, the transmission of rounded values containing less figures means that the work
cannot be correctly evaluated. Expressed as a w/w percentage, values should generally be written under the
form listed below, i.e., containing 3 or 4 significant figures:
xx,xx
x,xxx
0,xxxx
0,0xxx
0,00xxx
0,000xxx
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5 Procedure
5.1 Bases
Here we look at the only case where the data population is strictly obtained by the methods defined in § 3, that
is to say, 3 determinations for each sample and from each laboratory:
two determinations in repeatability conditions called ‘Day 1,1’ et ‘Day 1,2’;
supplementary determination in reproducibility conditions called ‘Day 2’.
Statistical data evaluation is performed for each content level that is to say in the present case, sample by
sample.
5.2 Raw data examination
Raw data must be typed into a table and then printed. The raw data table should be studied in order to detect
potential typing errors in the data supplied by each participating laboratory and/or in the final input stage
(ISO 5725-2 § 7.2.6).
NOTE Performing a normality test of the data population to be tested is recommended.
5.3 Intra laboratory repeatability variance (Cochran’s test)
A first graphical evaluation of the raw data may be performed in order to test the intra laboratory repeatability
consistency by using Mandel’s k test (all data included): its only purpose is to get an overview of the data
population.
Further statistical treatments are carried out under the hypothesis that the intra laboratory repeatability
variances belong to the same normal population. Cochran’s test should therefore be performed (ISO 5725-2 §
7.3.3) in order to detect unexpected values of intra laboratory variances, which must then be discarded so that
statistical analysis may be pursued.
NOTE 1 Strictly speaking, Cochran’s test should only be used to evaluate a population of measurements obtained in
repeatability conditions.
In practice, it is advisable to proceed as follows:
perform Cochran’s test with ‘Day 1,1’ and ‘Day 1,2’ values, after a normality test for this data population;
if necessary, discard laboratories having an unexpected variance.
NOTE 2 It is advisable not to perform an iteration when using Cochran’s test, except in the case of a large laboratory
population (i.e. greater than 15), or when there is a particular statistical reason to justify it. A common rule sometimes used
is that the outliers shall not represent more than 10 % of the whole data.
In practice, in order to have a clear view of the data after the Cochran’s test has been performed, it is
advisable either to print a new table of the remaining data or to clearly identify discarded data.
5.4 Intra laboratory reproducibility variance (Grubbs’ test)
Further statistical evaluations are carried out under the hypothesis that intermediate variances (intra
laboratory reproducibility) belong to the same normal population. Grubbs’ test should be applied (ISO 5725-2
§ 7.3.4) in order to detect unexpected means that should then be discarded so that statistical analysis may be
pursued.
In practice, it is advisable to proceed in the following order:
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apply Grubbs’ test to the ‘daily means’ data, that is to say to the pair of values ‘(Day 1,1 + Day 1,2)/2’ and
‘Day 2’ for all of the laboratories;
firstly, test the highest ‘mean’ after having confirmed that the data population is normal;
if the test is positive, discard the laboratory concerned;
secondly, test the lowest ‘mean’;
if the test is positive, discard the laboratory concerned;
if neither of the two former tests detect an unexpected ‘mean’, perform the test with the two highest
‘mean’ values;
if the test is positive discard the laboratory(ies) concerned;
perform the test with the two lowest ‘mean’ values;
if the test is positive discard the laboratory(ies) concerned.
NOTE 1 It is advisable not to perform iterations when using Grubbs’ test.
NOTE 2 It is not necessary to perform the test whenever the value or the two values to be tested come from a
population containing respectively a second or a third identical value.
5.5 Inter laboratory reproducibility variance (Grubbs’ test)
A first graphical evaluation of the raw data may be performed in order to test the inter laboratory consistency
using Mandel’s h test (all retained data remaining after the application of Cochran and Grubbs’ tests are
included).
Further statistical treatments are carried out under the hypothesis that the laboratories means belong to the
same normal population. Grubbs’ test should be performed (ISO 5725-2 § 7.3.4) in order to detect unexpected
laboratories mean values which must then be discarded so that statistical analysis may be pursued.
In practice, it is advisable to proceed in the following order:
firstly, test the highest ‘laboratory mean’, ‘(Day 1,1 + Day 1,2 + Day 2)/3’, after having confirmed that the
data population is normal;
if the test is positive discard the laboratory concerned;
secondly, test the lowest ‘laboratory mean’;
if the test is positive discard the laboratory concerned;
if neither of the two former tests detect an unexpected ‘laboratory mean’, perform the test with the two
highest ‘laboratory mean’ values;
if the test is positive discard the laboratories concerned;
perform the test with the two lowest ‘laboratory mean’ values;
if the test is positive discard the laboratories concerned.
NOTE 1 It is advisable not to perform iterations when using Grubbs’ test.
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NOTE 2 It is not necessary to perform the test whenever the value or the two values to be tested come from a
population containing respectively a second or a third identical value.
5.6 Retained data examination
The application of Cochran and Grubbs’ tests eventually leads to the elimination of raw data from some
laboratories. These eliminations have been performed for each content level tested: therefore it is necessary
to carry out a critical inter level examination that may lead to discard all data from one or more laboratories if it
is established that multiple outlier or straggler values come from these laboratories. These eliminations have
to be justified.
In practice, in order to have a clear view of the remaining data, it is advisable either to print a new table of the
retained data or to clearly identify discarded data.
5.7 Calculation of the variances associated to the tested method
Calculations are performed with a strict application of the ISO 5725-3 standard (Annex C); it generally results
in three variances labelled Vr, VRw and VR.
It is the result of a variance analysis evaluation assessment (ANOVA) which assumes that all the former
stages were performed, and which presupposes that intra laboratory repeatability (residual, Vr), intra
laboratory reproducibility (VRw) and inter laboratory reproducibility variances (VR) are discernible and
quantifiable within the test experiment conditions.
5.8 Treatment for unexpected calculated variances
Despite the implementation of all of the above specifications there could still exist some anomalies:
variances are normally graded in the order Vr < VRw < VR; if this is not the case it could be that the
results of the calculation are not realistic because an hypothesis was not verified; in particular this may
occur when the conditions to detect a difference between the intra laboratory reproducibility variance and
the residual variance (intra laboratory repeatability variance) don’t exist; then strictly speaking, the
ISO 5725:1994 standard formulas are not applicable and consequently only one global residual intra
laboratory variance can be calculated; the same approach should be taken concerning VRw and VR;
variances are of course positive numbers (they are the sum of square numbers); nevertheless the
ISO 5725:1994 standard formulas can lead to negative values. In such cases these results should not be
taken into account because some hypotheses may not have been satisfied or because of the lack in
variability of the transmitted data (rounded values or an insufficient number of figures);
etc.
These anomalies should be dealt with by an expert and the resulting position taken by the committee could be
that standard deviation values for repeatability and/or reproducibility don’t fit the criteria for publication
(ISO 5725-2 § 7.7.2).
5.9 Estimation of a function linking variance and level
Calculations are performed in strict agreement with the specifications of the ISO 5725-2 standard (§ 7.5).
A particular attention should be paid to the correlation coefficient functions between:
lg m = a + b ⋅ lg r
lg m = a + b ⋅ lg Rw
lg m = a + b ⋅ lg R
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Typically, the value of each correlation coefficient should be at least greater than 0,9.
Nevertheless, correlation coefficient with values from 0,7 to 0,9 can be admitted, after consensus.
Values lower than 0,7 should be rejected as they show a lack of correlation. In such cases, only individual r,
Rw and R should be edited in the validated method (the edition of the smoothed r, Rw and R values is not
allowed).
6 Report
The report of the statistical evaluation must be submitted to all of the participating laboratories, so that they
can verify that there was no error in the transcription of their results and in order to get their opinion
concerning the evaluation performed.
The report of the working group convenor must include:
complete statistical report;
participating laboratories corresponding remarks;
comments and answers of the convenor concerning these remarks.
This report is then sent to the technical committee together with the method accompanied by the remarks and
technical comments of the working group members.
7 General remarks
Most of the inter laboratory tests for the validation of standard methods have not been evaluated under the
rules of the present document. Indeed there is no standardised method which mentions the impossibility of the
evaluation of one of the three variances, based on the data produced by an inter laboratory test (variances
and the corresponding standard deviations calculations are systematically performed and published). It is
important to verify if the present document is mentioned in a particular standard for the section concerning the
statistical evaluation of the data issued from the corresponding validation inter laboratory test.
It is also hoped to have a software able to perform the statistical evaluation of data produced by an inter
laboratory test for method validation, accordingly to the ISO 5725:1994 standard. Nevertheless, it should be
kept in mind that there is no software able to make decisions concerning abnormal situations.
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Annex A
Steps for the validation of a Draft Standard
A.1 Decision from a TC to create a working group
Selection of N laboratories: minimum 8 laboratories from not less than 5 countries.
Selection of P samples: minimum 5 and minimum 2 by factor 10 within the measurement range.
Selection of samples: minimum 50 % CRM (if possible).
A.2 Laboratories performance on the specified tests
Rigorous application of the draft standard.
Rigorous application of the previous scheme in order to produce: two results under repeatability conditions
"Day 1,1" and "Day 1,2" and one under reproducibility conditions "Day 2".
Transmission of results (%) with the appropriate number of figures: 4 significant figures for values < 1.000 %
and 3 significant figures for values > 1.000 %.
A.3 Statistical work to be done at each level (for each of the P samples)
A.3.1 General
General table including all values produced.
Examination of the raw data, for typing errors detection.
Normality test.
A.3.2 Intra laboratory repeatability variance (Cochran's test: ISO 5725-2 § 7.3.3)
Apply only to the set of N couples of values "Day 1,1" and "Day 1,2".
Discard the eventual laboratory(ies) which shows unexpected variance (outliers).
If the outliers represent more than 10 % of the total number of the laboratories, ask for a statistician
advice.
Edit a new table containing the set of laboratories having the same “intra laboratory repeatability variance” for
further tests.
Normality test.
A.3.3 Intra laboratory reproducibility variance (Grubbs' test: ISO 5725-2 § 7.3.4)
Apply only to the 'daily means': set of 2N values "(A+B)/2" and "C".
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Test the highest 'daily mean'.
Discard the eventual laboratory that shows the unexpected variance (outlier).
Test the lowest 'daily mean'.
Discard the eventual laboratory that shows the unexpected variance (outlier).
If neither if the two tests above detect an unexpected 'mean':
Test the couple of highest 'daily mean'.
Discard the eventual laboratory(ies) that show the unexpected variances (outliers).
Test the couple of lowest 'daily mean'.
Discard the eventual laboratory(ies) that show the unexpected variances (outliers).
Edit a new table containing the set of laboratories having the same “intra laboratory reproducibility variance”
for further tests.
Normality test.
A.3.4 Inter laboratories reproducibility variance (Grubbs' test: ISO 5725-2 § 7.3.4)
Apply only to the “laboratory means”: set of N values "(A+B+C)/3".
Test the highest "mean value".
Discard the eventual laboratory that shows the unexpected variance (outlier).
Test the lowest “mean value”.
Discard the eventual laboratory that shows the unexpected variance (outlier).
If neither if the two tests above detect an unexpected 'mean':
Test the couple of highest “mean values”.
Discard the eventual laboratories that show the unexpected variances (outliers).
Test the couple of lowest “mean values”.
Discard the eventual laboratories that show the unexpected variances (outliers).
Edit a new table containing the set of laboratories having the same inter laboratory reproducibility variance.
A.3.5 Inter level laboratory performance
Discard the whole data from the laboratory(ies) that produced values detected as outliers or stragglers from
the 3 tests above at several levels.
Consider, if possible, the levels of the h and k Mendel's consistency statistics for the laboratory(ies) to be
discarded as a tool to support the decision.
Restart the entire processes of statistical evaluation, without this (or these) laboratory(ies).
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Annex B
Synoptic of the operations described in Annex A
Draft standard and
P samples sent to N
i
laboratories
Laboratory n° 1
Laboratory n° 2 Laboratory n° Ni
sample 1
sample 1 sample 1
Day 1,1/Day 1,2/Day 2
Day 1,1/Day 1,2/Day 2 Day 1,1/Day 1,2/Day 2
Laboratory n° 1 Laboratory n° 2 Laboratory n° Ni
sample 2 sample 2
sample 2
Day 1,1/Day 1,2/Day 2 Day 1,1/Day 1,2/Day 2
Day 1,1/Day 1,2/Day 2
Laboratory n° 1 Laboratory n° 2 Laboratory n° Ni
sample P sample P
sample P
Day 1,1/Day 1,2/Day 2 Day 1,1/Day 1,2/Day 2
Day 1,1/Day 1,2/Day 2
Sample j [ 1 ≤ j ≤ P ]
Discard or correct typing errors
A = Day 1,1 value
B = Day 1,2 value
C = Day 2 value
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Edit data table including all values
(A,B,C) accepted for the N
laboratories
[ N ≤ N ]
i
NO
ASK FOR THE ADVICE OF A
Normality test
STATISTIEN BEFORE ANY
OTHER ACTION
YES
Intra laboratory variance
Repeatability
Cochran's test
Apply to the N couples (A, B)
Discard data from
laboratory(ies) which is
(are) outlier(s)
Edit data table including all
retained values (A,B,C) for N'
laboratories having the same
repeatability
[ N' ≤ N ]
NO
ASK FOR THE ADVICE OF A
Normality test
STATISTIEN BEFORE ANY
OTHER ACTION
YES
Intra laboratory variance
Reproducibility
Grubbs' test
Apply to the 2 N' daily mean values
[ (A+B)/2, C ]
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Test the highest
daily mean
YES
Detected
Discard data
as
from outlier
outlier?
laboratory
NO
Test Test
the highest the lowest
daily mean daily mean
YES YES
Discard data Detected Detected Discard data
from outlier as as from outlier
laboratory outlier? outlier? laboratory
NO
NO
Test the highest couple of
Edit data table including all
daily means
retained values (A,B,C) for N"
laboratories having the same
repeatability and a similar intra
laboratory reproducibility
YES
Detected
Discard data
as
from outlier
[ (N' - 4) ≤ N" ≤ N' ]
outlier?
laboratories
NO
Normality test
Test the lowest of
couple daily means
NO YES
NO
YES
Discard data Detected
from outlier as
laboratories outlier?
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ASK FOR THE ADVICE OF A
STATISTIEN BEFORE ANY
OTHER ACTION
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Inter laboratory variance
Reproducibility
Grubbs' test
Apply to the N" laboratory mean values
[ (A+B+C)/3 ]
Test the highest
mean value
YES
Detected
Discard data
as
from outlier
outlier?
laboratory
NO
Test Test
the highest the lowest
mean value mean value
YES
YES
Detected Detected
Discard data Discard data
as as
...
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