# ISO 5725-4-1994

INTERNATIONAL STANDARD IS0 5725-4 First edition 1994-l 2-l 5 Accuracy (trueness and precision) of measurement methods and results - Part 4: Basic methods for the determination of the trueness of a standard measurement method Exactitude (justesse et fid6W des r International Organization for Standardization Document provided by IHS Licensee=Shell Services International B.V./5924979112,User=, 03/09/2003 21:24:44 MST Questions or comments about this message: pleasecall the Document Policy Management Group at 1-800-451-1584.--``````,,,,````,,````,,,````-`-`,,`,,`,`,,`---www.bzfxw.comIS0 5725-4:1994(E) Contents Page 1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _. 1 2 Normative references . . . . . . . . . f.__.__. 1 3 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 Determination of the bias of a standard measurement method by an interlaboratory experiment . . . . . . . . . - 2 4.1 The statistical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _.__. 2 4.2 Reference material requirements . . . __._._ _ _ _. 2 4.3 Experimental design considerations when estimating the bias of a measurement method .,,. 3 4.4 Cross-references to IS0 5725-1 and IS0 5725-2 . . . . . __. 3 4.5 Required number of laboratories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4.6 Statistical evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . _._. 4 4.7 Interpretation of the results of the statistical evaluation . . . . . . . 4 5 Determination of the laboratory bias of one laboratory using a standard measurement method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5.1 Carrying out the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _. 5 5.2 Cross-references to IS0 5725-l and IS0 5725-2 _. _. 6 5.3 Number of test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _._ 6 5.4 Choice of reference materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5.5 Statistical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 6 The report to, and the decisions to be taken by, the panel . . . . . 7 6.1 Report by the statistical expert . . . . **.**. 7 6.2 Decisions by the panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 7 Utilization of trueness data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Annexes A Symbols and abbreviations used in IS0 5725 . . . . . . . . . . . . . . . . . . . . . . . . . 6 53 IS0 1994 All rights reserved. Unless otherwise specified, no part of this publrcation may be reproduced or utrlized In any form or by any means, electronrc or mechanical, rncludrng photocopyrng and mrcrofilm, wrthout permission in writing from the publisher. lnternatronal Organization for Standardrzatron Case Postale 56 l CH-1211 Geneve 20 . Switzerland Printed In Swrtzerland ii COPYRIGHT 2003; International Organization for Standardization Document provided by IHS Licensee=Shell Services International B.V./5924979112,User=, 03/09/2003 21:24:44 MST Questions or comments about this message: pleasecall the Document Policy Management Group at 1-800-451-1584.--``````,,,,````,,````,,,````-`-`,,`,,`,`,,`---www.bzfxw.com0 IS0 IS0 5725-4:1994(E) B Example of an accuracy experiment B.l Description of the experiment . B.2 Precision assessment B.3 Trueness assessment 8.4 Further analysis C Derivation of equations C.l Equations (5) and (6) (see 4.5) . C.2 Equations (19) and (20) (see 5.3) . D Bibliography 10 10 10 10 11 21 21 22 23 COPYRIGHT 2003; International Organization for Standardization Document provided by IHS Licensee=Shell Services International B.V./5924979112,User=, 03/09/2003 21:24:44 MST Questions or comments about this message: pleasecall the Document Policy Management Group at 1-800-451-1584.--``````,,,,````,,````,,,````-`-`,,`,,`,`,,`---www.bzfxw.comForeword IS0 (the International Organization for Standardization) is a worldwide federation of national standards bodies (IS0 member bodies). The work of preparing International Standards is normally carried out through IS0 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. IS0 collaborates closely with the International Electrotechnical Commission (I EC) on all matters of electrotechnical standardization. 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. International Standard IS0 5725-4 was prepared by Technical Committee lSO/lC 69, Applications of statistical methods, Subcommittee SC 6, Measurement methods and results. IS0 5725 consists of the following parts, under the general title Accuracy (trueness and precision) of measurement methods and results: - Part 1: General principles and definitions - Part 2: Basic method for the determination of repeatability and re- producibility of a standard measurement method - Part 3: Intermediate measures of the precision of a standard measurement method - Part 4: Basic methods for the determination of the trueness of a standard measurement method - Part 5: Alternative methods for the determination of the precision of a standard measurement method - Part 6: Use in practice of accuracy values Parts 1 to 6 of IS0 5725 together cancel and replace IS0 5725:1986, which has been extended to cover trueness (in addition to precision) and intermediate precision conditions (in addition to repeatability and repro- ducibility conditions). Annex A forms an integral part of this part of IS0 5725. Annexes B, C and D are for information only. COPYRIGHT 2003; International Organization for Standardization Document provided by IHS Licensee=Shell Services International B.V./5924979112,User=, 03/09/2003 21:24:44 MST Questions or comments about this message: pleasecall the Document Policy Management Group at 1-800-451-1584.--``````,,,,````,,````,,,````-`-`,,`,,`,`,,`---www.bzfxw.com0 IS0 IS0 5725-4:1994(E) Introduction 0.1 IS0 5725 uses two terms “trueness” and “precision” to describe the accuracy of a measurement method. “Trueness” refers to the close- ness of agreement between the arithmetic mean of a large number of test results and the true or accepted reference value. “Precision” refers to the closeness of agreement between test results. 0.2 General consideration of these quantities is given in IS0 5725-l and so has not been repeated in this part of IS0 5725. IS0 5725-l should be read in conjunction with all other parts of IS0 5725, including this part, because it gives the underlying definitions and general principles. 0.3 The “trueness” of a measurement method is of interest when it is possible to conceive of a true value for the property being measured. Al- though, for some measurement methods, the true value cannot be known exactly, it may be possible to have an accepted reference value for the property being measured; for example, if suitable reference materials are available, or if the accepted reference value can be established by refer- ence to another measurement method or by preparation of a known sample. The trueness of the measurement method can be investigated by comparing the accepted reference value with the level of the results given by the measurement method. Trueness is normally expressed in terms of bias. Bias can arise, for example, in chemical analysis if the measurement method fails to extract all of an element, or if the presence of one element interferes with the determination of another. 0.4 Two measures of trueness may be of interest and both are consid- ered in this part of IS0 5725. a) Bias of the measurement method: where there is a possibility that the measurement method may give rise to a bias, which persists wher- ever and whenever the measurement is done, then it is of interest to investigate the “bias of the measurement method” (as defined in IS0 5725-l). This requires an experiment involving many laboratories, very much as described in IS0 5725-2. b) Laboratory bias: measurements within a single laboratory can reveal the “laboratory bias” (as defined in IS0 5725-l). If it is proposed to undertake an experiment to estimate laboratory bias, then it should be realized that the estimate will be valid only at the time of the ex- periment. Further regular testing is required to show that the labora- tory bias does not vary; the method described in IS0 5725-6 may be used for this. V COPYRIGHT 2003; International Organization for Standardization Document provided by IHS Licensee=Shell Services International B.V./5924979112,User=, 03/09/2003 21:24:44 MST Questions or comments about this message: pleasecall the Document Policy Management Group at 1-800-451-1584.--``````,,,,````,,````,,,````-`-`,,`,,`,`,,`---www.bzfxw.comINTERNATIONAL STANDARD 0 ISO IS0 5725-4:1994(E) Accuracy (trueness and precision) of measurement methods and results - Part 4: Basic methods for the determination of the trueness of a standard measurement method 1 Scope 1.1 This part of IS0 5725 provides basic methods for estimating the bias of a measurement method and the laboratory bias when a measurement method is applied. 1.2 It is concerned exclusively with measurement methods which yield measurements on a continuous scale and give a single value as the test result, al- though the single value may be the outcome of a calculation from a set of observations. 1.3 In order that the measurements are made in the same way, it is important that the measurement method has been standardized. All measurements are to be carried out according to that standard method. 1.4 Bias values give quantitative estimates of the ability of a measurement method to give the correct (true) result. When a value for the bias of a measure- ment method is quoted, together with a test result obtained by that method, there is an implication that the same characteristic is being measured in exactly the same way. 1.5 This part of IS0 5725 can be applied only if the accepted reference value can be established as a conventional true value, for example by measurement standards or suitable reference materials or by refer- ring to a reference measurement method or by prep- aration of a known sample. Reference materials could be either a) certified reference materials; b) materials manufactured for the purpose of the experiment with known properties; or c) materials whose properties have been established by measurements using an alternative measure- ment method whose bias is known to be negligi- ble. 1.6 This part of IS0 5725 considers only those cases where it is sufficient to estimate bias on one level at a time. It is not applicable if the bias in the measurement of one property is affected by the level of a second property (i.e. it does not consider inter- ferences). Comparison of the trueness of two measurement methods is considered in IS0 5725-6. NOTE 1 In this part of IS0 5725, bias is considered only at one level at a time. Therefore the Index j for the level has been omitted throughout. 2 Normative references The following standards contain provisions which, through reference in this text, constitute provisions of this part of IS0 5725. At the time of publication, the 1 COPYRIGHT 2003; International Organization for Standardization Document provided by IHS Licensee=Shell Services International B.V./5924979112,User=, 03/09/2003 21:24:44 MST Questions or comments about this message: pleasecall the Document Policy Management Group at 1-800-451-1584.--``````,,,,````,,````,,,````-`-`,,`,,`,`,,`---www.bzfxw.comIS0 5725-4: 1994(E) Q IS0 editions indicated were valid. All standards are subject to revision, and parties to agreements based on this part of IS0 5725 are encouraged to investigate the possibility of applying the most recent editions of the standards indicated below. Members of IEC and IS0 maintain registers of currently valid International Standards. IS0 3534-l :1993, Statistics - Vocabulary and sym- bols - Part I: Probability and genera/ statistical terms. IS0 5725-l :I 994, Accuracy (trueness and precision) of measurement methods and results - Part 1: General principles and definitions. IS0 5725-2: 1994, Accuracy (trueness and precision) of measurement methods and results - Part 2: Basic method for the determination of repeatability and re- producibility of a standard measurement method. 3 Definitions For the purposes of this part IS0 5725, the definitions given in IS0 3534-l and in IS0 5725-l apply. The symbols used in IS0 5725 are given in annex A. 4 Determination of the bias of a standard measurement method by an interlaboratory experiment 4.1 The statistical model In the basic model described in subclause 5.1 of IS0 5725-1:1994, the general mean m may be re- placed by m=p+6 . . . (1) where p is the accepted reference value of the prop- erty being measured; 6 is the bias of the measurement method. The model becomes y=p+d+B+e . . . (2) Equation (21 is used when d is of interest. Here B is the laboratory component of bias, i.e. the component in a test result representing the between-laboratory variation. The laboratory bias, A, is given by d=G+B so the model may be written y=p+A+e Equation (4) is used when A is of interest. 4.2 Reference material requirements . . (3) (4) If reference materials are used, the requirements given in 4.2.1 and 4.2.2 shall be satisfied. Reference materials shall be homogeneous. 4.2.1 Choice of reference materials 4.2.1.1 The reference material shall have known properties at the level appropriate to the level at which the standard measurement method is intended to be applied, e.g. concentration. In some cases it will be important to include, in the assessment exper- iment, a series of reference materials, each corre- sponding to a different level of the property, as the bias of the standard measurement method may be different at different levels. The reference material should have a matrix as close as possible to the matrix of the material to be subjected to the standard measurement method, e.g. carbon in coal or carbon in steel. 4.2.1.2 The quantity of the reference material shall be sufficient for the entire experimental programme, including some in reserve if this is considered n