BS ISO 16269-4-2010 Statistical interpretation of data Detection and treatment of outliers《数据的统计说明 异常值的检测和处理》.pdf
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1、raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI Standards PublicationBS ISO 16269-4:2010Statistical interpretation ofdataPart 4: Detection and treatment of outliersBS ISO 16269-4:2010 BRITISH STANDARDNational forewordThis British Standard is the U
2、K implementation of ISO 16269-4:2010.The UK participation in its preparation was entrusted to TechnicalCommittee SS/2, Statistical Interpretation of Data.A list of organizations represented on this committee can beobtained on request to its secretary.This publication does not purport to include all
3、the necessaryprovisions of a contract. Users are responsible for its correctapplication. BSI 2010ISBN 978 0 580 65939 3ICS 03.120.30Compliance with a British Standard cannot confer immunity fromlegal obligations.This British Standard was published under the authority of theStandards Policy and Strat
4、egy Committee on 31 October 2010.Amendments issued since publicationDate Text affectedBS ISO 16269-4:2010Reference numberISO 16269-4:2010(E)ISO 2010INTERNATIONAL STANDARD ISO16269-4First edition2010-10-15Statistical interpretation of data Part 4: Detection and treatment of outliers Interprtation sta
5、tistique des donnes Partie 4: Dtection et traitement des valeurs aberrantes BS ISO 16269-4:2010ISO 16269-4:2010(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobes licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces
6、which are embedded are licensed to and installed on the computer performing the editing. In downloading this file, parties accept therein the responsibility of not infringing Adobes licensing policy. The ISO Central Secretariat accepts no liability in this area. Adobe is a trademark of Adobe Systems
7、 Incorporated. Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely eve
8、nt that a problem relating to it is found, please inform the Central Secretariat at the address given below. COPYRIGHT PROTECTED DOCUMENT ISO 2010 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mec
9、hanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISOs member body in the country of the requester. ISO copyright office Case postale 56 CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.i
10、so.org Published in Switzerland ii ISO 2010 All rights reservedBS ISO 16269-4:2010ISO 16269-4:2010(E) ISO 2010 All rights reserved iiiContents Page Foreword iv Introduction.v 1 Scope1 2 Terms and definitions .1 3 Symbols10 4 Outliers in univariate data 11 4.1 General .11 4.1.1 What is an outlier? 11
11、 4.1.2 What are the causes of outliers? .11 4.1.3 Why should outliers be detected?.11 4.2 Data screening.12 4.3 Tests for outliers .14 4.3.1 General .14 4.3.2 Sample from a normal distribution14 4.3.3 Sample from an exponential distribution16 4.3.4 Samples taken from some known non-normal distributi
12、ons18 4.3.5 Sample taken from unknown distributions.19 4.3.6 Cochrans test for outlying variance .21 4.4 Graphical test of outliers 22 5 Accommodating outliers in univariate data23 5.1 Robust data analysis.23 5.2 Robust estimation of location24 5.2.1 General .24 5.2.2 Trimmed mean .24 5.2.3 Biweight
13、 location estimate .25 5.3 Robust estimation of dispersion .25 5.3.1 General .25 5.3.2 Median-median absolute pair-wise deviation.25 5.3.3 Biweight scale estimate26 6 Outliers in multivariate and regression data 26 6.1 General .26 6.2 Outliers in multivariate data .26 6.3 Outliers in linear regressi
14、on.28 6.3.1 General .28 6.3.2 Linear regression models.29 6.3.3 Detecting outlying Y observations.31 6.3.4 Identifying outlying X observations.31 6.3.5 Detecting influential observations.32 6.3.6 A robust regression procedure35 Annex A (informative) Algorithm for the GESD outliers detection procedur
15、e .36 Annex B (normative) Critical values of outliers test statistics for exponential samples 37 Annex C (normative) Factor values of the modified box plot 44 Annex D (normative) Values of the correction factors for the robust estimators of the scale parameter .47 Annex E (normative) Critical values
16、 of Cochrans test statistic 48 Annex F (informative) A structured guide to detection of outliers in univariate data .51 Bibliography54 BS ISO 16269-4:2010ISO 16269-4:2010(E) iv ISO 2010 All rights reservedForeword ISO (the International Organization for Standardization) is a worldwide federation of
17、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. Inte
18、rnational 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 th
19、e 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 b
20、y 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 16269-4 was prepared by Technical Committee
21、ISO/TC 69, Applications of statistical methods. ISO 16269 consists of the following parts, under the general title Statistical interpretation of data: Part 4: Detection and treatment of outliers Part 6: Determination of statistical tolerance intervals Part 7: Median Estimation and confidence interva
22、ls Part 8: Determination of prediction intervals BS ISO 16269-4:2010ISO 16269-4:2010(E) ISO 2010 All rights reserved vIntroduction Identification of outliers is one of the oldest problems in interpreting data. Causes of outliers include measurement error, sampling error, intentional under- or over-r
23、eporting of sampling results, incorrect recording, incorrect distributional or model assumptions of the data set, and rare observations, etc. Outliers can distort and reduce the information contained in the data source or generating mechanism. In the manufacturing industry, the existence of outliers
24、 will undermine the effectiveness of any process/product design and quality control procedures. Possible outliers are not necessarily bad or erroneous. In some situations, an outlier may carry essential information and thus it should be identified for further study. The study and detection of outlie
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