ISO INTERNATIONAL STANDARD 16269-4 First edition 2010-10-15 Statistical interpretation of data - Part 4: Detection and treatment of outliers Interpretation statistique des données - Partie 4: Détection et traitement des valeurs aberrantes Reference number ISO 16269-4:2010(E) @ISO 2010 ISO 16269-4:2010(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces 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 Adobe's licensing policy. The Iso Central Secretariat accepts no liability in this area. Adobe is a trademark of Adobe Systems 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 COPYRIGHTPROTECTEDDOCUMENT ? ISO2010 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 mechanical, including photocopying and microfilm, without permission in writing from either isO at the address below or IsO's 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 copyright@iso.org Web www.iso.org Published in Switzerland @ ISO 2010 - All rights reserved ISO 16269-4:2010(E) Contents Page Foreword .iv Introduction. V 1 Scope 2 Terms and definitions . 3 4 Outliers in univariate data .. 4.1 4.1.1 What is an outlier? ... 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 distribution.. 14 4.3.3 Sample from an exponential distribution.. 16 4.3.4 Samples taken from some known non-normal distributions.... 18 4.3.5 Sample taken from unknown distributions... 19 4.3.6 Cochran's test for outlying variance .... 21 4.4 Graphical test of outliers .... 22 5 Accommodating outliers in univariate data... 23 5.1 23 5.2 Robust estimation of location.... 5.2.1 General ... .24 5.2.2 Trimmed mean.... 24 5.2.3 Biweight 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 estimate.............. 6 Outliers in multivariate and regression data .. 26 6.1 General..... 26 6.2 Outliers in multivariate data ......... 26 6.3 Outliers in linear regression.. .28 6.3.1 General .... 28 6.3.2 Linear regression models..... 29 6.3.3 Detecting outlying Y observations.... 6.3.4 Identifying outlying X observations.. 31 6.3.5 Detecting influential observations... 32 6.3.6 A robust regression procedure... 35 Annex A (informative) Algorithm for the GESD outliers detection procedure . .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 of Cochran's test statistic ... ...48 Annex F (informative) A structured guide to detection of outliers in univariate data ... .51 Bibliography. .54 ganization for Standar izalion'ghts reserved ili