TECHNICALREPORT7242 Published 1981-06-01 INTERNATIONAL ORGANIZATION FOR STANDARDIZATION+MEKAYHAPOAHAH OPTAHM3ALWA O CTAHAAPTM3AUWW+ORGANISATION INTERNATIONALE DE NORMALISATION Chemical analysis of light metals and their alloys Statistical interpretation of inter-laboratory trials Analyse chimique des metaux et des alliages legers -Interpretation statistique des circuits interlaboratoires Technical Report 7242 was drawn up by Technical Committee ISO/TC 79, Light metals and their alloys, and has been approved by the majority of its members. Sub-committee ISO/TC 79/SC 1 considered it preferable to publish this document in the form of a Technical Report, as its purpose is to provide information which could not be considered as a suitable subject for standardization but which is useful for users of stan- dards confronted with the complex problems encountered during statistical studies resulting from round-robin,comparative analytical trials. 0 Introduction The purpose of inter-laboratory trials is to compare the results obtained in terms of two parameters : the methods and the laboratories. The following combinations can therefore be considered : a method tested by several laboratories; several methods tested within one laboratory; two or more methods tested by several laboratories As an example, see tables 1, 2 and 3 relating to the determination of chromium. Whichever combination is selected for the trial, interpretation of the results seeks to establish whether the recorded numerical dif- ferences are mainly due to the influence of the parameter studied (laboratory, method) or whether they can be explained by the dispersionobservedbetween individualresults(repeatability orexperimental error).Inall cases,the results of thestatistical examina- tion should be interpreted from an analytical viewpoint. The repeatability of a method can be sufficiently good for the small inter- laboratory differences to be significant from the statistical point of view, although they can be considered negligible in practice. Con- versely, poor repeatability does not imply that differences considered important by the user are significant. Statistical interpretation, even when using very sophisticated calculation methods, has never corrected the failures of a method, nor hasitimprovedtheresultsfromalaboratory. It is a tool leading very often to conclusions, the essential merit of which is objectivity. SO/TR 7242-1981 (E) UDC669.71/.72:543 Ref.No.ISO/TR7242-1981(E) Descriptors : metals, light alloys, chemical analysis, statistical analysis, determination of content, chromium, spectrophotometric analysis, statistical tables. Price based on 15 pages ISO/TR7242-1981(E) 1 Scopeandfield of application This Technical Report constitutes anattemptto explain thenumerical results of a statistical examination in the simplest possibleway and to show how statistical results can be used in laboratory practice. This simplified method is applicable when the number of laboratories is not more than 20 and when the number of results per laboratory is not more than 10. 2 Symbols Xn : arithmetic mean of n results; Sn : estimated standard deviation of n results; Sx, : estimated standard deviation of the mean of n results : Sn/n; Sn/xn:relative standard deviation or coefficient of variation, as a percentage. NOTE - To add or subtract two standard deviations, determine the sum or difference of their squares and take the square root. 3 Exampleofinterpretationofstatisticalparameters- Determinationof chromium Resuits of an inter-laboratory trial of two methods, A and B, for the determination of chromium are given. It is not intended to give a Individual results are given in tables 1 and 2. The statistical parameters relating to the comparison of both methods are given in table 3. These parameters can be explained, or at standardized method of calculating these parameters. Table 4summarizes explanations relative to the parametersgiven in table3. ISO/TR7242-1981(E) 30 Cr % % DE A