ASTM_E_2586_-_14.pdf

Designation:E258614An American National StandardStandard Practice forCalculating and Using Basic Statistics1This standard is issued under the fixed designation E2586;the number immediately following the designation indicates the year oforiginal adoption or,in the case of revision,the year of last revision.A number in parentheses indicates the year of last reapproval.Asuperscript epsilon()indicates an editorial change since the last revision or reapproval.1.Scope1.1 This practice covers methods and equations for comput-ing and presenting basic descriptive statistics using a set ofsample data containing a single variable or two variables.Thispractice includes simple descriptive statistics for variable data,tabular and graphical methods for variable data,and methodsfor summarizing simple attribute data.Some interpretation andguidance for use is also included.1.2 The system of units for this practice is not specified.Dimensional quantities in the practice are presented only asillustrations of calculation methods.The examples are notbinding on products or test methods treated.1.3 This standard does not purport to address all of thesafety concerns,if any,associated with its use.It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2.Referenced Documents2.1 ASTM Standards:2E178 Practice for Dealing With Outlying ObservationsE456 Terminology Relating to Quality and StatisticsE2282 Guide for Defining the Test Result of a Test Method2.2 ISO Standards:3ISO 3534-1 StatisticsVocabulary and Symbols,part 1:Probability and General Statistical TermsISO 3534-2 StatisticsVocabulary and Symbols,part 2:Applied Statistics3.Terminology3.1 Definitions:3.1.1 Unless otherwise noted,terms relating to quality andstatistics are as defined in Terminology E456.3.1.2 characteristic,na property of items in a sample orpopulation which,when measured,counted,or otherwiseobserved,helps to distinguish among the items.E22823.1.3 coeffcient of determination,nsquare of the correla-tion coefficient,r.3.1.4 coeffcient of variation,CV,nfor a nonnegativecharacteristic,the ratio of the standard deviation to the meanfor a population or sample3.1.4.1 DiscussionThe coefficient of variation is oftenexpressed as a percentage.3.1.4.2 DiscussionThis statistic is also known as therelative standard deviation,RSD.3.1.5 confidence bound,nsee confidence limit.3.1.6 confidence coeffcient,nsee confidence level.3.1.7 confidence interval,nan interval estimate L,Uwith the statistics L and U as limits for the parameter andwith confidence level 1 ,where Pr(L U)1 .3.1.7.1 DiscussionThe confidence level,1 ,reflects theproportion of cases that the confidence interval L,U wouldcontain or cover the true parameter value in a series of repeatedrandom samples under identical conditions.Once L and U aregiven values,the resulting confidence interval either does ordoes not contain it.In this sense confidence applies not to theparticular interval but only to the long run proportion of caseswhen repeating the procedure many times.3.1.8 confidence level,nthe value,1 ,of the probabilityassociated with a confidence interval,often expressed as apercentage.3.1.8.1 Discussion is generally a small number.Confi-dence level is often 95%or 99%.3.1.9 confidence limit,neach of the limits,L and U,of aconfidence interval,or the limit of a one-sided confidenceinterval.3.1.10 correlation coeffecient,nfor a population,ademensionless measure of association between two variables Xand Y,equal to the covariance divided by the product of Xtimes Y.3.1.11 correlation coeffecient,nfor a sample,r,the quan-tity:1This practice is under the jurisdiction ofASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.10 on Sampling/Statistics.Current edition approved June 1,2014.Published January 2015.Originallyapproved in 2007.Last previous edition approved in 2014 as E2586 13.DOI:10.1520/E2586-14.2For referenced ASTM standards,visit the ASTM website,www.astm.org,orcontact ASTM Customer Service at serviceastm.org.For Annual Book of ASTMStandards volume information,refer to the standards Document Summary page onthe ASTM website.3Available from American National Standards Institute(ANSI),25 W.43rd St.,4th Floor,New York,NY 10036,http:/www.ansi.org.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 x 2 x!y 2 y!n 2 1!sxsy(1)3.1.12 covariance,nof a population,cov(X,Y),for twovariables,X and Y,the expected value of(X X)(Y Y).3.1.13 covariance,nof a sample;the quantity:x 2 x!y 2 y!n 2 1!(2)3.1.14 dependent variable,na variable to be predictedusing an equation.3.1.15 degrees of freedom,nthe number of independentdata points minus the number of parameters that have to beestimated before calculating the variance.3.1.16 estimate,nsample statistic used to approximate apopulation parameter.3.1.17 histogram,ngra