ASTM_E_1970_-_11.pdf

Designation:E197011Standard Practice forStatistical Treatment of Thermoanalytical Data1This standard is issued under the fixed designation E1970;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 details the statistical data treatment used insome thermal analysis methods.1.2 The method describes the commonly encountered sta-tistical tools of the mean,standard derivation,relative standarddeviation,pooled standard deviation,pooled relative standarddeviation and the best fit to a straight line,all calculationsencountered in thermal analysis methods.1.3 Some thermal analysis methods derive the analyticalvalue from the slope or intercept of a best fit straight lineassigned to three or more sets of data pairs.Such methods mayrequire an estimation of the precision in the determined slopeor intercept.The determination of this precision is not acommon statistical tool.This practice details the process forobtaining such information about precision.1.4 There are no ISO methods equivalent to this practice.2.Referenced Documents2.1 ASTM Standards:2E177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE456 Terminology Relating to Quality and StatisticsE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE2161 Terminology Relating to Performance Validation inThermal AnalysisF1469 Guide for Conducting a Repeatability and Reproduc-ibility Study on Test Equipment for Nondestructive Test-ing3.Terminology3.1 DefinitionsThe technical terms used in this practiceare defined in Practice E177 and Terminologies E456 andE2161 including precision,relative standard deviation,repeat-ability,reproducibility,slope,standard deviation,thermoana-lytical,and variance.3.2 Symbols:3m=slopeb=interceptn=number of data sets(that is,xi,yi)xi=an individual independent variable observationyi=an individual dependent variable observationS=mathematical operation which means“the sum ofall”for the term(s)following the operatorX=mean values=standard deviationspooled=pooled standard deviationsb=standard deviation of the line interceptsm=standard deviation of the slope of a linesy=standard deviation of Y valuesRSD=relative standard deviationdyi=variance in y parameterr=correlation coefficientR=gage reproducibility and repeatability(see GuideF1469)an estimation of the combined variation ofrepeatability and reproducibility4sr=within laboratory repeatability standard deviation(see Practice E691)sR=between laboratory repeatability standard deviation(see Practice E691)4.Summary of Practice4.1 The result of a series of replicate measurements of avalue are typically reported as the mean value plus someestimation of the precision in the mean value.The standarddeviation is the most commonly encountered tool for estimat-ing precision,but other tools,such as relative standard devia-tion or pooled standard deviation,also may be encountered inspecific thermoanalytical test methods.This practice describesthe mathematical process of achieving mean value,standarddeviation,relative standard deviation and pooled standarddeviation.1This practice is under the jurisdiction of ASTM Committee E37 on ThermalMeasurements and is the direct responsibility of Subcommittee E37.10 on Funda-mental,Statistical and Mechanical Properties.Current edition approved Aug.1,2011.Published August 2011.Originallyapproved in 1998.Last previous edition approved in 2006 as E1970 06.DOI:10.1520/E1970-11.2For 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.3Taylor,J.K.,Handbook for SRM Users,Publication 260-100,National Instituteof Standards and Technology,Gaithersburg,MD,1993.4Measurement System Analysis,third edition,Automotive Industry ActionGroup,Southfield,MI,2003,pp.55,177184.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 4.2 In some thermal analysis experiments,a linear or astraight line,response is assumed and desired values areobtained from the slope or intercept of the straight line throughthe experimental data.In any practical experiment,however,there will be some uncertainty in the data so that results arescattered about such a straight line.The least squares method isan objective tool for determining the“best fit”straight linedrawn through a set of experimental results and for obtaininginformation concerning the precision of determined values.4.2.1 For the purposes of this practice,it is assumed that thephysical behavior,which the experimental results approximate,are linear with respect to the controlled value,and may berepresent