# ASTM C670-15

Designation: C670 − 15Standard Practice forPreparing Precision and Bias Statements for Test Methodsfor Construction Materials1This standard is issued under the fixed designation C670; 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.This standard has been approved for use by agencies of the U.S. Department of Defense.1. Scope*1.1 The Form and Style for ASTM Standards requires thatall test methods contain statements on precision and bias.Further, the precision statement is required to contain astatement on single-operator precision (repeatability) and astatement on multilaboratory precision (reproducibility). Thispractice provides guidance for preparing precision and biasstatements that comply with these requirements. Discussion ofthe purpose and significance of precision and bias statementsfor users of test methods is also provided. Examples ofprecision statements that conform to this practice are includedin Appendix X1. This practice supplements Practice E177 andhas been developed to meet the needs of ASTM Committeesdealing with construction materials.NOTE 1—Although this practice is under the jurisdiction of CommitteeC09, the current version was developed jointly by Committees C01 andC09 and has subsequently been adopted for use by other committeesdealing with construction materials.1.2 This practice assumes that an interlaboratory study(ILS) has been completed in accordance with Practice C802 orPractice E691. The interlaboratory study provides the neces-sary statistical values to write the precision and bias state-ments.1.3 The system of units for this practice is not specified.Dimensional quantities in the practice are presented only inexamples of precision and bias statements.1.4 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:2C802 Practice for Conducting an Interlaboratory Test Pro-gram to Determine the Precision of Test Methods forConstruction MaterialsC1067 Practice for Conducting a Ruggedness Evaluation orScreening Program for Test Methods for ConstructionMaterialsD6607 Practice for Inclusion of Precision Statement Varia-tion in Specification LimitsE177 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 Method3. Terminology3.1 Definitions:3.1.1 For definitions of general statistical terms, refer toTerminology E456.3.2 Definitions of Terms Specific to This Standard:33.2.1 test determination, n—the value of a characteristic ofa single test specimen obtained by a specified test method.3.2.1.1 Discussion—The term “replicate“ is often used for atest determination.3.2.2 test result, n—the value of a characteristic of amaterial obtained by carrying out a specified test method.3.2.2.1 Discussion—A test result may be a single testdetermination or the average of a specified number of testdeterminations, or replicates (see 4.1 for additional discussion).3.2.3 identical test specimens, n—test specimens selected atrandom and made from a single quantity or batch of materialthat is as homogeneous as possible.1This practice is under the jurisdiction of ASTM Committee C09 on Concreteand Concrete Aggregates and is the direct responsibility of Subcommittee C09.94on Evaluation of Data (Joint C09 and C01).Current edition approved June 15, 2015. Published August 2015. Originallyapproved in 1971. Last previous edition approved in 2013 as C670 – 13. DOI:10.1520/C0670-15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3Terms are listed in order of hierarchy beginning with the basic concept.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.3.1 Discussion—In interlaboratory studies of test meth-ods for fresh cementitious mixtures, a practicable approach forobtaining identical tests specimens is to assemble techniciansfrom different laboratories at one location and test specimensare made from the same batch of the fresh mixture. Forinterlaboratory studies of nondestructive test methods, thesame test specimens can be circulated among participatinglaboratories, provided the characteristic of interest does notchange during the time to complete the study.3.2.4 single-operator standard deviation, sr, (or coeffıcientof variation, CVr), n—the standard deviation (or coefficient ofvariation) of test determinations obtained on identical testspecimens by a single operator using the same apparatus in thesame laboratory over a relatively short period of time.3.2.4.1 Discussion—The single-operator standard deviation,or coefficient of variation, is the fundamental statistic under-lying the single-operator indexes of precision. The single-operator standard deviation, or coefficient of variation, is anindication of the variability of a large group of test determina-tions by the same operator on the same material. This value isobtained from an interlaboratory study and is equal to thepooled standard deviation of test determinations obtained bythe operators. The coefficient of variation (ratio of standarddeviation to the average expressed as a percentage) is used ifthe standard deviation is proportional to the level of thecharacteristic being measured. The single-operator standarddeviation, usually considered a property of the test method,will generally be lower than the multilaboratory standarddeviation. In Practice E177, the single-operator standard de-viation is referred to as the repeatability standard deviation,and the subscript r is used. In previous versions of PracticeC670, the terms one-sigma limit (1s) or one sigma limit inpercent (1s%) were used for the single-operator standarddeviation or single-operator coefficient of variation, respec-tively. In some publications, the term within-test standarddeviation (or coeffıcient of variation) has been used. The termwithin-laboratory standard deviation (or coefficient of varia-tion) should not be used for this statistic (see 4.2.3).3.2.5 multilaboratory standard deviation, sR(or coeffıcientof variation, CVR), n—the standard deviation or coefficient ofvariation of test results obtained with the same test method onidentical test specimens in different laboratories with differentoperators using different equipment.3.2.5.1 Discussion—The multilaboratory standarddeviation, or coefficient of variation, is the fundamental statis-tic underlying the indexes of precision under multilaboratoryconditions. The multilaboratory standard deviation is an indi-cation of the variability of a group of test results obtained bydifferent laboratories for identical test specimens. The multi-laboratory standard deviation (or coefficient of variation) isusually greater than the single-operator standard deviation (orcoefficient of variation), because different operators and differ-ent apparatus have been used in different laboratories for whichthe environments may have differed. In Practice E177, themultilaboratory standard deviation is referred to as the repro-ducibility standard deviation and the subscript R is used.3.2.6 difference limit (d2s or d2s%), n—the difference be-tween two test results that is expected to be exceeded with aprobability of about 5 % in the normal and correct operation ofthe test method; used as an index of precision of the testmethod.3.2.6.1 Discussion—The difference limit has been selectedas the appropriate index of precision in most precision state-ments. A difference limit (d2s) indicates the maximum accept-able difference between two results obtained on identical testspecimens (see 3.2.3.1) under the applicable system of causes(single-operator or multilaboratory conditions). The (d2s%)limit is the maximum acceptable difference between two testresults expressed as a percentage of their average. Thesedifference limits are calculated by multiplying the appropriatestandard deviation (sror sR) or coefficient of variation (CVrorCVR) by the factor 1.96 =2, which for the purpose of thisPractice is taken to be equal to 2.8. In Practice E177, the termsrepeatability limit and reproducibility limit are used for thesedifference limits under single-operator and multilaboratoryconditions, respectively.3.2.7 acceptable range, n—the difference between the larg-est and smallest of three or more test determinations or testresults that is expected to be exceeded with a probability ofabout 5 % in the normal and correct operation of the testmethod; used as an index of precision of the test method, ifapplicable.3.2.7.1 Discussion—This index is usually reported in preci-sion statements of test methods that define a test result as theaverage of three or more determinations. Otherwise, thedifference limit (d2s or d2s%) is used. See 4.3 for additionaldiscussion on how to determine this index.4. General Concepts4.1 Test Result—The result of a test method may be a singletest determination or the average of two or more test determi-nations (or replicates). The precision statement of a test methodapplies to a test result as defined in the test method and shouldstate clearly this fact.4.1.1 Number of Test Determinations—The number of testdeterminations required to obtain a test result by a test methodmust be taken into account when evaluating testing variations.The statistic used in evaluating single-operator precision isbased usually on the standard deviation (or coefficient ofvariation) of single test determinations. The single-operatorstandard deviation (or coefficient of variation) may be used inevaluating the acceptable range of test determinations.4.1.2 Test Result Based on Averages of Determinations—For test methods that define a test result as the average of twoor more test determinations (or replicates), the fundamentalstatistic is still the standard deviation (or coefficient of varia-tion) of single test determinations. The report of the analysis ofthe interlaboratory study (see 5.2) must include this statistic.The single-operator standard deviation of test determinationscan be used to calculate the standard deviation of a test resultthat is the average of multiple determinations and therebydefine the maximum acceptable difference between two testC670 − 152results obtained by the same operator on identical test speci-mens. The precision statement may also include the maximumacceptable range of individual determinations that comprise thetest result (see 4.3).4.1.3 Standard Deviation of an Average—The standarddeviation of the average of n test determinations obtained fromidentical specimens taken from the same population is equal tothe standard deviation of the individual determinations dividedby the square root of n. This relationship is valid, however,only if the determinations are obtained using identical speci-mens. It is not applicable to averages obtained on specimensmade from different batches of cementitious mixtures asdiscussed in 4.2.3.4.2 Types of Precision—A precision statement meeting therequirements of this practice normally contains two mainelements: (1) single-operator precision, and (2) multilaboratoryprecision. For test methods that require test results on speci-mens made from more than one batch, the single-operator,multi-batch precision is also included.4.2.1 Single-Operator Precision—The pooled, single-operator standard deviation (or coefficient of variation) of testdeterminations obtained from the interlaboratory study is theunderlying statistic of the test method. This is used to calculatethe greatest difference between two or more determinationsthat would be considered acceptable when properly conductedrepetitive determinations are made on the same material by acompetent operator. As discussed in 4.1.2, the single-operatorstandard deviation (or coefficient of variation) of test determi-nations is also used to calculate the greatest acceptabledifference between test results defined as the average of two ormore determinations. The single-operator precision provides aquantitative guide to acceptable performance by an operator. Iftwo determinations or test results by the same operator differby more than the difference limit, (d2s) or (d2s%), or if therange of more than two determinations or test results exceedsthe values defined in 4.3, there is a high probability that anerror has occurred and retests should be made.NOTE 2—It is beyond the scope of this practice to describe in detailwhat action should be taken in all cases if two test results differ by morethan the (d2s) or (d2s%) limits or the range of more than two determina-tions exceeds the maximum expected range. Such an occurrence is awarning that there may have been some error in the test procedure, orsome departure from the prescribed conditions of the test on which thelimits appearing in the test method are based; for example, faulty ormisadjusted apparatus or improper conditions in the laboratory. In judgingwhether or not results are in error, information other than the differencebetween two test results is needed. Often a review of the circumstancesunder which the test results in question were obtained will reveal somereason for a departure. In this case, the data should be discarded and newtest results obtained and evaluated separately. If no physical reason for adeparture is found, retests should still be made, but the original testsshould not be ignored. If the second set of results also differs by more thanthe applicable limit, the evidence is very strong that something is wrongor that a real difference exists between the specimens tested. If the secondset produces a result within the limit, it may be taken as a valid test, butthe operator or laboratory may then be suspected of producing erraticresults, and a closer examination of the procedures would be in order. Ifknowledge about the test method in question indicates that certain actionsmay be appropriate in cases where deviant results occur, then suchinformation should be included in the test method, but details of how thisshould be done will depend upon the particular test method.4.2.2 Multilaboratory Precision—The multilaboratory stan-dard deviation (or coefficient of variation) obtained from theinterlaboratory study provides a measure of the greatest differ-ence between two test det