1、Designation: E1950 10E1950 17Standard Practice forReporting Results from Methods of Chemical Analysis1This standard is issued under the fixed designation E1950; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revis
2、ion. 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 the approximate number of digits required to express the expected precision of results reported fromstandar
3、d methods of chemical analysis. This practice provides selection criteria and proper form and symbols for coding resultswhen necessary to indicate the relative reliability of results having small values.1.2 Specifically excluded is consideration of report forms and the associated informational conte
4、nt of reports in which resultsare tabulated or transmitted. It is assumed that the reporting laboratory has established a report format to ensure properidentification of the materials tested, the nature and conditions of the test, the responsible personnel, and other related informationin accordance
5、 with existing regulations and good laboratory practices.1.3 This international standard was developed in accordance with internationally recognized principles on standardizationestablished in the Decision on Principles for the Development of International Standards, Guides and Recommendations issue
6、dby the World Trade Organization Technical Barriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E29 Practice for Using Significant Digits in Test Data to Determine Conformance with SpecificationsE135 Terminology Relating to Analytical Chemistry for Metals, Ores, and Related M
7、aterialsE1601 Practice for Conducting an Interlaboratory Study to Evaluate the Performance of an Analytical MethodE1763 Guide for Interpretation and Use of Results from Interlaboratory Testing of Chemical Analysis Methods (Withdrawn2015)33. Terminology3.1 Definitions:3.1.1 For definitions of terms,
8、refer to Terminology E135.3.2 Definitions of Terms Specific to This Standard:3.2.1 lower limit, L, nthe lower limit of the quantitative analyte mass fraction or concentration range (see Annex A1).3.2.2 low-level reproducibility index, KR, nthe reproducibility index constant (for low analyte levels)
9、determined inaccordance withas directed by Guide E1763.3.2.3 null limit, NL, nthe analyte content below which results are so near zero that averaging is unlikely to yield a valuesignificantly different from zero.3.2.4 quantitative, adjrelating to results, having a numerical value that includes at le
10、ast one significant digit (see PracticeE29).4. Significance and Use4.1 A result must be stated to a sufficient number of digits so that a user receives both quantitative information and a measureof the variability of the value reported.1 This practice is under the jurisdiction of ASTM Committee E01
11、on Analytical Chemistry for Metals, Ores, and Related Materials and is the direct responsibility ofSubcommittee E01.22 on Laboratory Quality.Current edition approved Oct. 1, 2010Nov. 15, 2017. Published December 2010 December 2017. Originally approved in 1998. Last previous edition approved in 20032
12、010as E1950 98 (2003).E1950 10. DOI: 10.1520/E1950-10.10.1520/E1950-17.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the AST
13、M website.3 The last approved version of this historical standard is referenced on www.astm.org.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically po
14、ssible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700,
15、West Conshohocken, PA 19428-2959. United States14.2 The range of application of most methods of chemical analysis is based upon the presumption that the quantitative resultsproduced are to be used to compare the analyte content of the test material with specified limiting values. However, analytical
16、results may be used legitimately for other purposes. If the same material is analyzed a number of times or a product is analyzedperiodically during an interval of production, each set of results may be averaged to yield an average result having improvedreliability, provided nothing has been done bet
17、ween analyses to modify the composition of the analyzed material. Results that fallbelow the lower limit, although not quantitative individually, contain compositional information and may be reported. Thereporting system in this practice permits the analyst to indicate which values are likely to be
18、rendered quantitative by averagingand which are not.4.3 The system is simple enough to be used routinely in reporting results from standard methods and assists those untrained instatistics to apply results appropriately.5. Rounding Calculated Values5.1 Use information from the precision section of t
19、he method to determine the appropriate number of digits to report as follows:5.1.1 Estimate the reproducibility index, R, at the analyte level of the result, C, from an equation of R as a function ofconcentration or mass fraction, or from the table of statistical information.5.1.2 Calculate the perc
20、ent relative reproducibility index:Rrel%51003R/C (1)5.1.3 For results within the range of application specified in the method, round the values to the number of digits specified inTable 1 (see A1.1.1 through A1.1.2).5.1.4 For results less than the lower limit, proceed in accordance withas directed i
21、n Section 6 to establish the number of digitsand appropriate coding for rounding and reporting the values.5.2 Calculated values shall be rounded to the required number of digits in accordance with the rounding method of Practice E29.5.2.1 The procedure is summarized as follows:5.2.1.1 When rounding
22、a number to a specified number of digits, choose that digit that is nearest. If two choices are possible,as when the digits dropped are exactly a five or a five followed only by zeros, choose that end in an even digit.6. Procedure6.1 Preliminary PrecautionFor a method to be used to analyze materials
23、 with analyte content very near zero, the analyst shalldetermine that it is capable of producing “unbiased” estimates of zero. If the method occasionally yields negative results for lowanalyte levels, that capability is demonstrated. Proceed in accordance withas directed in 6.2.6.1.1 Test for “Biase
24、d-Zero” MethodsPrepare the method to perform determinations. Include all aspects of instrumentpreparation and calibration.Apply the method to a “blank” sample or one known to have negligible analyte content but that meetsthe methods scope requirements in all other respects. If the method yields a ne
25、gative result, it is not a “biased-zero” method;proceed in accordance with method as directed in 6.2. If, during the course of at least ten replicate determinations, several zerosbut no negative values are observed, it is a “biased-zero” method.Apply the biased-zero rule of 6.4 in reporting results
26、lower thanNL (see 6.2.2).6.2 Critical Concentrations: Concentrations or Mass Fractions:6.2.1 From the method, obtain the value of the lower limit, L, to two digits (add a final zero, if necessary). Determine thedecimal place of the second digit.6.2.2 Calculate the null limit as follows:NL5L/4 (2)6.3
27、 Basic Rules:6.3.1 Numerical values shall be reported for every result (including negative values) obtained from a properly conductedmethod except as provided for certain results from “biased-zero” methods in accordance withas directed in 6.1.1 and 6.4.6.3.2 Results Less Than LRound values to the se
28、cond decimal place of L, and enclose in parentheses before reporting.Examples: For L equal to 1.5, round to x.x and report (x.x); for L equal to 0.22, round to 0.xx and report (0.xx); for L equal to0.00050, round to 0.000xx and report (0.000xx).TABLE 1 Rounding GuideRrel % Number of Digits5 % 50 % 2
29、0.5 % 5 % 30.05 % 0.5 % 4 0.05 % 5E1950 1726.3.3 Results Less Than NLIf the method is a “biased-zero” procedure, treat in accordance with “biased-zero,” treat as directedin 6.4; otherwise, round in accordance with 6.3.2, and enclose in parentheses followed by an asterisk before reporting. Examples:(
30、0.2)*, (0.04)*, and (0.00003)*.6.4 Special Rule for “Biased-Zero” Methods:6.4.1 For results from “biased-zero” methods only, do not report numerical values for results less than NL. Replace them withthe symbol ( )*.6.5 Reference to the Method:6.5.1 Cite the designation of the standard method used to
31、 determine each analyte reported.6.6 Explanations of Coding Symbols:6.6.1 If results less than L are reported for any analyte, append the following explanation:explanation (results in parentheses arenot reliable for individual comparisons):NOTE 1Results in parentheses are not reliable for individual
32、 comparisons.6.6.2 If results less than NL are reported for any analyte, append the following explanation: * These values cannot bedistinguished from zero.6.6.3 If the symbol ( )* is reported for any analyte, append the following explanation: ( )* The method cannot report anunbiased estimate at this
33、 low analyte level.7. Use of Uncoded and Coded Values7.1 Uncoded Data:7.1.1 Numerical values reported not enclosed in parentheses are quantitative results and may be used for comparisons withspecified limiting values.7.2 Coded Data:7.2.1 Values enclosed in parentheses are not quantitative, that is,
34、individual values are not suitable for comparisons. However,data in parentheses not followed by an asterisk may yield values that are quantitative if a sufficient number are averaged (seeA2.2.3).7.2.2 Values coded with an asterisk are from materials that are likely to produce randomly occurring nega
35、tive values forrepeated determinations. They may be averaged, but unless the average includes a large number of individual results (more than25), even the first digit is not likely to be significant.8. Keywords8.1 quantitative results; reporting resultsANNEXES(Mandatory Information)A1. STATISTICAL B
36、ASIS FOR QUANTIFICATION CRITERIAA1.1 Quantification is the ability to determine a result whose value may be compared with specified limiting values. Practice E29adds the concept of significant digits. This term is used in this practice to identify the digits in a value that are not expected tochange
37、 appreciably if the result is redetermined. The statistical basis for quantification is found in Practice E1601 and GuideE1763. The lower limit (L) of a methods quantitative range is calculated from its reproducibility index, R, which is determinedin the interlaboratory study (ILS). The analyte cont
38、ent of a material must be greater than that limit if results are to exhibit at leastone significant digit.A1.1.1 R represents the largest difference between results obtained in two laboratories on the same material that is not expectedto be exceeded in more than 1 in 20 comparisons (95 % confidence
39、level). L is arbitrarily defined as the analyte content at whichR represents a 50 % relative error. At this analyte content, the average difference (50 % confidence level) between results in twolaboratories is about 18 % of their mean.Aresult at this analyte level is quantitative with approximately
40、one significant digit, and,in accordance withas directed in Practice E29 and common statistical practice, is reported with two digits to preserve the statisticalinformation it contains. Only the first digit is considered significant.A1.1.2 Users of standard methods (or data obtained from them) can u
41、se R values reported at the analyte levels of the test materials(Practice E1601) or the equation relating R to analyte concentration or mass fractions (for ILS evaluated in accordance withasE1950 173directed in Guide E1763) to estimate the reliability of data at any concentration within the quantita
42、tive range of the method. If Rrel%is 5 % or less relative to the determined value, report results with three digits (the first two are significant.) If Rrel% is 0.5 % orless, report four digits (the first three are significant.) If Rrel% is 0.05 % or less, report five digits (the first four are sign
43、ificant.)A1.2 Results from materials with analyte content less than L are not quantitative as defined in this practice, but their values containinformation concerning the analyte content. These results are reported, but their use for individual comparisons is discouraged.A1.2.1 Guide E1763 provides
44、calculations for KR, the constant value R achieves at analyte contents near L and lower. This valueof R divided by 2.8 yields the reproducibility standard deviation, sR, which, added to and subtracted from a result, signifies aconfidence interval. While indicating uncertainty, this approach does not
45、 lend itself to easy recognition of a values reliabilitybecause the user must apply a rather complex interpretive process to decide how the data may be used.A1.2.2 The ultimate user, if willing to expend time and resources, can reduce variability by averaging a number of results fromthe same materia
46、l obtained in different laboratories. For example, if a material having an analyte content of R is analyzed once infour laboratories, the relative variability of such an average (four values) is 50 %, the same as the variability of single results froma material with twice the analyte content (that i
47、s, at L).A1.2.3 The limit to the enhancement in precision by replication is established only by the resources the user is willing to expend.A reasonable (though arbitrary) limit is the null limit, NL = R/2 (which is equivalent to L/4). The null limit is the lowest analytelevel at which the average o
48、f 16 or more results yields an average value having at least one significant digit. Results below NLare, for practical purposes, indistinguishable from zero.A2. PRACTICAL BASIS FOR QUANTIFICATION CRITERIAA2.1 The practical basis for quantification must provide guidance to analysts and users of resul
49、ts who have little statisticaltraining. The criteria should be consistent with the ILS statistics and criteria discussed in Annex A1, simple to understand, andconvenient to use. The coding applied to each value should give an unmistakable visual indication of its reliability.A2.2 A system to meet these requirements classifies results into three concentration or mass fraction ranges:A2.2.1 Class 1 consists of results with values falling between the upper and lower application limits stated in the method. Theseresults are expected to be quantitative as
