1、Designation: E1950 10Standard 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 revision. A n
2、umber 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 digitsrequired to express the expected precision of results reportedfrom standard methods
3、 of chemical analysis. This practiceprovides selection criteria and proper form and symbols forcoding results when necessary to indicate the relative reliabilityof results having small values.1.2 Specifically excluded is consideration of report formsand the associated informational content of report
4、s in whichresults are tabulated or transmitted. It is assumed that thereporting laboratory has established a report format to ensureproper identification of the materials tested, the nature andconditions of the test, the responsible personnel, and otherrelated information in accordance with existing
5、 regulations andgood laboratory practices.2. Referenced Documents2.1 ASTM Standards:2E29 Practice for Using Significant Digits in Test Data toDetermine Conformance with SpecificationsE135 Terminology Relating to Analytical Chemistry forMetals, Ores, and Related MaterialsE1601 Practice for Conducting
6、 an Interlaboratory Study toEvaluate the Performance of an Analytical MethodE1763 Guide for Interpretation and Use of Results fromInterlaboratory Testing of Chemical Analysis Methods3. Terminology3.1 Definitions:3.1.1 For definitions of terms, refer to Terminology E135.3.2 Definitions of Terms Speci
7、fic to This Standard:3.2.1 lower limit, L, nthe lower limit of the quantitativeanalyte concentration range (see Annex A1).3.2.2 low-level reproducibility index, KR, nthe reproduc-ibility index constant (for low analyte levels) determined inaccordance with Guide E1763.3.2.3 null limit, NL, nthe analy
8、te content below whichresults are so near zero that averaging is unlikely to yield avalue significantly different from zero.3.2.4 quantitative, adjrelating to results, having a numeri-cal value that includes at least one significant digit (see PracticeE29).4. Significance and Use4.1 Aresult must be
9、stated to a sufficient number of digits sothat a user receives both quantitative information and ameasure of the variability of the value reported.4.2 The range of application of most methods of chemicalanalysis is based upon the presumption that the quantitativeresults produced are to be used to co
10、mpare the analyte contentof the test material with specified limiting values. However,analytical results may be used legitimately for other purposes.If the same material is analyzed a number of times or a productis analyzed periodically during an interval of production, eachset of results may be ave
11、raged to yield an average result havingimproved reliability, provided nothing has been done betweenanalyses to modify the composition of the analyzed material.Results that fall below the lower limit, although not quantita-tive individually, contain compositional information and maybe reported. The r
12、eporting system in this practice permits theanalyst to indicate which values are likely to be renderedquantitative by averaging and which are not.4.3 The system is simple enough to be used routinely inreporting results from standard methods and assists thoseuntrained in statistics to apply results a
13、ppropriately.5. Rounding Calculated Values5.1 Use information from the precision section of themethod to determine the appropriate number of digits to reportas follows:5.1.1 Estimate the reproducibility index, R, at the analytelevel of the result, C, from an equation of R as a function ofconcentrati
14、on or from the table of statistical information.5.1.2 Calculate the percent relative reproducibility index:Rrel%5 100 3 R / C (1)1This practice is under the jurisdiction of ASTM Committee E01 on AnalyticalChemistry for Metals, Ores, and Related Materials and is the direct responsibility ofSubcommitt
15、ee E01.22 on Laboratory Quality.Current edition approved Oct. 1, 2010. Published December 2010. Originallyapproved in 1998. Last previous edition approved in 2003 as E1950 98 (2003).DOI: 10.1520/E1950-10.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Se
16、rvice at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.5.1.3 For results within the range of appl
17、ication specified inthe method, round the values to the number of digits specifiedin Table 1 (see A1.1.1 through A1.1.2).5.1.4 For results less than the lower limit, proceed inaccordance with Section 6 to establish the number of digits andappropriate coding for rounding and reporting the values.5.2
18、Calculated values shall be rounded to the requirednumber of digits in accordance with the rounding method ofPractice E29.5.2.1 The procedure is summarized as follows:5.2.1.1 When rounding a number to a specified number ofdigits, choose that digit that is nearest. If two choices arepossible, as when
19、the digits dropped are exactly a five or a fivefollowed only by zeros, choose that end in an even digit.6. Procedure6.1 Preliminary PrecautionFor a method to be used toanalyze materials with analyte content very near zero, theanalyst shall determine that it is capable of producing “unbi-ased” estima
20、tes of zero. If the method occasionally yieldsnegative results for low analyte levels, that capability isdemonstrated. Proceed in accordance with 6.2.6.1.1 Test for “Biased-Zero” MethodsPrepare the methodto perform determinations. Include all aspects of instrumentpreparation and calibration. Apply t
21、he method to a “blank”sample or one known to have negligible analyte content butthat meets the methods scope requirements in all otherrespects. If the method yields a negative result, it is not a“biased-zero” method; proceed in accordance with 6.2. If,during the course of at least ten replicate dete
22、rminations,several zeros but no negative values are observed, it is a“biased-zero” method. Apply the biased-zero rule of 6.4 inreporting results lower than NL (see 6.2.2).6.2 Critical Concentrations:6.2.1 From the method, obtain the value of the lower limit,L, to two digits (add a final zero, if nec
23、essary). Determine thedecimal place of the second digit.6.2.2 Calculate the null limit as follows:NL 5 L / 4 (2)6.3 Basic Rules:6.3.1 Numerical values shall be reported for every result(including negative values) obtained from a properly con-ducted method except as provided for certain results from“
24、biased-zero” methods in accordance with 6.1.1 and 6.4.6.3.2 Results Less Than LRound values to the seconddecimal place of L, and enclose in parentheses before report-ing. 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 equalto 0
25、.00050, round to 0.000xx and report (0.000xx).6.3.3 Results Less Than NLIf the method is a “biased-zero” procedure, treat in accordance with 6.4; otherwise, roundin accordance with 6.3.2, and enclose in parentheses followedby an asterisk before reporting. Examples: (0.2)*, (0.04)*,and (0.00003)*.6.4
26、 Special Rule for “Biased-Zero” Methods:6.4.1 For results from “biased-zero” methods only, do notreport numerical values for results less than NL. Replace themwith the symbol ( )*.6.5 Reference to the Method:6.5.1 Cite the designation of the standard method used todetermine each analyte reported.6.6
27、 Explanations of Coding Symbols:6.6.1 If results less than L are reported for any analyte,append the following explanation:NOTE 1Results in parentheses are not reliable for individual compari-sons.6.6.2 If results less than NL are reported for any analyte,append the following explanation: * These va
28、lues cannot bedistinguished from zero.6.6.3 If the symbol ( )* is reported for any analyte,append the following explanation: ( )* The method cannotreport an unbiased estimate at this low analyte level.7. Use of Uncoded and Coded Values7.1 Uncoded Data:7.1.1 Numerical values reported not enclosed in
29、parenthesesare 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, individual values are not suitable for comparisons.However, data in parentheses not followed by an asterisk mayyield val
30、ues that are quantitative if a sufficient number areaveraged (see A2.2.3).7.2.2 Values coded with an asterisk are from materials thatare likely to produce randomly occurring negative values forrepeated determinations. They may be averaged, but unless theaverage includes a large number of individual
31、results (morethan 25), even the first digit is not likely to be significant.8. Keywords8.1 quantitative results; reporting resultsTABLE 1 Rounding GuideRrel %Number of Digits5%50% 20.5%5% 30.05 % 0.5 % 40.05% 5E1950 102ANNEXES(Mandatory Information)A1. STATISTICAL BASIS FOR QUANTIFICATION CRITERIAA1
32、.1 Quantification is the ability to determine a resultwhose value may be compared with specified limiting values.Practice E29 adds the concept of significant digits. This term isused in this practice to identify the digits in a value that are notexpected to change appreciably if the result is redete
33、rmined.The statistical basis for quantification is found in PracticeE1601 and Guide E1763. The lower limit (L) of a methodsquantitative range is calculated from its reproducibility index,R, which is determined in the interlaboratory study (ILS). Theanalyte content of a material must be greater than
34、that limit ifresults are to exhibit at least one significant digit.A1.1.1 R represents the largest difference between resultsobtained in two laboratories on the same material that is notexpected to be exceeded in more than 1 in 20 comparisons (95% confidence level). L is arbitrarily defined as the a
35、nalytecontent at which R represents a 50 % relative error. At thisanalyte content, the average difference (50 % confidence level)between results in two laboratories is about 18 % of their mean.A result at this analyte level is quantitative with approximatelyone significant digit, and, in accordance
36、with Practice E29 andcommon statistical practice, is reported with two digits topreserve the statistical information it contains. Only the firstdigit is considered significant.A1.1.2 Users of standard methods (or data obtained fromthem) can use R values reported at the analyte levels of the testmate
37、rials (Practice E1601) or the equation relating R to analyteconcentration (for ILS evaluated in accordance with GuideE1763) to estimate the reliability of data at any concentrationwithin the quantitative range of the method. If Rrel%is5%orless relative to the determined value, report results with th
38、reedigits (the first two are significant.) If Rrel%is 0.5 % or less,report four digits (the first three are significant.) If Rrel%is 0.05% or less, report five digits (the first four are significant.)A1.2 Results from materials with analyte content less thanL are not quantitative as defined in this
39、practice, but theirvalues contain information concerning the analyte content.These results are reported, but their use for individual com-parisons is discouraged.A1.2.1 Guide E1763 provides calculations for KR, theconstant value R achieves at analyte contents near L and lower.This value of R divided
40、 by 2.8 yields the reproducibilitystandard deviation, sR, which, added to and subtracted from aresult, signifies a confidence interval. While indicating uncer-tainty, this approach does not lend itself to easy recognition ofa values reliability because the user must apply a rathercomplex interpretiv
41、e process to decide how the data may beused.A1.2.2 The ultimate user, if willing to expend time andresources, can reduce variability by averaging a number ofresults from the same material obtained in different laborato-ries. For example, if a material having an analyte content of Ris analyzed once i
42、n four laboratories, the relative variability ofsuch an average (four values) is 50 %, the same as thevariability of single results from a material with twice theanalyte content (that is, at L).A1.2.3 The limit to the enhancement in precision by repli-cation is established only by the resources the
43、user is willing toexpend. A reasonable (though arbitrary) limit is the null limit,NL = R/2 (which is equivalent to L/4). The null limit is thelowest analyte level at which the average of 16 or more resultsyields an average value having at least one significant digit.Results below NL are, for practic
44、al purposes, indistinguishablefrom zero.A2. PRACTICAL BASIS FOR QUANTIFICATION CRITERIAA2.1 The practical basis for quantification must provideguidance to analysts and users of results who have littlestatistical training. The criteria should be consistent with theILS statistics and criteria discusse
45、d in Annex A1, simple tounderstand, and convenient to use. The coding applied to eachvalue should give an unmistakable visual indication of itsreliability.A2.2 A system to meet these requirements classifies resultsinto three concentration ranges:A2.2.1 Class 1 consists of results with values falling
46、 be-tween the upper and lower application limits stated in themethod. These results are expected to be quantitative asdiscussed in Annex A1.A2.2.2 Class 3 consists of results with values less than NL.As discussed in A1.2.3, not only are individual results notquantitative, but averages are also unlik
47、ely to be quantitative.Individual and average values that are less than NL areexpected to be estimates of zero.A2.2.3 Class 2 consists of results with values falling withinthe range NL to L. Individual results are not quantitative, butaverages of values obtained in different laboratories may bequant
48、itative. The number of values needed to obtain a quanti-tative average ranges from 2 (at analyte levels just less than L)to 16 (at analyte levels just greater than NL).A2.3 The classifications in A2.2 meet the requirements inA2.1. The analyst classifies each result by comparing its valuewith L (from
49、 the methods scope) and the calculated value ofNL (L/4). Class 1 results are quantitative and are reporteduncoded. Class 2 and Class 3 results are not quantitative; thisE1950 103fact is visually indicated by enclosing their values in parenthe-ses. Class 2 results produce quantitative values if a sufficientnumber of independent results are averaged. Class 3 results areunlikely to produce quantitative average values, a fact visuallyindicated by enclosing the results in parentheses and adding anasterisk. This type of coding is simple, easy to implement andint
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