1、Designation: E 1950 98 (Reapproved 2003)Standard Practice forReporting Results from Methods of Chemical Analysis1This standard is issued under the fixed designation E 1950; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year o
2、f last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) 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 reported
3、from standard methods 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 informatio
4、nal content of reports 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 acc
5、ordance with existing regulations andgood laboratory practices.2. Referenced Documents2.1 ASTM Standards:2E 29 Practice for Using Significant Digits in Test Data toDetermine Conformance with SpecificationsE 135 Terminology Relating to Analytical Chemistry forMetals, Ores, and Related MaterialsE 1601
6、 Practice for Conducting an Interlaboratory Study toEvaluate the Performance of an Analytical MethodE 1763 Guide for Interpretation and Use of Results from theInterlaboratory Testing of Chemical Analysis Methods3. Terminology3.1 Definitions:3.1.1 For definitions of terms, refer to Terminology E 135.
7、3.2 Definitions of Terms Specific to This Standard:3.2.1 lower limit, L, nthe lower limit of the quantitativeanalyte concentration range.3.2.2 low-level reproducibility index, KR, nthe reproduc-ibility index constant (for low analyte levels) determined inaccordance with Guide E 1763.3.2.3 null limit
8、, NL, nthe analyte 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 PracticeE 29).4. Significance and Use4.1
9、 A result should be stated to a sufficient number of digitsso that 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
10、are to be used to compare 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 o
11、f results may be averaged to yield an average result havingimproved reliability. Results that fall below the lower limit,although not quantitative individually, contain compositionalinformation and shall be reported. The reporting system in thispractice permits the analyst to indicate which values a
12、re likelyto be rendered quantitative 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 appropriately.5. Rounding Calculated Values5.1 Use information from the precisi
13、on 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 ofconcentration or from the table of statistical information.5.1.2 Calculate the percent re
14、lative reproducibility index:Rrel%5 100 3 R / C (1)5.1.3 For results within the range of application 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 es
15、tablish the number of digits andappropriate coding for rounding and reporting the values.1This practice is under the jurisdiction of ASTM Committee E01 on AnalyticalChemistry for Metals, Ores and Related Materials and is the direct responsibility ofSubcommittee E01.22 on Statistics and Quality Contr
16、ol.Current edition approved Oct. 1, 2003. Published November 2003. Originallyapproved in 1998. Last previous edition approved in 1998 as E 1950 98.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandard
17、s 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.5.2 Calculated values shall be rounded to the requirednumber of digits in accordance with the round
18、ing-off methodof Practice E 29.5.2.1 The procedure is summarized as follows:5.2.1.1 When rounding off a number to a specified numberof digits, choose that digit that is nearest. If two choices arepossible, as when the digits dropped are exactly a five or a fivefollowed only by zeros, choose that end
19、ing 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” estimates of zero. If the method occasionally yieldsnegative results for low analyte leve
20、ls, 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 the method to a “blank”sample or one known to have a negligible analyte content butt
21、hat 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 determinations,several zeros but no negative values are observed, it is a“biased-zero
22、” 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 necessary). Determine thedecimal place of the second digit.6.2.2 Calculate the null
23、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“biased-zero” methods in accordance with 6.1.1 and 6.4.6.3.2 Results Less Than LRo
24、und 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 0.00050, round to 0.000xx and report (0.000xx).6.3.3 Results Less Than NLIf the me
25、thod 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 Special Rule for “Biased-Zero” Methods:6.4.1 For results from “biased-zero” me
26、thods 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 Explanations of Coding Symbols:6.6.1 If results less than L are reported for a
27、ny 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 values cannot bedistinguished from zero.6.6.3 If the symbol ( )* is reported for
28、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 without enclosing paren-theses are quantitative results and may be used for comparisonswith spe
29、cified 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 values that are quantitative if a sufficient number areaveraged (see A2.2.3).
30、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 results (morethan 25), even the first digit is not likely to be significan
31、t.8. Keywords8.1 quantitative results; reporting resultsTABLE 1 Rounding GuideRrel%Numberof Digits5-50% 20.5-5% 30.05 - 0.5 % 40.05 % 5E 1950 98 (2003)2ANNEXES(Mandatory Information)A1. STATISTICAL BASIS FOR QUANTITATION CRITERIAA1.1 Quantitation is the ability to determine a result whosevalue may b
32、e compared with specified limiting values. PracticeE 29 adds the concept of significant digits. This term is used inthis practice to identify the digits in a value that are notexpected to change appreciably if the result is redetermined.The statistical basis for quantitation is found in Practice E 1
33、601and Guide E 1763. 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 that limit ifresults are to exhibit at least one significant digit.A1.
34、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 analytecontent at which R represents a 50 % relative error. At thisanal
35、yte content, the average difference (50 % confidence level)between results in two laboratories is about 18 % of their mean.Results at this analyte level are quantitative with approximatelyone significant digit, and, in accordance with Practice E 29 andcommon statistical practice, are reported with t
36、wo 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 testmaterials (Practice E 1601) or the equation relating R to analyteconcent
37、ration (for ILS evaluated in accordance with Guide E1763) 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 threedigits (the first two are significant.) If Rrel%is 0.5 % or les
38、s,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 practice, but theirvalues contain information concerning the analy
39、te content.These results are reported, but their use for individual com-parisons is discouraged.A1.2.1 Guide E 1763 provides calculations for KR, theconstant value R achieves at analyte contents near L and lower.This value of R divided by 2.8 yields the reproducibilitystandard deviation, sR, which,
40、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 interpretive process to decide how the data may beused.A1.2.2 The ultimate u
41、ser, 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 in four laboratories, the relative variability ofsuch an average (
42、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 user is willing toexpend. A reasonable (though arbitrary) limit i
43、s 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 practical purposes, indistinguishablefrom zero.A2. PRACTICAL BASIS FOR Q
44、UANTITATION CRITERIAA2.1 The practical basis for quantitation must provideguidance to analysts and users of results who have littlestatistical training. The criteria should be consistent with theILS statistics and criteria discussed in Annex A1, simple tounderstand, and convenient to use. The coding
45、 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 be-tween the upper and lower application limits stated in themethod.
46、 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 unlikely to be quantitative.Individual and average values that are less th
47、an 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 bequantitative. The number of values needed to obtain a quanti-tative averag
48、e 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 the methods scope) and the calculated value ofNL (L/4). Class 1 resu
49、lts are quantitative and are reporteduncoded. Class 2 and Class 3 results are not quantitative; thisE 1950 98 (2003)3fact 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 andinterpret, and does not affect the readability of tables of data.APPEND
