Designation: E1950 − 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 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 covers the approximate number of digitsrequired to express the expected precision of results reportedfrom 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 informational 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 accordance with existing regulations andgood laboratory practices.1.3 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.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 an Interlaboratory Study toEvaluate the Performance of an Analytical MethodE1763 Guide for Interpretation and Use of Results fromInterlaboratory Testing of Chemical Analysis Methods(Withdrawn 2015)33. Terminology3.1 Definitions:3.1.1 For definitions of terms, refer to Terminology E135.3.2 Definitions of Terms Specific to This Standard:3.2.1 lower limit, L, n—the lower limit of the quantitativeanalyte mass fraction or concentration range (see Annex A1).3.2.2 low-level reproducibility index, KR,n—the reproduc-ibility index constant (for low analyte levels) determined asdirected by Guide E1763.3.2.3 null limit, NL, n—the analyte content below whichresults are so near zero that averaging is unlikely to yield avalue significantly different from zero.3.2.4 quantitative, adj—relating to results, having a numeri-cal value that includes at least one significant digit (see PracticeE29).4. Significance and Use4.1 Aresult must be 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 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 of results may be averaged 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 reporting system in this practice permits theanalyst to indicate which values are likely to be renderedquantitative by averaging and which are not.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 Laboratory Quality.Current edition approved Nov. 15, 2017. Published December 2017. Originallyapproved in 1998. Last previous edition approved in 2010 as E1950 – 10. DOI:10.1520/E1950-17.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3The last approved version of this historical standard is referenced onwww.astm.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States14.3 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 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 ofconcentration or mass fraction, or from the table of statisticalinformation.5.1.2 Calculate the percent relative reproducibility index:Rrel%5 100 3R/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 asdirected in Section 6 to establish the number of digits andappropriate coding for rounding and reporting the values.5.2 Calculated values shall be rounded to the requirednumber of digits in accordance with the rounding method ofPractice E29.6. Procedure6.1 Preliminary Precaution—For 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 levels, that capability isdemonstrated. Proceed as directed in 6.2.6.1.1 Test for “Biased-Zero” Methods—Prepare the methodto perform determinations. Include all aspects of instrumentpreparation and calibration. Apply the method to a “blank”sample or one known to have negligible analyte content butthat meets the method’s scope requirements in all otherrespects. If the method yields a negative result, it is not a“biased-zero” method as directed in 6.2. If, during the courseof at least ten replicate determinations, several zeros but nonegative values are observed, it is a “biased-zero” method.Apply the biased-zero rule of 6.4 in reporting results lowerthan NL (see 6.2.2).6.2 Critical 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: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 as directed in 6.1.1 and 6.4.6.3.2 Results Less Than L—Round 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 NL—If the method is “biased-zero,”treat as directed in 6.4; otherwise, round in accordance with6.3.2, and enclose in parentheses followed by an asteriskbefore 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” 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 Explanations of Coding Symbols:6.6.1 If results less than L are reported for any analyte,append the following explanation (results in parentheses arenot reliable for individual 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 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 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 values 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 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 − 172ANNEXES(Mandatory Information)A1. STATISTICAL BASIS FOR QUANTIFICATION CRITERIAA1.1 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 redetermined.The statistical basis for quantification is found in PracticeE1601 and Guide E1763. The lower limit (L) of a method’squantitative 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.A1.1.1 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 thisanalyte content, the average difference (50 % confidence level)between results in two laboratories is about 18 % of their mean.Aresult at this analyte level is quantitative with approximatelyone significant digit, and, as directed in 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 testmaterials (Practice E1601) or the equation relating R to analyteconcentration or mass fractions (for ILS evaluated as directedin Guide E1763) to estimate the reliability of data at anyconcentration within the quantitative range of the method. IfRrel%is 5 % or less relative to the determined value, reportresults with three digits (the first two are significant.) If Rrel%is 0.5 % or less, report four digits (the first three aresignificant.) If Rrel%is 0.05 % or less, report five digits (the firstfour are significant.)A1.2 Results from materials with analyte content less than Lare not quantitative as defined in this practice, but their valuescontain information concerning the analyte content. Theseresults are reported, but their use for individual comparisons isdiscouraged.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 by 2.8 yields the reproducibilitystandard deviation, sR, which, added to and subtracted from aresult, signifies a confidence interval. While indicatinguncertainty, this approach does not lend itself to easy recogni-tion of a value’s reliability because the user must apply a rathercomplex interpretive process to decide how the data may beused.A1.2.2 The user, if willing to expend time and resources,can reduce variability by averaging a number of results fromthe same material obtained in different laboratories. Forexample, if a material having an analyte content of R isanalyzed once in 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 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 practical 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 discussed 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 or mass fraction ranges:A2.2.1 Class 1 consists of results with values falling 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 unlikely to be quantitative.Individual and average values that are less than NL areexpected to be estimates of zero.E1950 − 173A2.2.3 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 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 the method’s 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; thisfact 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,