# ASTM E1950-17 Standard Practice for Reporting Results from Methods of Chemical A

Designation E1950 17Standard Practice forReporting Results from s 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 s of chemical analysis. This practiceprovides selection criteria and proper and symbols forcoding results when necessary to indicate the relative reliabilityof results having small values.1.2 Specifically excluded is consideration of report sand the associated inational content of reports in whichresults are tabulated or transmitted. It is assumed that thereporting laboratory has established a report at to ensureproper identification of the materials tested, the nature andconditions of the test, the responsible personnel, and otherrelated ination 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 Standards2E29 Practice for Using Significant Digits in Test Data toDetermine Conance with SpecificationsE135 Terminology Relating to Analytical Chemistry etals, Ores, and Related MaterialsE1601 Practice for Conducting an Interlaboratory Study touate the Perance of an Analytical E1763 Guide for Interpretation and Use of Results fromInterlaboratory Testing of Chemical Analysis sWithdrawn 201533. Terminology3.1 Definitions3.1.1 For definitions of terms, refer to Terminology E135.3.2 Definitions of Terms Specific to This Standard3.2.1 lower limit, L, nthe lower limit of the quantitativeanalyte mass fraction or concentration range see Annex A1.3.2.2 low-level reproducibility index, KR,nthe reproduc-ibility index constant for low analyte levels determined asdirected by Guide E1763.3.2.3 null limit, 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 PracticeE29.4. Significance and Use4.1 Aresult must be stated to a sufficient number of digits sothat a user receives both quantitative ination and ameasure of the variability of the value reported.4.2 The range of application of most s 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 ination 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. DOI10.1520/E1950-17.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume ination, refer to the standards 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 s and assists thoseuntrained in statistics to apply results appropriately.5. Rounding Calculated Values5.1 Use ination from the precision section of the to determine the appropriate number of digits to reportas follows5.1.1 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 statisticalination.5.1.2 Calculate the percent relative reproducibility indexRrel5 100 3R/C 15.1.3 For results within the range of application specified inthe , 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 ofPractice E29.6. Procedure6.1 Preliminary PrecautionFor a 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 occasionally yieldsnegative results for low analyte levels, that capability isdemonstrated. Proceed as directed in 6.2.6.1.1 Test for “Biased-Zero” sPrepare the to per determinations. Include all aspects of instrumentpreparation and calibration. Apply the to a “blank”sample or one known to have negligible analyte content butthat meets the s scope requirements in all otherrespects. If the yields a negative result, it is not a“biased-zero” 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” .Apply the biased-zero rule of 6.4 in reporting results lowerthan NL see 6.2.2.6.2 Critical Concentrations or Mass Fractions6.2.1 From the , 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 followsNL 5 L/4 26.3 Basic Rules6.3.1 Numerical values shall be reported for every resultincluding negative values obtained from a properly con-ducted except as provided for certain results from“biased-zero” s as directed in 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 0.00050, round to 0.000 xx and report 0.000 xx.6.3.3 Results Less Than NLIf the 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” s6.4.1 For results from “biased-zero” s only, do notreport numerical values for results less than NL. Replace themwith the symbol *.6.5 Reference to the 6.5.1 Cite the designation of the standard used todetermine each analyte reported.6.6 Explanations of Coding Symbols6.6.1 If results less than L are reported for any analyte,append the following explanation results in parentheses arenot reliable for individual comparisons6.6.2 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 cannotreport an unbiased estimate at this low analyte level.7. Use of Uncoded and Coded Values7.1 Uncoded Data7.1.1 Numerical values reported not enclosed in parenthesesare quantitative results and may be used for comparisons withspecified limiting values.7.2 Coded Data7.2.1 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 Digits550 20.55 30.05 0.5 40.05 5E1950 172ANNSMandatory InationA1. 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 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 levelbetween 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 ination it contains. Only the firstdigit is considered significant.A1.1.2 Users of standard s 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 uated as directedin Guide E1763 to estimate the reliability of data at anyconcentration within the quantitative range of the . IfRrelis 5 or less relative to the determined value, reportresults with three digits the first two are significant. If Rrelis 0.5 or less, report four digits the first three aresignificant. If Rrelis 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 ination 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 values 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 rangesA2.2.1 Class 1 consists of results with values falling be-tween the upper and lower application limits stated in the. 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 Lto 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 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,