ASTM E1950-98(2003)

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Designation:E1950–98 (Reapproved 2003)
Standard Practice for
Reporting Results from Methods of Chemical Analysis
This standard is issued under the fixed designation E1950; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3.2.1 lower limit, L, n—the lower limit of the quantitative
analyte concentration range.
1.1 This practice covers the approximate number of digits
3.2.2 low-level reproducibility index, K , n—the reproduc-
R
required to express the expected precision of results reported
ibility index constant (for low analyte levels) determined in
from standard methods of chemical analysis. This practice
accordance with Guide E1763.
provides selection criteria and proper form and symbols for
3.2.3 null limit, NL, n—the analyte content below which
codingresultswhennecessarytoindicatetherelativereliability
results are so near zero that averaging is unlikely to yield a
of results having small values.
value significantly different from zero.
1.2 Specifically excluded is consideration of report forms
3.2.4 quantitative, adj—relating to results,havinganumeri-
and the associated informational content of reports in which
calvaluethatincludesatleastonesignificantdigit(seePractice
results are tabulated or transmitted. It is assumed that the
E29).
reporting laboratory has established a report format to ensure
proper identification of the materials tested, the nature and
4. Significance and Use
conditions of the test, the responsible personnel, and other
4.1 Aresult should be stated to a sufficient number of digits
relatedinformationinaccordancewithexistingregulationsand
so that a user receives both quantitative information and a
good laboratory practices.
measure of the variability of the value reported.
2. Referenced Documents 4.2 The range of application of most methods of chemical
analysis is based upon the presumption that the quantitative
2.1 ASTM Standards:
results produced are to be used to compare the analyte content
E29 Practice for Using Significant Digits in Test Data to
of the test material with specified limiting values. However,
Determine Conformance with Specifications
analytical results may be used legitimately for other purposes.
E135 Terminology Relating to Analytical Chemistry for
If the same material is analyzed a number of times or a product
Metals, Ores, and Related Materials
is analyzed periodically during an interval of production, each
E1601 Practice for Conducting an Interlaboratory Study to
setofresultsmaybeaveragedtoyieldanaverageresulthaving
Evaluate the Performance of an Analytical Method
improved reliability. Results that fall below the lower limit,
E1763 Guide for Interpretation and Use of Results from
although not quantitative individually, contain compositional
Interlaboratory Testing of Chemical Analysis Methods
information and shall be reported. The reporting system in this
3. Terminology practice permits the analyst to indicate which values are likely
to be rendered quantitative by averaging and which are not.
3.1 Definitions:
4.3 The system is simple enough to be used routinely in
3.1.1 For definitions of terms, refer to Terminology E135.
reporting results from standard methods and assists those
3.2 Definitions of Terms Specific to This Standard:
untrained in statistics to apply results appropriately.
5. Rounding Calculated Values
This practice is under the jurisdiction of ASTM Committee E01 on Analytical
Chemistry for Metals, Ores and Related Materials and is the direct responsibility of
5.1 Use information from the precision section of the
Subcommittee E01.22 on Statistics and Quality Control.
method to determine the appropriate number of digits to report
Current edition approved Oct. 1, 2003. Published November 2003. Originally
as follows:
approved in 1998. Last previous edition approved in 1998 as E1950 – 98. DOI:
10.1520/E1950-98R03.
5.1.1 Estimate the reproducibility index, R, at the analyte
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
level of the result, C, from an equation of R as a function of
contactASTM Customer Service at service@astm.org. ForAnnual Book ofASTM
concentration or from the table of statistical information.
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. 5.1.2 Calculate the percent relative reproducibility index:
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E1950–98 (2003)
R 5 100 3 R / C (1)
ducted method except as provided for certain results from
rel%
“biased-zero” methods in accordance with 6.1.1 and 6.4.
5.1.3 For results within the range of application specified in
6.3.2 Results Less Than L—Round values to the second
the method, round the values to the number of digits specified
decimal place of L, and enclose in parentheses before report-
in Table 1 (see A1.1.1 through A1.1.2).
ing.Examples:For Lequalto1.5,roundtox.xandreport(x.x);
5.1.4 For results less than the lower limit, proceed in
for Lequal to 0.22, round to 0.xx and report (0.xx); for Lequal
accordancewithSection6toestablishthenumberofdigitsand
to 0.00050, round to 0.000xx and report (0.000xx).
appropriate coding for rounding and reporting the values.
6.3.3 Results Less Than NL—If the method is a “biased-
5.2 Calculated values shall be rounded to the required
zero” procedure, treat in accordance with 6.4; otherwise, round
number of digits in accordance with the rounding-off method
in accordance with 6.3.2, and enclose in parentheses followed
of Practice E29.
byanasteriskbeforereporting.Examples:(-0.2)*,(0.04)*,and
5.2.1 The procedure is summarized as follows:
(-0.00003)*.
5.2.1.1 When rounding off a number to a specified number
6.4 Special Rule for “Biased-Zero” Methods:
of digits, choose that digit that is nearest. If two choices are
6.4.1 For results from “biased-zero” methods only, do not
possible, as when the digits dropped are exactly a five or a five
report numerical values for results less than NL. Replace them
followed only by zeros, choose that ending in an even digit.
with the symbol (– –)*.
6. Procedure
6.5 Reference to the Method:
6.1 Preliminary Precaution—For a method to be used to 6.5.1 Cite the designation of the standard method used to
determine each analyte reported.
analyze materials with analyte content very near zero, the
analyst shall determine that it is capable of producing “unbi- 6.6 Explanations of Coding Symbols:
ased” estimates of zero. If the method occasionally yields 6.6.1 If results less than L are reported for any analyte,
negative results for low analyte levels, that capability is append the following explanation:
demonstrated. Proceed in accordance with 6.2.
NOTE 1—Results in parentheses are not reliable for individual compari-
6.1.1 Test for “Biased-Zero” Methods—Prepare the method
sons.
to perform determinations. Include all aspects of instrument
6.6.2 If results less than NL are reported for any analyte,
preparation and calibration. Apply the method to a “blank”
append the following explanation: * These values cannot be
sample or one known to have a negligible analyte content but
distinguished from zero.
that meets the method’s scope requirements in all other
6.6.3 If the symbol (– –)* is reported for any analyte,
respects. If the method yields a negative result, it is not a
append the following explanation: (– –)* The method cannot
“biased-zero” method; proceed in accordance with 6.2. If,
report an unbiased estimate at this low analyte level.
during the course of at least ten replicate determinations,
several zeros but no negative values are observed, it is a
7. Use of Uncoded and Coded Values
“biased-zero” method. Apply the biased-zero rule of 6.4 in
reporting results lower than NL (see 6.2.2).
7.1 Uncoded Data:
6.2 Critical Concentrations:
7.1.1 Numerical values reported without enclosing paren-
6.2.1 From the method, obtain the value of the lower limit,
thesesarequantitativeresultsandmaybeusedforcomparisons
L, to two digits (add a final zero, if necessary). Determine the
with specified limiting values.
decimal place of the second digit.
7.2 Coded Data:
6.2.2 Calculate the null limit as follows:
7.2.1 Values enclosed in parentheses are not quantitative,
NL 5 L / 4 (2) that is, individual values are not suitable for comparisons.
However, data in parentheses not followed by an asterisk, may
6.3 Basic Rules:
yield values that are quantitative if a sufficient number are
6.3.1 Numerical values shall be reported for every result
averaged (see A2.2.3).
(including negative values) obtained from a properly con-
7.2.2 Values coded with an asterisk are from materials that
are likely to produce randomly occurring negative values for
TABLE 1 Rounding Guide
repeated determinations.They may be averaged, but unless the
R Number
rel%
average includes a large number of individual results (more
of Digits
than 25), even the first digit is not likely to be significant.
5-50% 2
0.5-5% 3
0.05 - 0.5 % 4
8. Keywords
<0.05 % 5
8.1 quantitative results; reporting results
E1950–98 (2003)
ANNEXES
(Mandatory Information)
A1. STATISTICAL BASIS FOR QUANTITATION CRITERIA
A1.1 Quantitation is the ability to determine a result whose report four digits (the first three are significant.) If R is 0.05
rel%
valuemaybecomparedwithspecifiedlimitingvalues.Practice % or less, report five digits (the first four are significant.)
E29 adds the concept of significant digits. This term is used in
A1.2 Results from materials with analyte content less than
this practice to identify the digits in a value that are not
L are not quantitative as defined in this practice, but their
expected to change appreciably if the result is redetermined.
values contain information concerning the analyte content.
The statistical basis for quantitation is found in Practice E1601
These results are reported, but their use for individual com-
and Guide E1763. The lower limit (L) of a method’s quanti-
parisons is discouraged.
tative range is calculated from its reproducibility index, R,
A1.2.1 Guide E1763 provides calculations for K , the
R
which is determined in the interlaboratory study (ILS). The
constant value R achieves at analyte contents near Land lower.
analyte content of a material must be greater than that limit if
This value of R divided by 2.8 yields the reproducibility
results are to exhibit at least one significant digit.
standard deviation, s , which, added to and subtracted from a
R
result, signifies a confidence interval. While indicating uncer-
A1.1.1 R represents the largest difference between results
tainty, this approach does not lend itself to easy recognition of
obtained in two laboratories on the same material that is not
a value’s reliability because the user must apply a rather
expected to be exceeded in more than 1 in 20 comparisons (95
complex interpretive process to decide how the data may be
% confidence level). L is arbitrarily defined as the analyte
used.
content at which R represents a 50 % relative error. At this
A1.2.2 The ultimate user, if willing to expend time and
analyte content, the average difference (50 % confidence level)
resources, can reduce variability by averaging a number of
betweenresultsintwolaboratoriesisabout18%oftheirmean.
results from the same material obtained in different laborato-
Resultsatthisanalytelevelarequantitativewithapproximately
ries. For example, if a material having an analyte content of R
one significant digit, and, in accordance with Practice E29 and
is analyzed once in four laboratories, the relative variability of
common statistical practice, are reported with two digits to
such an average (four values) is 50 %, the same as the
preserve the statistical information it contains. Only the first
variability of single results from a material with twice the
digit is considered significant.
analyte content (that is, at L).
A1.1.2 Users of standard methods (or data obtained from
A1.2.3 The limit to the enhancement in precision by repli-
them) can use R values reported at the analyte levels of the test
cation is established only by the resources the user is willing to
materials (Practice E1601) or the equation relating R to analyte
expend. A reasonable (though arbitrary) limit is the null limit,
concentration (for ILS evaluated in accordance with Guide
NL = R/2 (which is equivalent to L/4). The null limit is the
E1763) to estimate the reliability of data at any concentration
lowest analyte level at which the average of 16 or more results
within the quantitative range of the method. If R is5%or
yields an average value having at least one significant digit.
rel%
less relative to the determined value, report results with three
Results below NL are, for practical purposes, indistinguishable
digits (the first two are significant.) If R is 0.5 % or less, from zero.
rel%
A2. PRACTICAL BASIS FOR QUANTITATION CRITERIA
A2.1 The practical basis for quantitation must provide quantitative, but averages are also unlikely to be quantitative.
guidance to analysts and users of results who have little
Individual and average values that are less than NL are
statistical training. The criteria should be consistent with the
expected to be estimates of zero.
ILS statistics and criteria discussed in Annex A1, simple to
A2.2.3 Class 2 consists of results with values falling within
understand, and convenient to use. The coding applied to each
the range NL to L. Individual results are not quantitative, but
value should give an unmistakable visual indication of its
averages of values obtained in different laboratories may be
reliability.
quantitative. The number of values needed to obtain a quanti-
A2.2 Asystem to meet these requirements classifies results tative average ranges from 2 (at analyte levels just less than L)
into three concentration ranges: to 16 (at analyte levels just greater than NL).
A2.2.1 Class 1 consists of results with values falling be-
A2.3 The classifications in A2.2 meet the requirements in
tween the upper and lower application limits stated in the
A2.1. The analyst classifies each result by comparing its value
method. These results are expected to be quantitative as
with L (from the method’s scope) and the calculated value of
discussed in Annex A1.
NL (L/4). Class 1 results are quantitative and are reported
A2.2.2 Class 3 consists of results with values less than NL.
As discussed in A1.2.3, not only are individual results not uncoded. Class 2 and Class 3 results are not quantitative; this
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