ASTM C670-96
(Practice)Standard Practice for Preparing Precision and Bias Statements for Test Methods for Construction Materials
Standard Practice for Preparing Precision and Bias Statements for Test Methods for Construction Materials
SCOPE
1.1 This practice supplements Practice E177, in order to provide guidance in preparing precision and bias statements for ASTM test methods pertaining to certain construction materials (Note 1). Recommended forms for precision and bias statements are included. A discussion of the purpose and significance of these statements for the users of those test methods is also provided. Note 1-Although under the jurisdiction of Committee C-9, this practice was developed jointly by Committees C-1, D-4, and C-9, and has been endorsed by all three committees. It has subsequently been adopted for use by Committee D-18.
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Designation: C 670 – 96
Standard Practice for
Preparing Precision and Bias Statements for Test Methods
for Construction Materials
This standard is issued under the fixed designation C 670; 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 (e) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the Department of Defense.
1. Scope above and below the average) of a large group of individual
test results obtained under similar conditions.
1.1 This practice supplements Practice E 177, in order to
3.2.1 single-operator one-sigma limit—the one-sigma limit
provide guidance in preparing precision and bias statements for
for single-operator precision is a quantitative estimate of the
ASTM test methods pertaining to certain construction materi-
variability of a large group of individual test results when the
als (Note 1). Recommended forms for precision and bias
tests have been made on the same material by a single operator
statements are included. A discussion of the purpose and
using the same apparatus in the same laboratory over a
significance of these statements for the users of those test
relatively short period of time. This statistic is the basic one
methods is also provided.
used to calculate the single-operator index of precision given in
NOTE 1—Although under the jurisdiction of Committee C-9, this
the precision statement for guidance of the operator.
practice was developed jointly by Committees C-1, D-4, and C-9, and has
3.2.2 multilaboratory one-sigma limit—the one-sigma limit
been endorsed by all three committees. It has subsequently been adopted
for multilaboratory precision is a quantitative estimate of the
for use by Committee D-18.
variability of a large group of individual test results when each
2. Referenced Documents test has been made in a different laboratory and every effort has
been made to make the test portions of the material as nearly
2.1 ASTM Standards:
identical as possible. Under normal circumstances the esti-
C 109/C 109M Test Method for Compressive Strength of
mates of one-sigma limit for multilaboratory precision are
Hydraulic Cement Mortars (Using 2-in. or 50-mm Cube
larger than those for single-operator precision, because differ-
Specimens)
ent operators and different apparatus are being used in different
C 802 Practice for Conducting an Interlaboratory Test Pro-
laboratories for which the environment may be different.
gram to Determine the Precision of Test Methods for
3.2.3 one-sigma limit in percent (1s%)—in some cases the
Construction Materials
coefficient of variation is used in place of the standard
E 177 Practice for Use of the Terms Precision and Bias in
deviation as the fundamental statistic. This statistic is termed
ASTM Test Methods
the “one-sigma limit in percent” (abbreviated (1s%)) and is the
3. Terminology
appropriate standard deviation (1s) divided by the average of
the measurements and expressed as a percent. When it is
3.1 Definitions of Terms Specific to This Standard:
appropriate to use (1s%) in place of (1s) is discussed in Section
3.2 one-sigma limit (1s)—the fundamental statistic underly-
6.
ing all indexes of precision is the standard deviation of the
3.3 Acceptable Range of Results:
population of measurements characteristic of the test method
3.3.1 acceptable difference between two results—the “dif-
when the latter is applied under specifically prescribed condi-
ference two-sigma limit (d2s)” or “difference two-sigma limit
tions (a given system of causes). The terminology “one-sigma
in percent (d2s%),” as defined in Practice E 177, has been
limit” (abbreviated (1s)) is used in Practice E 177 to denote the
selected as the appropriate index of precision in most precision
estimate of the standard deviation or sigma that is characteristic
statements. These indexes indicate a maximum acceptable
of the total statistical population. The one-sigma limit is an
difference between two results obtained on test portions of the
indication of the variability (as measured by the deviations
same material under the applicable system of causes described
in 4.1.1 and 4.1.2 (or whatever other system of causes is
This practice is under the jurisdiction of ASTM Committee C-9 on Concrete
appropriate). The (d2s) index is the difference between two
and Concrete Aggregatesand is the direct responsibility of Subcommittee C09.94on
individual test results that would be equaled or exceeded in the
Evaluation of Data.
Current edition approved May 10, 1996. Published July 1996. Originally long run in only 1 case in 20 in the normal and correct
published as C 670 – 71 T. Last previous edition C 670 – 95.
operation of the method. The (d2s%) index is the difference
Annual Book of ASTM Standards, Vol 04.01.
between two individual test results expressed as a percent of
Annual Book of ASTM Standards, Vol 04.02.
their average that meets the same requirements. These indexes
Annual Book of ASTM Standards, Vol 14.02.
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NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
C 670
suspected of producing erratic results, and a closer examination of the
are calculated by multiplying the appropriate standard devia-
procedures would be in order. If knowledge about the test method in
tion (1s) or coefficient of variation (1s%) by the factor 2 2
=
question indicates that certain actions may be appropriate in cases where
(equal to 2.83).
deviant results occur, then such information should be included in the test
3.3.2 acceptable range of more than two results—in cases
method, but details of how this should be done will depend upon the
where the test method calls for more than two test results to be
particular test method.
obtained, the range (difference between highest and lowest) of
3.3.4 variations between laboratories—the system of
the group of test results must be compared to a maximum
causes designated for obtaining the quantitative guide for
acceptable range for the applicable system of causes and
acceptance of results by different laboratories as given in 4.1.2
number of test results. The range for different numbers of test
is multilaboratory precision, using the system of modifiers
results including two that would be equaled or exceeded in
given in Practice E 177 (Note 3). When results differ by more
only 1 case in 20 is obtained by multiplying the appropriate
than (d2s) there is a significantly large probability that one or
standard deviation (1s) or coefficient of variation (1s%) by the
both laboratories are in error or that a difference exists in the
appropriate factor from the second column of Table 1 (Note 2):
portions of material being used for the tests. In such cases,
NOTE 2—It is important to note that when more than two test results are
retests should be made. When possible, newly drawn test
obtained, an index of precision for the difference between two results can
samples should be used for such retests as directed in Note 4.
not be used as a criterion for judging acceptability of the range of the
3.4 Number of Tests:
group or for other pairs of results selected from the group.
3.4.1 single test results—the number of tests run must be
3.3.3 variations for single operators—the system of causes
taken into account when evaluating testing variations. Usually,
designated for obtaining the quantitative guide to acceptable
the statistics used in evaluating precision and the indexes of
performance by an operator as stated in 4.1.1 leads to single-
precision based on them are based on the population distribu-
operator precision, using the system of modifiers given in
tion of single test results. When this is the case, the index of
Practice E 177 (Note 3). When two results by the same
precision may be used in comparing single tests results only,
operator differ by more than (d2s) or (d2s%) or the range of
not averages of two or more tests.
more than two results exceeds that obtained by the method
3.4.2 test results based on averages—if the precision state-
described in 3.2.2 there is a significantly large probability that
ment is based on test results that are averages of two or more
an error has occurred and retests should be made as directed in
measurements, then the number of measurements averaged
Note 4.
must be stated, and in using the index of precision, averages of
NOTE 3—Single-operator precision is often referred to as “repeatabil-
exactly that number of measurements must be used. In some
ity,” and multilaboratory precision is often referred to as “reproducibility.”
cases a test result is defined in the method as the average of two
NOTE 4—It is beyond the scope of this practice to describe in detail
or more individual measurements. In such cases the index of
what action should be taken in all cases when results occur that differ by
precision for a test result applies to a test result as so defined,
more than the (d2s) limits or by more than the maximum allowable range.
although indexes of precision for ranges of individual mea-
Such an occurrence is a warning that there may have been some error in
surements within a laboratory may also be included as de-
the test procedure, or some departure from the prescribed conditions of the
test on which the limits appearing in the test method are based; for scribed in 3.3.3.
example, faulty or misadjusted apparatus, improper conditions in the
3.4.3 precision of individual measurements averaged to
laboratory, etc. In judging whether or not results are in error, information
obtain a test result—when two or more measurements are
other than the difference between two test results is needed. Often a review
averaged to obtain a test result, the range of the individual
of the circumstances under which the test results in question were obtained
measurements may be examined to determine whether the
will reveal some reason for a departure. In this case the data should be
latter meet the criterion of being valid individual measurements
discarded and new test results obtained and evaluated separately. If no
physical reason for a departure is found, retests should still be made, but under the conditions of the test method. The maximum
the original tests should not be completely ignored. If the second set of
acceptable range for individual measurements is obtained by
results also differs by more than the applicable limit, the evidence is very
multiplying the appropriate standard deviation (1s) or, coeffi-
strong that something is wrong or that a real difference exists between the
cient of variation (1s%) obtained from averages by the appro-
two samples tested. If the second set produces a result within the limit, it
priate factor from the second column of Table 2 (Note 5). The
may be taken as a valid test, but the operator or laboratory may then be
maximum acceptable range for individual measurements ob-
tained by this method may be included in the precision
TABLE 1 Maximum Acceptable Range
statement as an index of precision for individual measurements
Number of Multiplier of (1s) or (1s%) for
A
in the same laboratory as described in Example 8.
Test Results Maximum Acceptable Range
2 2.8
NOTE 5—This procedure is only valid if the individual measurements
3 3.3
are subject to the same sources of variation as the test result. For example,
4 3.6
the single-operator precision of Test Method C 109/C 109M mortar cubes
5 3.9
is calculated from test results that include a contribution from variation
6 4.0
among batches of mortar. Variation among individual cubes from a single
7 4.2
8 4.3
batch does not contain this component of variation. Therefore, differences
9 4.4
among individual cubes from a single batch cannot be inferred from the
10 4.5
single-operator standard deviation given in Test Method C 109/C 109M
A
Values were obtained from Table A7 of “Order Statistics and Their Use in
and the values in Table 2.
Testing and Estimation,” Vol 1, by Leon Harter, Aerospace Research Laboratories,
United States Air Force. 3.4.4 multilaboratory precision expressed as a maximum
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
C 670
TABLE 2 Maximum Acceptable Range of Individual
acceptable when properly conducted determinations are made
Measurements
by two different operators in different laboratories on portions
Multiplier of (1s) or (1s%) for
of a material that are intended to be identical, or as nearly
Number of Measurements Averaged to Averages to Obtain Maximum
identical as possible.
Obtain a Test Result Acceptable Range of
A
Individual Measurements 4.2 Other Measures of Precision—The two elements de-
scribed in 4.1.1 and 4.1.2 involve the main systems of causes
2 3.9
3 5.7
of interest to users of test methods involving construction
4 7.3
materials. In cases where other systems of causes apply, the
5 8.6
appropriate statistics for those systems should be used and the
6 9.9
7 11.0
appropriate combination of modifiers given in Practice E 177
8 12.1
should be used to describe those statistics.
9 13.2
4.3 Use of Indexes of Precision in Specifications—The
10 14.1
A
indexes of precision described in this practice are to be used as
Values were calculated from Table 1.
guides to determine (with a prescribed degree of certainty)
whether a given series of results can be considered as valid
allowable difference between two averages—when the test
tests under the conditions assumed in the test method. Com-
method calls for the reporting of more than one test result,
parisons of test results with specification limits should be made
multi-laboratory precision may be expressed as a maximum
only after there is reasonable assurance that the determinations
allowable difference between averages of such groups, one
are adequate. Writers of specifications have the responsibility
from each laboratory, and both the (d2s) or (d2s%) limit for
of recognizing the variability of results characteristic of a given
individual results and this maximum allowable difference of
test method in setting specification limits, but indexes of
two averages may be included in the multilaboratory precision
precision of the test method should never be added to specifi-
statement (Note 6). The maximum allowable difference for
cation limits by the users of those specifications for the purpo
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