ASTM E2489-21

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E2489 − 16 E2489 − 21 An American National Standard
Standard Practice for
Statistical Analysis of One-Sample and Two-Sample
Interlaboratory Proficiency Testing Programs
This standard is issued under the fixed designation E2489; 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 Scope*
1.1 This practice describes methods for the statistical analysis of laboratory results obtained from interlaboratory proficiency
testing programs. As in accordance with Practice E1301, proficiency testing is the use of interlaboratory comparisons for the
determination of laboratory testing or measurement performance. Conversely, collaborative study (or collaborative trial) is the use
of interlaboratory comparisons for the determination of the precision of a test method, as covered by Practice E691.
1.1.1 Method A covers testing programs using single test results obtained by testing a single sample (each laboratory submits a
single test result).
1.1.2 Method B covers testing programs using paired test results obtained by testing two samples (each laboratory submits one
test result for each of the two samples). The two samples should be of the same material or two materials similar enough to have
approximately the same degree of variation in test results.
1.2 Methods A and B are applicable to proficiency testing programs containing a minimum of 10 participating laboratories.
1.3 The methods provide direction for assessing and categorizing the performance of individual laboratories based on the relative
likelihood of occurrence of their test results, and for determining estimates of testing variation associated with repeatability and
reproducibility. Assumptions are that a majority of the participating laboratories execute the test method properly and that samples
are of sufficient homogeneity that the testing results represent results obtained from each laboratory testing essentially the same
material. Each laboratory receives the same instructions or protocol.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.20 on Test Method
Evaluation and Quality Control.
Current edition approved Nov. 15, 2016Dec. 1, 2021. Published November 2016December 2021. Originally approved in 2006. Last previous edition approved in 20112016
as E2489 – 11.E2489 – 16. DOI: 10.1520/E2489-16.10.1520/E2489-21.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2489 − 21
E177 Practice for Use of the Terms Precision and Bias in ASTM Test Methods
E178 Practice for Dealing With Outlying Observations
E456 Terminology Relating to Quality and Statistics
E691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
E1301 Guide for Proficiency Testing by Interlaboratory Comparisons (Withdrawn 2012)
E2586 Practice for Calculating and Using Basic Statistics
3. Terminology
3.1 Definitions—The terminology defined in Terminology—Unless otherwise noted in this E456 applies to this practice unless
modified herein.standard, all terms relating to quality and statistics are defined in Terminology E456.
3.1.1 collaborative study, n—interlaboratory study in which each laboratory uses the defined method of analysis to analyze
identical portions of homogeneous materials to assess the performance characteristics obtained for that method of analysis.
Horwitz
3.1.2 collaborative trial, n—see collaborative study.
3.1.3 interlaboratory comparison, n—organization, performance, and evaluation of tests on the same or similar test items by two
or more laboratories in accordance with predetermined conditions.
th
3.1.4 median, X˜, n—the 50 percentile in a population or sample. E2586
3.1.4.1 Discussion—
The sample median is the [(n + 1) ⁄2] order statistic if the sample size n is odd and is the average of the [n/2] and [n/2 + 1] order
statistics if n is even.
3.1.5 outlier, n—see outlying observation. E178
3.1.6 outlying observation, n—observation that appears to deviate markedly in value from other members of the sample in which
it appears. E178
3.1.7 proficiency testing, n—determination of laboratory testing performance by means of interlaboratory comparisons.
3.1.8 repeatability standard deviation (S ), n—standard deviation of test results obtained under repeatability conditions. E177
r
3.1.9 reproducibility standard deviation (S ), n—standard deviation of test results obtained under reproducibility conditions. E177
R
3.2 Definitions of Terms Specific to This Standard:
3.2.1 hinge (upper or lower), n—median of the upper or lower half of a set of data when the data is arranged in order of size.
3.2.1.1 Discussion—
When there is an odd number of items in the data set, the middle value is included in both the upper and lower halves. The upper
hinge is an estimate of the 75th percentile; the lower hinge is an estimate of the 25th percentile.
3.2.2 inner fence (upper or lower), n—value equal to the upper or lower hinge of a data set plus (upper) or minus (lower) 1.5 times
the difference between upper and lower hinges.
3.2.3 interquartile range, n—distance between the upper and lower hinges of a data set.
3.2.4 outer fence (upper or lower), n—value equal to the upper or lower hinge of a data set plus (upper) or minus (lower) three
times the difference between upper and lower hinges.
4. Summary of Practice
4.1 This practice describes methods of displaying interlaboratory data that visually show individual laboratory results.
The last approved version of this historical standard is referenced on www.astm.org.
Horwitz, W., “Protocol for the Design, Conduct and Interpretation of Collaborative Studies,” Pure and Applied Chemistry, Vol 60, No. 6, 1988, pp. 855–864.
E2489 − 21
4.2 The methods described in this practice can be applied to large and small sample populations from any distribution expected
to have a general mound shape. It is recommended that in cases in which it is suspected that the data may be highly unsymmetrical
or very unusual in some other manner a statistician should be consulted regarding the applicability of the analysis method.
4.2.1 The median is used as the “consensus” value of the measured test property.
4.2.2 The interquartile range (IQR) is used as the basis for estimating the spread in the data. Because the median and the
interquartile range are not affected by the magnitude of extreme values of a data set, the analysis approach presented in this practice
effectively eliminates the need to identify outlying observations (outliers).
4.3 Laboratory results are categorized according to how far the results lie outside of the interquartile range.
4.4 The upper and lower ends of the interquartile range are referred to as the hinges. The limits for categorizing laboratory results
lying outside of the interquartile range are determined by multiplying the extent of the interquartile range by the fixed factors of
1.5 and 3.0. The upper and lower limits lying a distance of 1.5 times the range of the IQR beyond the hinges are referred to as
the inner fences. The upper and lower limits for results lying at 3.0 times the range of the IQR beyond the hinges are referred to
as the outer fences.
4.5 Guidance is provided for proficiency testing programs wishing to establish additional limits (or fences). The user is directed
to Guide E1301 for additional guidance.
4.6 When using the methods in this practice, the number of participating laboratories should be at least ten. Since the degree of
confidence is lower for analyses performed on small sample populations, caution should be used in applying statistics obtained
from small sample populations.
4.7 When possible, it is generally desirable to have 30 or more participants when estimating the precision of test methods.
4.8 Estimates of the repeatability standard deviation and the reproducibility standard deviation are determined by dividing the
interquartile ranges of appropriate data sets by a factor of 1.35.
4.8.1 The number 1.35 used in determining the repeatability and reproducibility standard deviations is based on an assumption of
similarity to a normal distribution. Therefore, the estimate of the standard deviation using the methods described in this practice
may not supply the desired accuracy if the distribution differs too much from the general shape of a normal curve. It is beyond
the scope of this practice to describe procedures for determining when the analysis methods described in this practice are not
applicable.
5. Significance and Use
5.1 This practice is specifically designed to describe simple robust statistical methods for use in proficiency testing programs.
5.2 Proficiency testing programs can use the methods in this practice for the purpose of comparing testing results obtained from
a group of participating laboratories. The laboratory comparisons can then be used for practice describes evaluation of individual
laboratory performance.results using the interquartile range and Tukey inner and outer fences.
5.3 In addition, the data obtained in proficiency testing programs may contain information regarding repeatability (within-lab) and
reproducibility (between-lab) testing variation. Repeatability information is possible only if the program uses more than one
sample. See Method B. Proficiency testing programs often have a greater number of participants than might be available for
conducting an interlaboratory study to determine the precision of a test method (such as described in Practice E691). Precision
estimates obtained for the larger number of participants in a proficiency testing program, along with the corresponding wider
variation of test conditions, can provide useful information to standards developers regarding the precision of test results that can
be expected for a test method when in actual use in the general testing community.
5.4 To estimate the precision of a test method, the participants must use the same test method to obtain their test results, and testing
must be performed under the conditions required for repeatability and reproducibility. The precision estimates are applicable to the
E2489 − 21
TABLE 1 Original Data for a One-Sample Program
Lab Test Result
1 1.22
2 1.62
3 1.82
4 0.60
5 2.75
6 1.55
7 1.17
8 1.76
9 1.35
10 1.18
11 1.19
12 1.71
13 2.03
14 1.10
15 1.84
16 1.39
17 1.13
18 1.66
19 1.28
20 1.24
21 0.69
22 1.54
23 1.43
24 0.84
25 0.98
26 1.97
27 4.89
28 1.85
29 1.09
30 1.07
property levels and material types included in the testing program. The precision of a test method may vary considerably for
different material types and at different property levels.
5.5 This practice may be useful to proficiency testing program administrators and provides examples of statistical methods along
with explanations of some of the advantages of the suggested methods of analysis. The analyses resulting from the application of
methods described in this practice may be used by laboratories as part of their quality control procedures, accrediting bodies to
assist in the evaluation of laboratory performance, and ASTM International technical committees (and other organizations charged
with the task of writing, maintaining, or improving test methods) to obtain information regarding reproducibility and repeatability.
5.6 There are many types of proficiency testing programs in existence and many methods exist for analyzing the data resulting
from the interlaboratory testing. It is not the intention of this practice to call into question the integrity of programs using other
methods of analysis. Testing programs using replicate testing of one or more samples (each laboratory submits two or more results
for each sample) are directed to Practice E691 or other practices for the description of a method of analysis that may be more
suitable to that type of program.
6. Analysis of a One-Sample Program (Method A)
6.1 Display of Data:
6.1.1 When possible, display the data in a table to show the actual results submitted by each laboratory. This may not be practical
if the number of participants is too large.
6.1.1.1 To assist in maintaining confidentiality, give each laboratory an identification number if one does not already exist.
6.1.1.2 List the laboratory results in increasing order by laboratory identification number to make it easy to locate the results for
a particular laboratory. See Table 1.
6.1.2 Sort the laboratory results in decreasing order by test result to show the range and distribution of the test results. See Table
2. Besides the laboratory identification number and corresponding test results, Table 2 contains columns of additional information
that will be explained in the following sections of this practice.
E2489 − 21
TABLE 2 Data in Descending Order for One-Sample Program
Test Number of
Count of Labs Lab Category
Result Occurrences
27 4.89 1 Extremely Unusual
5 2.75 1 Unusual
13 2.03 1 Typical
26 1.97 1 Typical
28 1.85 1 Typical
15 1.84 1 Typical
3 1.82 1 Typical
8th from Top 8 1.76 1 Typical
12 1.71 1 Typical
18 1.66 1 Typical
2 1.62 1 Typical
6 1.55 1 Typical
22 1.54 1 Typical
23 1.43 1 Typical
15th from Top 16 1.39 1 Typical
16th from Top 9 1.35 1 Typical
19 1.28 1 Typical
20 1.24 1 Typical
1 1.22 1 Typical
11 1.19 1 Typical
10 1.18 1 Typical
7 1.17 1 Typical
8th from Bottom 17 1.13 1 Typical
14 1.10 1 Typical
29 1.09 1 Typical
30 1.07 1 Typical
25 0.98 1 Typical
24 0.84 1 Typical
21 0.69 1 Typical
4 0.60 1 Typical
Shown Below Is Determination of “Fences” for Data Above
Median of All Test Results = 1.37
Upper hinge (Median of Top Half) = 1.76
Lower Hinge (Median of Bottom Half) = 1.13
Interquartile Range (IQR) = (1.76 – 1.13) = 0.63
(3 × IQR) = 1.89
Outer Fence (Upper) = (1.76 + 1.89) = 3.65
Outer Fence (Lower) = (1.13 – 1.89) = –0.76
(1.5 × IQR) = 0.945
Inner Fence (Upper) = (1.76 + 0.945) = 2.705
Inner Fence (Lower) = (1.13 – 0.945) = 0.185
Reproducibility Standard Deviation = (IQR / 1.35) =
0.467
6.1.3 Display the data in a dot diagram to show the location of each laboratory’s test result in the distribution of all test results.
For each test result, plot occurrence number of that test result value versus the value of the test result. As points are plotted from
the top of Table 2 to the bottom, the first time a test value occurs assign it an occurrence of “one.” The next time that test result
value occurs, assign it an occurrence of “two.” If the test result value appears a third time, assign it an occurrence of “three” and
so forth. If a test result value appears three times in the data, plot the test result value three times, once with an occurrence of “one,”
once with an occurrence of “two.” and once with an occurrence of “three.” The consequence is that each laboratory’s test result
will be plotted as an individual dot and no dots will be concealed by being plotted on top of one another.
6.1.3.1 Fig. 1 shows the dot diagram for the data in Table 2. There are no repeat values in the test results, so Column 3 of Table
2 shows that the number of occurrences is “one” for each test result and the dots in Fig. 1 appear in a single horizontal row. The
dot diagram in Fig. 1 also shows that the test result for Laboratory 5, at (2.75, 1), is slightly removed from the rest of the data.
The test result for Laboratory 27, at (4.89, 1), is farther removed.
6.1.3.2 A dot diagram with a different appearance can be obtained by classifying the results into multiple contiguous size classes
such that each class contains a portion of the data, but together, the classes cover the entire data range. Table 3 shows the number
of occurrences in each size class when the range of each class is 0.10. When the numbers of occurrences in each size class are
plotted versus the corresponding values of the lower ends of each size class (see Fig. 2), the display has the advantage of being
E2489 − 21
FIG. 1 Dot Diagram for Original Data
TABLE 3 Data Classified by Tenths
Size Class Range
Test Number of
Lab
Lower Upper
Result Occurrences
End End
27 4.89 4.80 # X < 4.90 1
5 2.75 2.70 # X < 2.80 1
13 2.03 2.00 # X < 2.10 1
26 1.97 1.90 # X < 2.00 1
28 1.85 1.80 # X < 1.90 1
15 1.84 1.80 # X < 1.90 2
3 1.82 1.80 # X < 1.90 3
8 1.76 1.70 # X < 1.80 1
12 1.71 1.70 # X < 1.80 2
18 1.66 1.60 # X < 1.70 1
2 1.62 1.60 # X < 1.70 2
6 1.55 1.50 # X < 1.60 1
22 1.54 1.50 # X < 1.60 2
23 1.43 1.40 # X < 1.50 1
16 1.39 1.30 # X < 1.40 1
9 1.35 1.30 # X < 1.40 2
19 1.28 1.20 # X < 1.30 1
20 1.24 1.20 # X < 1.30 2
1 1.22 1.20 # X < 1.30 3
11 1.19 1.10 # X < 1.20 1
10 1.18 1.10 # X < 1.20 2
7 1.17 1.10 # X < 1.20 3
17 1.13 1.10 # X < 1.20 4
14 1.10 1.10 # X < 1.20 5
29 1.09 1.00 # X < 1.10 1
30 1.07 1.00 # X < 1.10 2
25 0.98 0.90 # X < 1.00 1
24 0.84 0.80 # X < 0.90 1
21 0.69 0.60 # X < 0.70 1
4 0.60 0.60 # X < 0.70 2
more compact, and it is more apparent how test results are clustered. The dot diagram in Fig. 2 still shows that the test result for
Laboratory 5 is slightly removed from the rest of the data and that the test result for Laboratory 27 is farther removed.
6.1.3.3 Other ranges for the size classes are permitted to be used to classify the test results. For example, each size class could
have a range of 0.20 or 0.05. The corresponding dot diagrams will each have a different appearance.
6.1.3.4 The range of the size classes used for grouping the laboratory test results should be chosen carefully to show as much
information (regarding individual laboratory test results and the overall distribution of the test results) as possible in the dot
diagram. One consideration should be the number of test results that must be plotted. Generally, it is desirable to limit the number
of classes to be plotted along the x-axis of the dot diagram. For larger data sets, the range of each of the classes must be wider
E2489 − 21
FIG. 2 Dot Diagram—Data Classified by Tenths
to contain a larger number of test results. Another consideration should be the overall range of the test results in the data set. All
size classes should have the same width and each size class must be sufficiently wide to limit the number of classes to be plotted
along the x-axis of the dot diagram.
6.1.3.5 Various computer software programs can be used to generate similar types of diagrams. When other types of diagrams are
used, it is generally preferable to choose one in which each individual laboratory’s result is displayed as a single point on the
diagram. For example, Fig. 2 is similar in appearance to a histogram, but a typical histogram does not show individual data points.
Another example is a stem-and-leaf plot.
6.2 Steps for Evaluating Laboratory Performance:
6.2.1 Visually examine the dot plot (or graphic of the data) to confirm that the distribution is approximately mound shaped and
unimodal. If either condition is not met, the analysis prescribed may not be appropriate. See 4.2.
6.2.2 The steps for evaluating a laboratory’s performance are to determine the median and interquartile range (IQR), locate the
inner and outer fences, and then categorize the laboratories according to where their results lie relative to the fences.
6.2.3 The method for determining the median depends on whether there is an odd or even number of results in the data set.
6.2.3.1 Sort the data set into ascending or descending order. If there is an odd number of results in the data set, after the results
are placed in ascending or decreasing order, the median is the middle number of the data set. For example, consider the five results
in the data set 9, 1, 5, 4, 5. When placed in ascending order, the result is 1, 4, 5, 5, 9. The middle number, or median, is the
underlined 5. It does not matter that one of the numbers is repeated.
6.2.3.2 If there is an even number of results in the data set, after the results are placed in ascending or descending order, the median
is the average of the middle two numbers in the data set. For example, consider the eight results in the data set 2, 8, 5, 11, 4, 6,
9, 4. When placed in ascending order, the result is 2, 4, 4, 5, 6, 8, 9, 11. The middle two numbers are 5 and 6. The average is (5
+ 6)/2 or 5.5, so the median is 5.5.
6.2.4 The method for determining the interquartile range is to determine the middle number (or median) of the top and bottom
halves of the data set.
6.2.4.1 If there are an odd number of results in the data set, the median of the entire data set is included in both halves. For
example, consider again the data set 1, 4, 5, 5, 9. The underlined 5 is included in both halves. So, the middle number (or median)
of the top half of the data set, 5, 5, 9, is 5. The median of the top half of the data set is referred to as the upper hinge. The middle
number (or median) of the bottom half of the data set, 1, 4, 5, is 4. The median of the bottom half of the data set is referred to
as the lower hinge.
E2489 − 21
FIG. 3 Explanation of Hinges, Fences, and Categories
6.2.4.2 The IQR is the range from the upper hinge (the median of the top half of the data set) to the lower hinge (the median of
the bottom half of the data set).
6.2.4.3 Since the IQR of the data set 1, 4, 5, 5, 9, is the range from the upper hinge, 5, to the lower hinge, 4, the IQR is (5 – 4),
or 1.
6.2.4.4 If there is an even number of results in the data set, the data set is simply divided into a top half and a bottom half, each
containing an equal number of test results. For example, consider the data set 2, 4, 4, 5, 6, 8, 9, 11. The top half contains 6, 8,
9, 11 and the median (or upper hinge) is the average of 8 and 9, or 8.5. The bottom half contains 2, 4, 4, 5 and the median (or
lower hinge) is the average of 4 and 4, or 4.
6.2.4.5 Since the IQR of the data set 2, 4, 4, 5, 6, 8, 9, 11, is the range from the upper hinge, 8.5, to the lower hinge, 4, the IQR
is (8.5 – 4), or 4.5.
6.2.5 Once the IQR is determined, the outer fence is located three times the range of the IQR, (3 × IQR), beyond the upper and
lower hinges. See Fig. 3 and guidance provided in 4.8.1.
Outer Fence ~Upper!5 ~Upper Hinge!1~33IQR! (1)
Outer Fence Lower 5 Lower Hinge 2 33IQR (2)
~ ! ~ ! ~ !
6.2.5.1 For testing performed in strict accordance with a testing protocol, laboratory test results beyond the outer fence have an
extremely low likelihood of occurrence. Laboratory results occurring beyond the outer fence are categorized as “extremely
unusual.”
6.2.6 The inner fence is located 1.5 times the range of the IQR (1.5 × IQR) beyond the upper and lower hinges.
Inner Fence Upper 5 Upper Hinge 1 1.5 3IQR (3)
~ ! ~ ! ~ !
Inner Fence ~Lower!5 ~Lower Hinge!2 ~1.5 3IQR! (4)
6.2.6.1 Laboratory test results lying beyond the inner fence, but within the outer fence, have a low probability of occurrence when
testing is properly performed in accordance with the prescribed testing protocol. Laboratory results occurring beyond the inner
fence but within the outer fence are categorized as “unusual.”
E2489 − 21
TABLE 4 Alternative Intervals for Fences
Interval
Suggested
Beyond Approx. Number of Approx. Two-Tailed
Descriptive
the Upper Standard Deviations Probability for
Label for Results
and from the Consensus Results Outside
Occurring Outside
A A
Lower Value (Median) of the Interval
of the Interval
Hinges
1.0 IQR 2 0.04 typical
1.5 IQR 2.7 0.007 unusual
2.0 IQR 3.37 0.0008 very unusual
3.0 IQR 4.725 0.000 002 extremely unusual
A
The number of standard deviations from the consensus value and the probabili-
ties for being outside of the intervals are based on the assumption of a normal
distribution. The probabilities may vary for distributions that cannot be approxi-
mated by a normal distribution.
6.2.7 Most of the test results will fall within the inner fence. Laboratory test results falling at or within the inner fence are
categorized as “typical.”
6.2.8 If desired, other limits or fences can be used. Table 4 suggests several intervals that could be used to establish other fences
and gives the probabilities for results lying outside of each of the intervals listed in the table.
6.3 Example for Evaluating Laboratory Performance Using the Data in Table 2:
6.3.1 Table 2 shows test results for 30 laboratories, an even number of results, in descending order by test result. The median of
the data set is the average of the results for the 15th and 16th laboratories from the top of the table. The 15th and 16th laboratories
are #16 and #9. The median is the average of the results, (1.39 + 1.35)/2 or 1.37. See the analysis at the bottom of Table 2.
6.3.2 There are 15 results in the top half of the data in Table 2 and 15 in the bottom half. The middle (or median) value of the
top half is the eighth test result from the top, 1.76. This value, 1.76, is referred to as the upper hinge. The middle (or median) of
the bottom half is the eighth result from the bottom, 1.13. This value, 1.13, is referred to as the lower hinge.
6.3.3 The IQR is the range from the upper hinge (median of the top half) to the lower hinge (median of the bottom half), (1.76
– 1.13), or 0.63.
6.3.4 Since the outer fence is located three times the IQR beyond the hinges, the outer fence for the upper end of the data set is
located at [1.76 + (3 × IQR)], or [1.76 + (3 × 0.63)], or 3.65. The outer fence for the lower end of the data set is located at [1.13
– (3 × 0.63)], or –0.76.
6.3.5 Test results greater than 3.65 or less than –0.76 are categorized as “extremely unusual.” Only one test result, 4.89, is beyond
the outer fence. That test result, for laboratory #27, is greater than 3.65 and is categorized as “extremely unusual.” See Column
5 of Table 2. There are no test results below –0.76.
6.3.6 The inner fence is located 1.5 times the IQR beyond the hinges. The inner fence for the upper end of the data set is located
at [1.76 + (1.5 × 0.63)], or 2.705. The inner fence for the lower end of the data set is located at [1.13 – (1.5 × 0.63)], or 0.185.
6.3.7 On the upper end of the data, test results lying beyond the inner fence, but not beyond the outer fence (greater than 2.705,
but less than or equal to 3.65) are categorized as “unusual.” Test result 2.75, for laboratory #5, falls into that r
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