1、Designation: E2489 11E2489 16 An American National StandardStandard Practice forStatistical Analysis of One-Sample and Two-SampleInterlaboratory Proficiency Testing Programs1This standard is issued under the fixed designation E2489; the number immediately following the designation indicates the year
2、 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 describes methods for the statistical anal
3、ysis of laboratory results obtained from interlaboratory proficiencytesting programs. As in accordance with Practice E1301, proficiency testing is the use of interlaboratory comparisons for thedetermination of laboratory testing or measurement performance. Conversely, collaborative study (or collabo
4、rative trial) is the useof interlaboratory comparisons for the determination of the performance characteristics precision of a test method, as covered byPractice E691.1.1.1 Method A covers testing programs using single test results obtained by testing a single sample (each laboratory submitsa single
5、 test result).1.1.2 Method B covers testing programs using paired test results obtained by testing two samples (each laboratory submits onetest result for each of the two samples). The two samples should be of the same material or two materials similar enough to haveapproximately the same degree of
6、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 therelative likelihood of occurrence
7、 of their test results, and for determining estimates of testing variation associated with repeatabilityand reproducibility. Assumptions are that a majority of the participating laboratories execute the test method properly and thatsamples are of sufficient homogeneity that the testing results repre
8、sent results obtained from each laboratory testing essentially thesame 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 responsibilityof the user of this standard
9、to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E177 Practice for Use of the Terms Precision and Bias in ASTM Test MethodsE178 Practice for Dealing With Outlying ObservationsE456 Ter
10、minology Relating to Quality and StatisticsE691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test MethodE1301 Guide for Proficiency Testing by Interlaboratory Comparisons (Withdrawn 2012)3E2586 Practice for Calculating and Using Basic Statistics3. Terminology3.1 D
11、efinitions:Definitions3.1.1 The terminology defined in Terminology E456 applies to this practice unless modified herein.The terminology definedin Terminology E456 applies to this practice unless modified herein.1 This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics
12、 and is the direct responsibility of Subcommittee E11.20 on Test MethodEvaluation and Quality Control.Current edition approved Oct. 1, 2011Nov. 15, 2016. Published October 2011November 2016. Originally approved in 2006. Last previous edition approved in 20062011as E2489 06E2489 11.1. DOI: 10.1520/E2
13、489-11.10.1520/E2489-16.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.3 The last approved version of this h
14、istorical standard is referenced on www.astm.org.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. Becauseit may not be technically possible to adequately depict all changes accurat
15、ely, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
16、13.1.1 collaborative study, ninterlaboratory study in which each laboratory uses the defined method of analysis to analyzeidentical portions of homogeneous materials to assess the performance characteristics obtained for that method of analysis.Horwitz43.1.2 collaborative trial, nsee collaborative s
17、tudy.3.1.3 interlaboratory comparison, norganization, performance, and evaluation of tests on the same or similar test items by twoor more laboratories in accordance with predetermined conditions.3.1.4 median, X, nmiddle value of a data set when the datathe 50th is arranged in order of size or the a
18、verage of the middletwo values when there is an even number of items in the data set.percentile in a population or sample. E25863.1.4.1 DiscussionThe 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 orderstatistics if n is even.3.1.
19、5 outlier, nsee outlying observation. E1783.1.6 outlying observation, nobservation that appears to deviate markedly in value from other members of the sample in whichit appears. E1783.1.7 proficiency testing, ndetermination of laboratory testing performance by means of interlaboratory comparisons.3.
20、1.8 repeatability standard deviation (Sr), nstandard deviation of test results obtained under repeatability conditions. E1773.1.9 reproducibility standard deviation (SR), nstandard deviation of test results obtained under reproducibility conditions.E1773.2 Definitions of Terms Specific to This Stand
21、ard:3.2.1 hinge (upper or lower), nmedian of the upper or lower half of a set of data when the data is arranged in order of size.3.2.1.1 DiscussionWhen there is an odd number of items in the data set, the middle value is included in both the upper and lower halves. The upperhinge is an estimate of t
22、he 75th percentile; the lower hinge is an estimate of the 25th percentile.3.2.2 inner fence (upper or lower), nvalue equal to the upper or lower hinge of a data set plus (upper) or minus (lower) 1.5times the difference between upper and lower hinges.3.2.3 interquartile range, ndistance between the u
23、pper and lower hinges of a data set.3.2.4 outer fence (upper or lower), nvalue equal to the upper or lower hinge of a data set plus (upper) or minus (lower) threetimes the difference between upper and lower hinges.4. Summary of Practice4.1 This practice describes methods of displaying interlaborator
24、y data that visually show individual laboratory results.4.2 The methods described in this practice can be applied to large and small sample populations from any distribution expectedto have a general mound shape. It is recommended that in cases in which it is suspected that the data may be highly un
25、symmetricalor 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
26、the data. Because the median and theinterquartile range are not affected by the magnitude of extreme values of a data set, the analysis approach presented in this practiceeffectively eliminates the need to identify outlying observations (outliers).4.3 Laboratory results are categorized according to
27、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 laboratoryresults lying outside of the interquartile range are determined by multiplying the extent of the interquartile range
28、 by the fixedfactors 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 referredto 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 referredto as the outer fences
29、.4.5 Guidance is provided for proficiency testing programs wishing to establish additional limits (or fences). The user is directedto Guide E1301 for additional guidance.4 Horwitz, W., “Protocol for the Design, Conduct and Interpretation of Collaborative Studies,” Pure and Applied Chemistry, Vol 60,
30、 No. 6, 1988, pp. 855864.E2489 1624.6 When using the methods in this practice, the number of participating laboratories should be at least ten. Since the degreeof confidence is lower for analyses performed on small sample populations, caution should be used in applying statistics obtainedfrom small
31、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 theinterquartile ranges of appropr
32、iate 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 assumptionof similarity to a normal distribution. Therefore, the estimate of the standard deviation using the methods described in this practicemay no
33、t supply the desired accuracy if the distribution differs too much from the general shape of a normal curve. It is beyondthe scope of this practice to describe procedures for determining when the analysis methods described in this practice are notapplicable.5. Significance and Use5.1 This practice i
34、s 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 froma group of participating laboratories. The laboratory comparis
35、ons can then be used for evaluation of individual laboratoryperformance.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 th
36、e program uses more than onesample. See Method B. Proficiency testing programs often have a greater number of participants than might be available forconducting an interlaboratory study to determine the precision of a test method (such as described in Practice E691). Precisionestimates obtained for
37、the larger number of participants in a proficiency testing program, along with the corresponding widervariation of test conditions, can provide useful information to standards developers regarding the precision of test results that canbe expected for a test method when in actual use in the general t
38、esting community.5.4 To estimate the precision of a test method, the participants must use the same test method to obtain their test results, andtesting must be performed under the conditions required for repeatability and reproducibility. The precision estimates areapplicable to the property levels
39、 and material types included in the testing program. The precision of a test method may varyconsiderably 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 alongwith
40、explanations of some of the advantages of the suggested methods of analysis. The analyses resulting from the application ofmethods described in this practice may be used by laboratories as part of their quality control procedures, accrediting bodies toassist in the evaluation of laboratory performan
41、ce, andASTM International technical committees (and other organizations chargedwith 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 ex
42、ist for analyzing the data resultingfrom the interlaboratory testing. It is not the intention of this practice to call into question the integrity of programs using othermethods of analysis. Testing programs using replicate testing of one or more samples (each laboratory submits two or more resultsf
43、or each sample) are directed to Practice E691 or other practices for the description of a method of analysis that may be moresuitable 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
44、submitted by each laboratory. This may not bepractical 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 identi
45、fication number to make it easy to locate the resultsfor 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 Table2. Besides the laboratory identification number and corresponding test r
46、esults, Table 2 contains columns of additional informationthat will be explained in the following sections of this practice.6.1.3 Display the data in a dot diagram to show the location of each laboratorys test result in the distribution of all test results.For each test result, plot occurrence numbe
47、r of that test result value versus the value of the test result. As points are plotted fromthe 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 resultvalue occurs, assign it an occurrence of “two.” If the test result value app
48、ears a third time, assign it an occurrence of “three” andso 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 l
49、aboratorys test resultwill be plotted as an individual dot and no dots will be concealed by being plotted on top of one another.E2489 1636.1.3.1 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 Table2 shows that the number of occurrences is “one” for each test result and the dots in Fig. 1 appear in a single horizontal row. Thedot 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 Labora
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