1、Designation: C1215 92 (Reapproved 2012)1C1215 18Standard Guide forPreparing and Interpreting Precision and Bias Statements inTest Method Standards Used in the Nuclear Industry1This standard is issued under the fixed designation C1215; the number immediately following the designation indicates the ye
2、ar 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 NOTEChanges were made editorially in June 2012.INTRODUCTIONTest
3、method standards are required to contain precision and bias statements. This guide contains aglossary that explains various terms that often appear in these statements as well as an exampleillustrating such statements for a specific set of data. Precision and bias statements are shown to varyaccordi
4、ng to the conditions under which the data were collected. This guide emphasizes that the errormodel (an algebraic expression that describes how the various sources of variation affect themeasurement) is an important consideration in the formation of precision and bias statements.1. Scope1.1 This gui
5、de covers terminology useful for the preparation and interpretation of precision and bias statements. This guide doesnot recommend a specific error model or statistical method. It provides awareness of terminology and approaches and options touse for precision and bias statements.1.2 In formulating
6、precision and bias statements, it is important to understand the statistical concepts involved and to identifythe major sources of variation that affect results. Appendix X1 provides a brief summary of these concepts.1.3 To illustrate the statistical concepts and to demonstrate some sources of varia
7、tion, a hypothetical data set has been analyzedin Appendix X2. Reference to this example is made throughout this guide.1.4 It is difficult and at times impossible to ship nuclear materials for interlaboratory testing. Thus, precision statements for testmethods relating to nuclear materials will ordi
8、narily reflect only within-laboratory variation.1.5 No units are used in this statistical analysis.1.6 This guide does not involve the use of materials, operations, or equipment and does not address any risk associated.1.7 This international standard was developed in accordance with internationally
9、recognized principles on standardizationestablished in the Decision on Principles for the Development of International Standards, Guides and Recommendations issuedby the World Trade Organization Technical Barriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2C859 Terminology R
10、elating to Nuclear MaterialsE177 Practice for Use of the Terms Precision and Bias in ASTM Test MethodsE691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method2.2 ANSI Standard:ANSI N15.5 Statistical Terminology and Notation for Nuclear Materials Management31
11、This guide is under the jurisdiction of ASTM Committee C26 on Nuclear Fuel Cycle and is the direct responsibility of Subcommittee C26.08 on Quality Assurance,Statistical Applications, and Reference Materials.Current edition approved June 1, 2012July 1, 2018. Published June 2012July 2018. Originally
12、approved in 1992. Last previous edition approved in 20062012 asC121592(2006).C1215 92 (2012)1. DOI: 10.1520/C1215-92R12E01.10.1520/C1215-18.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume
13、 information, refer to the standards Document Summary page on the ASTM website.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 adequat
14、ely depict all changes accurately, 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
15、, PA 19428-2959. United States13. Terminology for Precision and Bias Statements3.1 For definitions of terms used in this guide but not defined herein, see Terminology C859.3.2 Definitions:Terminology for Precision and Bias Statements3.2.1 accuracy (seebias) (1) bias. (2) the closeness of a measured
16、value to the true value. (3) the closeness of a measured valueto an accepted reference or standard value.3.2.1.1 DiscussionFor many investigators, accuracy is attained only if a procedure is both precise and unbiased (see bias). Because this blending ofprecision into accuracy can result occasionally
17、 in incorrect analyses and unclear statements of results, ASTM requires statementon bias instead of accuracy.33.2.2 analysis of variance (ANOVA)the body of statistical theory, methods, and practices in which the variation in a set of datais partitioned into identifiable sources of variation. Sources
18、 of variation may include analysts, instruments, samples, andlaboratories. To use the analysis of variance, the data collection method must be carefully designed based on a model that includesall the sources of variation of interest. (See Example, X2.1.1)3.2.3 bias (see accuracy)a constant positive
19、or negative deviation of the method average from the correct value or acceptedreference value.3.2.3.1 DiscussionBias represents a constant error as opposed to a random error.(a) A method bias can be estimated by the difference (or relative difference) between a measured average and an acceptedstanda
20、rd or reference value. The data from which the estimate is obtained should be statistically analyzed to establish bias in thepresence of random error. A thorough bias investigation of a measurement procedure requires a statistically designed experimentto repeatedly measure, under essentially the sam
21、e conditions, a set of standards or reference materials of known value that coverthe range of application. Bias often varies with the range of application and should be reported accordingly.(b) In statistical terminology, an estimator is said to be unbiased if its expected value is equal to the true
22、 value of the parameterbeing estimated. (See Appendix X1.)(c) The bias of a test method is also commonly indicated by analytical chemists as percent recovery. A number of repetitionsof the test method on a reference material are performed, and an average percent recovery is calculated. This average
23、provides anestimate of the test method bias, which is multiplicative in nature, not additive. (See Appendix X2.)(d) Use of a single test result to estimate bias is strongly discouraged because, even if there were no bias, random error alonewould produce a nonzero bias estimate.3.2.4 coeffcient of va
24、riationsee relative standard deviation.3.2.5 confidence intervalan interval used to bound the value of a population parameter with a specified degree of confidence(this is an interval that has different values for different random samples).3.2.5.1 DiscussionWhen providing a confidence interval, anal
25、ysts should give the number of observations on which the interval is based. Thespecified degree of confidence is usually 90, 95, or 99 %. The form of a confidence interval depends on underlying assumptionsand intentions. Usually, confidence intervals are taken to be symmetric, but that is not necess
26、arily so, as in the case of confidenceintervals for variances. Construction of a symmetric confidence interval for a population mean is discussed in Appendix X3.It is When providing a confidence interval, analysts should give the number of observations on which the interval is based.The specified de
27、gree of confidence is usually 90, 95, or 99 %. The form of a confidence interval depends on underlyingassumptions and intentions. Usually, confidence intervals are taken to be symmetric, but that is not necessarily so, as in the caseof confidence intervals for variances. Construction of a symmetric
28、confidence interval for a population mean is discussed inAppendix X3.It is important to realize that a given confidence-interval estimate either does or does not contain the population parameter.The degree of confidence is actually in the procedure. For example, if the interval (9, 13) is a 90 % con
29、fidence interval for themean, we are confident that the procedure (take a sample, construct an interval) by which the interval (9, 13) was constructedwill 90 % of the time produce an interval that does indeed contain the mean. Likewise, we are confident that 10 % of the timethe interval estimate obt
30、ained will not contain the mean. Note that the absence of sample size information detracts from the3 Refer to Form and Style for ASTM Standards, 8th Ed., 1989, ASTM.C1215 182usefulness of the confidence interval. If the interval were based on five observations, a second set of five might produce a v
31、erydifferent interval. This would not be the case if 50 observations were taken.3.2.6 confidence levelthe probability, usually expressed as a percent, that a confidence interval will contain the parameter ofinterest. (See discussion of confidence interval in Appendix X3.)3.2.7 error modelan algebrai
32、c expression that describes how a measurement is affected by error and other sources of variation.The model may or may not include a sampling error term.3.2.7.1 DiscussionAmeasurement error is an error attributable to the measurement process. The error may affect the measurement in many ways andit i
33、s important to correctly model the effect of the error on the measurement.(a) Two common models are the additive and the multiplicative error models. In the additive model, the errors areindependent of the value of the item being measured. Thus, for example, for repeated measurements under identical
34、 conditions,the additive error model might beXi 51b1 i (1)where:Xi = the result of the ith measurement, = the true value of the item,b = a bias, andi = a random error usually assumed to have a normal distribution with mean zero and variance 2.In the multiplicative model, the error is proportional to
35、 the true value. A multiplicative error model for percent recovery (seebias) might be:Xi 5bi (2)and a multiplicative model for a neutron counter measurement might be:Xi 51b1 i (3)511b1 i!(b) Clearly, there are many ways in which errors may affect a final measurement. The additive model is frequently
36、 as-sumed and is the basis for many common statistical procedures. The form of the model influences how the error compo-nents will be estimated and is very important, for example, in the determination of measurement uncertainties. Further dis-cussion of models is given in the Example of Appendix X2
37、and in Appendix X4.3.2.8 precisiona generic concept used to describe the dispersion of a set of measured values.3.2.8.1 DiscussionIt is important that some quantitative measure be used to specify precision.Astatement such as, “The precision is 1.54 g” is useless.Measures frequently used to express p
38、recision are standard deviation, relative standard deviation, variance, repeatability,reproducibility, confidence interval, and range. In addition to specifying the measure and the precision, it is important that thenumber of repeated measurements upon which the precision estimated is based also be
39、given. (See Example, Appendix X2.)(a) It is strongly recommended that a statement on precision of a measurement procedure include the following:(a) It is strongly recommended that a statement on precision of a measurement procedure include the following:(1) A description of the procedure used to obt
40、ain the data,(2) The number of repetitions, n, of the measurement procedure,(3) The sample mean and standard deviation of the measurements,(4) The measure of precision being reported,(5) The computed value of that measure, and(6) The applicable range or concentration.The importance of items (3) and
41、(4) lies in the fact that with these a reader may calculate a confidence interval or relativestandard deviation as desired.(b) Precision is sometimes measured by repeatability and reproducibility (see Practice E177, and Mandel and Laskof (1).TheANSI and ASTM documents differ slightly in their usages
42、 of these terms. The following is quoted from Kendall and Buckland(2):“In some situations, especially interlaboratory comparisons, precision is defined by employing two additional concepts:repeatability and reproducibility. The general situation giving rise to these distinctions comes from the inter
43、est in assessing theC1215 183variability within several groups of measurements and between those groups of measurements. Repeatability, then, refers to thewithin-group dispersion of the measurements, while reproducibility refers to the between-group dispersion. In interlaboratorycomparison studies,
44、for example, the investigation seeks to determine how well each laboratory can repeat its measurements(repeatability) and how well the laboratories agree with each other (reproducibility). Similar discussions can apply to thecomparison of laboratory technicians skills, the study of competing types o
45、f equipment, and the use of particular procedureswithin a laboratory. An essential feature usually required, however, is that repeatability and reproducibility be measured asvariances (or standard deviations in certain instances), so that both within- and between-group dispersions are modeled as ara
46、ndom variable. The statistical tool useful for the analysis of such comparisons is the analysis of variance.”(c) In Practice E177 it is recommended that the term repeatability be reserved for the intrinsic variation due solely to themeasurement procedure, excluding all variation from factors such as
47、 analyst, time and laboratory and reserving reproducibilityfor the variation due to all factors including laboratory. Repeatability can be measured by the standard deviation, r, of nconsecutive measurements by the same operator on the same instrument. Reproducibility can be measured by the standardd
48、eviation, R, of m measurements, one obtained from each of m independent laboratories. When interlaboratory testing is notpractical, the reproducibility conditions should be described.The importance of items (3) and (4) lies in the fact that with these a reader may calculate a confidence interval or
49、relativestandard deviation as desired.(b) Precision is sometimes measured by repeatability and reproducibility (see Practice E177, and Mandel and Laskof (1).The ANSI and ASTM documents differ slightly in their usages of these terms. The following is quoted from Kendall andBuckland (2):“In some situations, especially interlaboratory comparisons, precision is defined by employing two additional concepts:repeatability and reproducibility. The general situation giving rise to these distinctions comes from the interest in assessing thevariabilit
