1、Designation: E141 10 (Reapproved 2018) An American National StandardStandard Practice forAcceptance of Evidence Based on the Results of ProbabilitySampling1This standard is issued under the fixed designation E141; the number immediately following the designation indicates the year oforiginal adoptio
2、n 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 presents rules for accepting or rejectingevidence based on a
3、sample. Statistical evidence for thispractice is in the form of an estimate of a proportion, anaverage, a total, or other numerical characteristic of a finitepopulation or lot. It is an estimate of the result which wouldhave been obtained by investigating the entire lot or populationunder the same r
4、ules and with the same care as was used for thesample.1.2 One purpose of this practice is to describe straightfor-ward sample selection and data calculation procedures so thatcourts, commissions, etc. will be able to verify whether suchprocedures have been applied. The methods may not give leastunce
5、rtainty at least cost, they should however furnish areasonable estimate with calculable uncertainty.1.3 This practice is primarily intended for one-of-a-kindstudies. Repetitive surveys allow estimates of sampling uncer-tainties to be pooled; the emphasis of this practice is onestimation of sampling
6、uncertainty from the sample itself. Theparameter of interest for this practice is effectively a constant.Thus, the principal inference is a simple point estimate to beused as if it were the unknown constant, rather than, forexample, a forecast or prediction interval or distributiondevised to match a
7、 random quantity of interest.1.4 A system of units is not specified in this standard.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety, health, and environmen
8、tal practices and deter-mine the applicability of regulatory limitations prior to use.1.6 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, G
9、uides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E105 Practice for Probability Sampling of MaterialsE122 Practice for Calculating Sample Size to Estimate, WithSpecified Precision, the Average for a
10、 Characteristic of aLot or ProcessE456 Terminology Relating to Quality and StatisticsE1402 Guide for Sampling DesignE2586 Practice for Calculating and Using Basic Statistics3. Terminology3.1 DefinitionsRefer to Terminology E456 for definitionsof other statistical terms used in this practice.3.1.1 au
11、dit subsample, na small subsample of a sampleselected for review of all sample selection and data collectionprocedures.3.1.2 equal complete coverage result, nthe numericalcharacteristic of interest calculated from observations made bydrawing randomly from the frame, all of the sampling unitscovered
12、by the frame.3.1.2.1 DiscussionLocating the units and evaluating themare supposed to be done in exactly the same way and at thesame time as was done for the sample. The quantity itself isdenoted . The equal complete coverage result is never actuallycalculated. Its purpose is to serve as the objectiv
13、ely definedconcrete goal of the investigation. The quantity may be thepopulation mean, (Y), total (Y), median (M), the proportion (P),or any other such quantity.3.1.3 frame, na list, compiled for sampling purposes,which designates all of the sampling units (items or groups) ofa population or univers
14、e to be considered in a specific study.E14023.1.4 probability sample, na sample in which the sam-pling units are selected by a chance process such that a1This practice is under the jurisdiction ofASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.10 on S
15、ampling /Statistics.Current edition approved April 1, 2018. Published May 2018. Originallyapproved in 1959. Last previous edition approved in 2010 as E141 10. DOI:10.1520/E0141-10R18.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.
16、org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with inte
17、rnationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1specified probability of selection can be attac
18、hed to eachpossible sample that can be selected. E14023.1.5 replicate subsamples, na number of disjointsamples, each one separately drawn from the frame in accordwith the same probability sampling plan.3.1.6 sample, na group of observations or test results,taken from a larger collection of observati
19、ons or test results,which serves to provide information that may be used as a basisfor making a decision concerning the larger collection. E25863.1.7 sampling unit, nan item, group of items, or segmentof material that can be selected as part of a probabilitysampling plan. E14024. Significance and Us
20、e4.1 This practice is designed to permit users of samplesurvey data to judge the trustworthiness of results from suchsurveys. Practice E105 provides a statement of principles forguidance of ASTM technical committees and others in thepreparation of a sampling plan for a specific material. GuideE1402
21、describes the principal types of sampling designs.Practice E122 aids in deciding on the required sample size.4.2 Section 5 gives extended definitions of the conceptsbasic to survey sampling and the user should verify that suchconcepts were indeed used and understood by those whoconducted the survey.
22、 What was the frame? How large (ex-actly) was the quantity N? How was the parameter estimatedand its standard error calculated? If replicate subsamples werenot used, why not? Adequate answers should be given for allquestions. There are many acceptable answers to the lastquestion.4.3 If the sample de
23、sign was relatively simple, such assimple random or stratified, then fully valid estimates ofsampling variance are easily available. If a more complexdesign was used then methods such as discussed in Ref (1)3orin Guide E1402 may be acceptable. Use of replicate sub-samples is the most straightforward
24、 way to estimate samplingvariances when the survey design is complex.4.4 Once the survey procedures that were used satisfySection 5, see if any increase in sample size is needed. Thecalculations for making it objectively are described in Section6.4.5 Refer to Section 7 to guide in the interpretation
25、 of theuncertainty in the reported value of the parameter estimate, ,that is, the value of its standard error, se(). The quantity se()should be reviewed to verify that the risks it entails arecommensurate with the size of the sample.4.6 When the audit subsample shows that there was reason-able confo
26、rmity with prescribed procedures and when theknown instances of departures from the survey plan can beshown to have no appreciable effect on the estimate, the valueof is appropriate for use.5. Concepts and Procedures of Sampling5.1 Probability sampling is a procedure by which oneobtains a result fro
27、m a selected set of sampling units that willagree, within calculable limits of variation, with the equalcomplete coverage result. Probability sampling plans includeinstructions for using either (1) prepared tables of randomnumbers, (2) computer algorithms to generate pseudo-randomnumbers, or (3) cer
28、tifiably honest physical devices to select thesample units so that inferences may be drawn from the testresults and decisions may be made with risks correctly calcu-lated by probability theory.5.1.1 Such plans are defined and their relative advantagesdiscussed in Guide E1402 and Refs (1-3).5.2 Proce
29、dures must be described in written form. Partiesinterested in collecting data should agree on the importance ofknowing and its definition including measurement methods.The frame shall be carefully and explicitly constructed. Everysampling unit in the frame (1) has a unique serial number,which may be
30、 preassigned or determined by some definite ruleand (2) has an addressa complete and clear instruction (orrules for its formulation) as to where and when to make theobservation or evaluation. Address instructions should refer toconcrete clerical materials such as directories, dials of clocksor of me
31、ters, ledgers, maps, aerial photographs, etc. Duplicatesin the frame shall be eliminated. N shall be well established.Random numbers (or a certifiably honest physical randomdevice) shall dictate selection of the sample. There shall be nosubstitution of one sampling unit for another. The method ofsam
32、ple selection shall permit calculation of a standard error ofthe estimate. The use of replicate subsamples is recommended(see 5.4).An audit subsample should be selected and processedand any departures from prescribed measurement methods andlocation instructions noted (see 5.5). A report should list
33、andits standard error with the degrees of freedom in the se().5.3 Parameter DefinitionThe equal complete coverageresult may or may not be acceptable evidence. Whether it isacceptable depends on many considerations such as definitions,method of test, care exercised in the testing, completeness ofthe
34、frame, and on other points not to be settled by statisticaltheory since these points belong to the subject matter, and arethe same whether one uses sampling or not. Mistakes, whetherin testing, counting, or weighing will affect the result of acomplete coverage just as such mistakes will affect the s
35、ampleresult. By a more expensive method of measurement or moreelaborate sampling frame, it may be possible to define aquantity, , as a target parameter or ideal goal of an investi-gation. Criticism that holds to be an inappropriate goal shoulddemonstrate that the numerical difference between and iss
36、ubstantial. Measurements may be imprecise but so long asmeasurement errors are not too biased, a large size of the lot orpopulation, N, insures that and are essentially equal.5.4 Replicate SubsamplesWhen appropriate, separatelaboratories should each work on separate replicate subsamplesand teams of
37、investigators should be assigned to separatereplicate subsamples. This approach insures that the calculatedstandard error will not be a systematic underestimate. Suchsubsamples were called interpenetrating in Ref (4) where many3The boldface numbers in parentheses refer to a list of references at the
38、 end ofthis standard.E141 10 (2018)2of their basic properties were described. See Ref (5) for furthertheory and applications.5.4.1 For some types of material, a sample selected withuniform spacing along the frame (systematic sample) hasincreased precision over a selection made with randomlyvarying s
39、pacings (simple random sample). Examples includesampling mineral ore or grain from a conveyor belt or samplingfrom a list of households along a street. If the systematicsample is obtained by a single random start the plan is then aprobability sampling plan, but it does not permit calculating thestan
40、dard error as required by this practice. After dividing thesample size by an integer k (such as k =4ork = 10) and usinga random start for each of k replicate subsamples, some of theincreased precision of systematic sampling (and a standarderror on k 1 degrees of freedom) can be achieved.5.5 An audit
41、 subsample of the survey sample should betaken for review of all procedures from use of the randomnumbers through locating and measurement, to editing, coding,data entry and tabulation. Selection of the audit subsample maybe done by putting the n sample observations in order as theyare collected, ca
42、lculating the nearest integer to =n , or someother convenient integer, and taking this number to be thespacing for systematic selection of the audit subsample.As fewas 10 observations may be adequate. The review shoulduncover any gross departures from prescribed practices or anyconceptual misunderst
43、andings in the definitions. If the auditsubsample is large enough (say 30 observations or more) theregression of audited values on initial observations may beused to calibrate the estimate. This technique is the method oftwo-phase sampling as discussed in Ref (1). Helpful discussionof an audit appea
44、rs in Ref (2).5.6 The estimate is a quantity calculated on the n sampleobservations in the same way as the equal complete coverageresult would have been calculated from the entire set of Npossible observations of the population; the symbol denotesthe estimate. In calculating , replicate subsample me
45、mbershipis ignored.5.6.1 An estimate has a sampling distribution induced fromthe randomness in sample selection. The equal completecoverage result is effectively a constant while any estimate isonly the value from one particular sample. Thus, there is amean value of the sampling distribution and the
46、re is also astandard deviation of the sampling distribution.5.7 The standard error is the quantity computed from theobservations as an estimate of the sampling standard deviationof the estimate; se() denotes the standard error.5.7.1 When is the population average of the N quantitiesand a simple rand
47、om sample of size n was drawn, then thesample average y becomes the usual estimate , where:5 yH 5(i51nyi/n (1)The quantities y1, y2, ., yndenote the observations. Thestandard error is calculated as:se! 5 seyH! 5(i51nyi2 yH!2/nn 2 1! (2)There are n 1 degrees of freedom in this standard error.5.7.1.1
48、ExampleWhen the observations are:81.6, 78.7, 79.7, 78.3, 80.9, 79.5, 79.8, 80.3, 79.5, 80.7then y = 79.90 and se(y) = 0.32.5.7.2 Finite Population Correction (fpc)Multiplying se(y)by =12n/N is always correct when the goal of the survey is toestimate the finite population mean ( =Y). If random mea-su
49、rement error exists in the observations, then based on areference measurement method may be a more appropriatesurvey goal than (see 5.3). If so, then se(y) would be furtheradjusted upward by an amount somewhat less than the down-ward adjustment of the fpc. Both of these adjustments are oftennumerically so small that these adjustments may be omittedleaving se(y) of Eq 2 as a slight overestimate.5.7.2.1 ExampleUsing the previous data and if N = 50,then se(y) becomes se(y) = 0.28 after applying the
