ASTM E1402-13(2018)
(Guide)Standard Guide for Sampling Design
Standard Guide for Sampling Design
ABSTRACT
This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards. This guide also describes the principal types of sampling designs and provides formulas for estimating population means and standard errors of the estimates.
Sampling, both discrete and bulk, is a clerical and physical operation. It generally involves training enumerators and technicians to use maps, directories and stop watches so as to locate designated sampling units. Once a sampling unit is located at its address, discrete sampling and area sampling enumeration proceeds to a measurement.
SIGNIFICANCE AND USE
4.1 This guide describes the principal types of sampling designs and provides formulas for estimating population means and standard errors of the estimates. Practice E105 provides principles for designing probability sampling plans in relation to the objectives of study, costs, and practical constraints. Practice E122 aids in specifying the required sample size. Practice E141 describes conditions to ensure validity of the results of sampling. Further description of the designs and formulas in this guide, and beyond it, can be found in textbooks (1-10).3
4.2 Sampling, both discrete and bulk, is a clerical and physical operation. It generally involves training enumerators and technicians to use maps, directories and stop watches so as to locate designated sampling units. Once a sampling unit is located at its address, discrete sampling and area sampling enumeration proceeds to a measurement. For bulk sampling, material is extracted into a composite.
4.3 A sampling plan consists of instructions telling how to list addresses and how to select the addresses to be measured or extracted. A frame is a listing of addresses each of which is indexed by a single integer or by an n-tuple (several integer) number. The sampled population consists of all addresses in the frame that can actually be selected and measured. It is sometimes different from a targeted population that the user would have preferred to be covered.
4.4 A selection scheme designates which indexes constitute the sample. If certified random numbers completely control the selection scheme the sample is called a probability sample. Certified random numbers are those generated either from a table (for example, Ref (11)) that has been tested for equal digit frequencies and for serial independence, from a computer program that was checked to have a long cycle length, or from a random physical method such as tossing of a coin or a casino-quality spinner.
4.5 The objective of sampling is often to estimate t...
SCOPE
1.1 This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards.
1.2 Sampling may be done for the purpose of estimation, of comparison between parts of a sampled population, or for acceptance of lots. Sampling is also used for the purpose of auditing information obtained from complete enumeration of the population.
1.3 No system of units is specified in this standard.
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, health, and environmental 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.
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Standards Content (Sample)
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.
Designation: E1402 − 13 (Reapproved 2018) An American National Standard
Standard Guide for
1
Sampling Design
This standard is issued under the fixed designation E1402; 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 3. Terminology
1.1 This guide defines terms and introduces basic methods 3.1 Definitions—For a more extensive list of statistical
for probability sampling of discrete populations, areas, and terms, refer to Terminology E456.
bulk materials. It provides an overview of common probability 3.1.1 area sampling, n—probability sampling in which a
sampling methods employed by users of ASTM standards. map, rather than a tabulation of sampling units, serves as the
sampling frame.
1.2 Sampling may be done for the purpose of estimation, of
3.1.1.1 Discussion—Area sampling units are segments of
comparison between parts of a sampled population, or for
land area and are listed by addresses on the frame prior to their
acceptance of lots. Sampling is also used for the purpose of
actual delineation on the ground so that only the randomly
auditing information obtained from complete enumeration of
selected ones need to be exactly identified.
the population.
3.1.2 bulk sampling, n—sampling to prepare a portion of a
1.3 No system of units is specified in this standard.
mass of material that is representative of the whole.
1.4 This standard does not purport to address all of the
3.1.3 cluster sampling, n—sampling in which the sampling
safety concerns, if any, associated with its use. It is the
unit consists of a group of subunits, all of which are measured
responsibility of the user of this standard to establish appro-
for sampled clusters.
priate safety, health, and environmental practices and deter-
3.1.4 frame, n—a list, compiled for sampling purposes,
mine the applicability of regulatory limitations prior to use.
which designates all of the sampling units (items or groups) of
1.5 This international standard was developed in accor-
a population or universe to be considered in a specific study.
dance with internationally recognized principles on standard-
ization established in the Decision on Principles for the
3.1.5 multi-stage sampling, n—sampling in which the
Development of International Standards, Guides and Recom-
sample is selected by stages, the sampling units at each stage
mendations issued by the World Trade Organization Technical
being selected from subunits of the larger sampling units
Barriers to Trade (TBT) Committee.
chosen at the previous stage.
3.1.5.1 Discussion—The sampling unit for the first stage is
2. Referenced Documents
the primary sampling unit. In multi-stage sampling, this unit is
2
further subdivided. The second stage unit is called the second-
2.1 ASTM Standards:
ary sampling unit. A third stage unit is called a tertiary
D7430 Practice for Mechanical Sampling of Coal
sampling unit. The final sample is the set of all last stage
E105 Practice for Probability Sampling of Materials
sampling units that are obtained.As an example of sampling a
E122 Practice for Calculating Sample Size to Estimate,With
lot of packaged product, the cartons of a lot could be the
Specified Precision, the Average for a Characteristic of a
primary units, packages within the carton could be secondary
Lot or Process
units, and items within the packages could be the third-stage
E141 Practice for Acceptance of Evidence Based on the
units.
Results of Probability Sampling
E456 Terminology Relating to Quality and Statistics
3.1.6 nested sampling, n—same as multi-stage sampling.
3.1.7 primary sampling unit, PSU, n—the item, element,
increment, segment or cluster selected at the first stage of the
1
This guide is under the jurisdiction of ASTM Committee E11 on Quality and
selection procedure from a population or universe.
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling /
Statistics.
3.1.8 probability proportional to size sampling, PPS,
Current edition approved Nov. 1, 2018. Published November 2018. Originally
n—probability sampling in which the probabilities of selection
approved in 2008. Last previous edition approved in 2013 as E1402 – 13. DOI:
of sampling units are proportional, or nearly proportional, to a
10.1520/E1402-13R18.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
quantity (the “size”) that is known for all sampling units.
contact ASTM Customer Service at service@astm.org. For Annual Book of
...
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E1402 − 13 (Reapproved 2018) An American National Standard
Standard Guide for
1
Sampling Design
This standard is issued under the fixed designation E1402; 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 3. Terminology
1.1 This guide defines terms and introduces basic methods 3.1 Definitions—For a more extensive list of statistical
for probability sampling of discrete populations, areas, and terms, refer to Terminology E456.
bulk materials. It provides an overview of common probability 3.1.1 area sampling, n—probability sampling in which a
sampling methods employed by users of ASTM standards. map, rather than a tabulation of sampling units, serves as the
sampling frame.
1.2 Sampling may be done for the purpose of estimation, of
3.1.1.1 Discussion—Area sampling units are segments of
comparison between parts of a sampled population, or for
land area and are listed by addresses on the frame prior to their
acceptance of lots. Sampling is also used for the purpose of
actual delineation on the ground so that only the randomly
auditing information obtained from complete enumeration of
selected ones need to be exactly identified.
the population.
3.1.2 bulk sampling, n—sampling to prepare a portion of a
1.3 No system of units is specified in this standard.
mass of material that is representative of the whole.
1.4 This standard does not purport to address all of the
3.1.3 cluster sampling, n—sampling in which the sampling
safety concerns, if any, associated with its use. It is the
unit consists of a group of subunits, all of which are measured
responsibility of the user of this standard to establish appro-
for sampled clusters.
priate safety, health, and environmental practices and deter-
3.1.4 frame, n—a list, compiled for sampling purposes,
mine the applicability of regulatory limitations prior to use.
which designates all of the sampling units (items or groups) of
1.5 This international standard was developed in accor-
a population or universe to be considered in a specific study.
dance with internationally recognized principles on standard-
ization established in the Decision on Principles for the
3.1.5 multi-stage sampling, n—sampling in which the
Development of International Standards, Guides and Recom-
sample is selected by stages, the sampling units at each stage
mendations issued by the World Trade Organization Technical
being selected from subunits of the larger sampling units
Barriers to Trade (TBT) Committee.
chosen at the previous stage.
3.1.5.1 Discussion—The sampling unit for the first stage is
2. Referenced Documents
the primary sampling unit. In multi-stage sampling, this unit is
2
further subdivided. The second stage unit is called the second-
2.1 ASTM Standards:
ary sampling unit. A third stage unit is called a tertiary
D7430 Practice for Mechanical Sampling of Coal
sampling unit. The final sample is the set of all last stage
E105 Practice for Probability Sampling of Materials
sampling units that are obtained. As an example of sampling a
E122 Practice for Calculating Sample Size to Estimate, With
lot of packaged product, the cartons of a lot could be the
Specified Precision, the Average for a Characteristic of a
primary units, packages within the carton could be secondary
Lot or Process
units, and items within the packages could be the third-stage
E141 Practice for Acceptance of Evidence Based on the
units.
Results of Probability Sampling
E456 Terminology Relating to Quality and Statistics
3.1.6 nested sampling, n—same as multi-stage sampling.
3.1.7 primary sampling unit, PSU, n—the item, element,
increment, segment or cluster selected at the first stage of the
1
This guide is under the jurisdiction of ASTM Committee E11 on Quality and
selection procedure from a population or universe.
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling /
Statistics.
3.1.8 probability proportional to size sampling, PPS,
Current edition approved Nov. 1, 2018. Published November 2018. Originally
n—probability sampling in which the probabilities of selection
approved in 2008. Last previous edition approved in 2013 as E1402 – 13. DOI:
of sampling units are proportional, or nearly proportional, to a
10.1520/E1402-13R18.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
quantity (the “size”) that is known for all sampling units.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.1.9 probability sample, n—a sample in which the sam-
Standards volume information, refer to the standard’s Document Summary page on
the AS
...
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: E1402 − 13 E1402 − 13 (Reapproved 2018) An American National Standard
Standard Guide for
1
Sampling Design
This standard is issued under the fixed designation E1402; 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
1.1 This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk
materials. It provides an overview of common probability sampling methods employed by users of ASTM standards.
1.2 Sampling may be done for the purpose of estimation, of comparison between parts of a sampled population, or for
acceptance of lots. Sampling is also used for the purpose of auditing information obtained from complete enumeration of the
population.
1.3 No system of units is specified in this standard.
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, health, and environmental 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
2.1 ASTM Standards:
D7430 Practice for Mechanical Sampling of Coal
E105 Practice for Probability Sampling of Materials
E122 Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or
Process
E141 Practice for Acceptance of Evidence Based on the Results of Probability Sampling
E456 Terminology Relating to Quality and Statistics
3. Terminology
3.1 Definitions—For a more extensive list of statistical terms, refer to Terminology E456.
3.1.1 area sampling, n—probability sampling in which a map, rather than a tabulation of sampling units, serves as the sampling
frame.
3.1.1.1 Discussion—
Area sampling units are segments of land area and are listed by addresses on the frame prior to their actual delineation on the
ground so that only the randomly selected ones need to be exactly identified.
3.1.2 bulk sampling, n—sampling to prepare a portion of a mass of material that is representative of the whole.
3.1.3 cluster sampling, n—sampling in which the sampling unit consists of a group of subunits, all of which are measured for
sampled clusters.
3.1.4 frame, n—a list, compiled for sampling purposes, which designates all of the sampling units (items or groups) of a
population or universe to be considered in a specific study.
1
This guide is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling / Statistics.
Current edition approved Aug. 1, 2013Nov. 1, 2018. Published August 2013November 2018. Originally approved in 2008. Last previous edition approved in 20082013
ε1
as E1402 – 0813. . DOI: 10.1520/E1402-13.10.1520/E1402-13R18.
2
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.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1
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E1402 − 13 (2018)
3.1.5 multi-stage sampling, n—sampling in which the sample is selected by stages, the sampling units at each stage being
selected from subunits of the larger sampling units chosen at the previous stage.
3.1.5.1 Discussion—
The sampling unit for the first stage is the primary sampling unit. In multi-stage sampling, this unit is further subdivided. The
second stage unit is called the secondary sampling unit. A third stage unit is called a tertiary sampling unit. The final sample is
the set of all last stage sampling units that are obtained. As an example of sampling a lot of packaged product, the cartons of a
lot could be the primary units, packages within the carton could be secondary units, and items within the packages could be the
third-stage un
...
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