ASTM E1402-08e1
(Guide)Standard Guide for Sampling Design
Standard Guide for Sampling Design
SIGNIFICANCE AND USE
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).
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.
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.
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.
The objective of sampling is often to estimate the mean of the populat...
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.
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Designation: E1402 − 08 AnAmerican National Standard
Standard Guide for
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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.
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´ NOTE—Section 1.4 was editorially corrected in July 2010.
1. Scope 3.1.2.1 Discussion—Area sampling units are segments of
land area and are listed by addresses on the frame prior to their
1.1 This guide defines terms and introduces basic methods
actual delineation on the ground so that only the randomly
for probability sampling of discrete populations, areas, and
selected ones need to be exactly identified.
bulk materials. It provides an overview of common probability
sampling methods employed by users of ASTM standards.
3.1.3 bulk sampling, n—sampling to prepare a portion of a
mass of material that is representative of the whole.
1.2 Sampling may be done for the purpose of estimation, of
comparison between parts of a sampled population, or for
3.1.4 cluster sampling, n—sampling in which the sampling
acceptance of lots. Sampling is also used for the purpose of
unit consists of a group of subunits, all of which are measured
auditing information obtained from complete enumeration of
for sampled clusters.
the population.
3.1.5 frame, n—a list, compiled for sampling purposes,
1.3 No system of units is specified in this standard.
which designates all of the sampling units (items or groups) of
1.4 This standard does not purport to address all of the
a population or universe to be considered in a specific study.
safety concerns, if any, associated with its use.
3.1.6 multi-stage sampling, n—sampling in which the
2. Referenced Documents sample is selected by stages, the sampling units at each stage
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being selected from subunits of the larger sampling units
2.1 ASTM Standards:
chosen at the previous stage.
D7430 Practice for Mechanical Sampling of Coal
3.1.6.1 Discussion—The sampling unit for the first stage is
E105 Practice for Probability Sampling of Materials
the primary sampling unit. In multi-stage sampling, this unit is
E122 PracticeforCalculatingSampleSizetoEstimate,With
Specified Precision, the Average for a Characteristic of a further subdivided. The second stage unit is called the second-
Lot or Process ary sampling unit. A third stage unit is called a tertiary
E141 Practice for Acceptance of Evidence Based on the sampling unit. The final sample is the set of all last stage
Results of Probability Sampling
sampling units that are obtained.As an example of sampling a
E456 Terminology Relating to Quality and Statistics
lot of packaged product, the cartons of a lot could be the
primary units, packages within the carton could be secondary
3. Terminology
units, and items within the packages could be the third-stage
3.1 Definitions: units.
3.1.1 Terminology E456 contains a more extensive list of
3.1.7 nested sampling, n—same as multi-stage sampling.
statistical terms.
3.1.8 primary sampling unit, PSU, n—the item, element,
3.1.2 area sampling, n—probability sampling in which a
increment, segment or cluster selected at the first stage of the
map, rather than a tabulation of sampling units, serves as the
selection procedure from a population or universe.
sampling frame.
3.1.9 probability proportional to size sampling, PPS,
n—probability sampling in which the probabilities of selection
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This guide is under the jurisdiction of ASTM Committee E11 on Quality and
of sampling units are proportional, or nearly proportional, to a
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling /
Statistics.
quantity (the “size”) that is known for all sampling units.
Current edition approved Oct. 1, 2008. Published January 2009. DOI: 10.1520/
E1402-08.
3.1.10 probability sample, n—a sample in which the sam-
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For referenced ASTM standards, visit the ASTM website, www.astm.org, or
pling units are selected by a chance process such that a
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
specified probability of selection can be attached to each
Standards volumeinformation,refertothestandard’sDocumentSummarypageon
the ASTM website. possible sample that can be selected.
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E1402 − 08
3.1.11 proportional sampling, n—a method of selection in
N = number of units in the population to be sampled.
stratified sampling such that the proportions of the sampling
n = number of units in the sample.
units(usually,PSUs)selectedforth
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