ASTM E2586-19e1
(Practice)Standard Practice for Calculating and Using Basic Statistics
Standard Practice for Calculating and Using Basic Statistics
ABSTRACT
This practice covers methods and equations for computing and presenting basic statistics. This practice includes simple descriptive statistics for variable and attribute data, elementary methods of statistical inference, and tabular and graphical methods for variable data. Some interpretation and guidance for use is also included.
This practice provides approaches for characterizing a sample of n observations that arrive in the form of a data set. Large data sets from organizations, businesses, and governmental agencies exist in the form of records and other empirical observations. Research institutions and laboratories at universities, government agencies, and the private sector also generate considerable amounts of empirical data.
SIGNIFICANCE AND USE
4.1 This practice provides approaches for characterizing a sample of n observations that arrive in the form of a data set. Large data sets from organizations, businesses, and governmental agencies exist in the form of records and other empirical observations. Research institutions and laboratories at universities, government agencies, and the private sector also generate considerable amounts of empirical data.
4.1.1 A data set containing a single variable usually consists of a column of numbers. Each row is a separate observation or instance of measurement of the variable. The numbers themselves are the result of applying the measurement process to the variable being studied or observed. We may refer to each observation of a variable as an item in the data set. In many situations, there may be several variables defined for study.
4.1.2 The sample is selected from a larger set called the population. The population can be a finite set of items, a very large or essentially unlimited set of items, or a process. In a process, the items originate over time and the population is dynamic, continuing to emerge and possibly change over time. Sample data serve as representatives of the population from which the sample originates. It is the population that is of primary interest in any particular study.
4.2 The data (measurements and observations) may be of the variable type or the simple attribute type. In the case of attributes, the data may be either binary trials or a count of a defined event over some interval (time, space, volume, weight, or area). Binary trials consist of a sequence of 0s and 1s in which a “1” indicates that the inspected item exhibited the attribute being studied and a “0” indicates the item did not exhibit the attribute. Each inspection item is assigned either a “0” or a “1.” Such data are often governed by the binomial distribution. For a count of events over some interval, the number of times the event is observed on the inspection interval ...
SCOPE
1.1 This practice covers methods and equations for computing and presenting basic statistics. This practice includes simple descriptive statistics for variable and attribute data, elementary methods of statistical inference, and tabular and graphical methods for variable data. Some interpretation and guidance for use is also included.
1.2 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.
1.3 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.
1.4 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.
General Information
Relations
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.
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Designation: E2586 − 19 An American National Standard
Standard Practice for
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Calculating and Using Basic Statistics
This standard is issued under the fixed designation E2586; 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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ε NOTE—Section 3.1.29 was corrected editorially in April 2020.
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1. Scope 2.2 ISO Standards:
ISO 3534-1 Statistics—Vocabulary and Symbols, part 1:
1.1 This practice covers methods and equations for comput-
Probability and General Statistical Terms
ing and presenting basic statistics. This practice includes
ISO 3534-2 Statistics—Vocabulary and Symbols, part 2:
simple descriptive statistics for variable and attribute data,
Applied Statistics
elementary methods of statistical inference, and tabular and
graphical methods for variable data. Some interpretation and
3. Terminology
guidance for use is also included.
3.1 Definitions—Unless otherwise noted, terms relating to
1.2 The system of units for this practice is not specified.
quality and statistics are as defined in Terminology E456.
Dimensional quantities in the practice are presented only as
3.1.1 alternative hypothesis, H,n—a probability distribu-
a
illustrations of calculation methods. The examples are not
tion or type of probability distribution distinguished from the
binding on products or test methods treated.
null hypothesis.
1.3 This standard does not purport to address all of the
3.1.1.1 Discussion—The alternative hypothesis is typically
safety concerns, if any, associated with its use. It is the
a research hypothesis or a statement that we hope to show is
responsibility of the user of this standard to establish appro-
more plausible than the null hypothesis using real data.
priate safety, health, and environmental practices and deter-
3.1.2 characteristic, n—a property of items in a sample or
mine the applicability of regulatory limitations prior to use.
population which, when measured, counted, or otherwise
1.4 This international standard was developed in accor-
observed, helps to distinguish among the items. E2282
dance with internationally recognized principles on standard-
3.1.3 coeffıcient of variation, CV, n—for a nonnegative
ization established in the Decision on Principles for the
characteristic, the ratio of the standard deviation to the mean
Development of International Standards, Guides and Recom-
for a population or sample
mendations issued by the World Trade Organization Technical
3.1.3.1 Discussion—The coefficient of variation is often
Barriers to Trade (TBT) Committee.
expressed as a percentage.
3.1.3.2 Discussion—This statistic is also known as the
2. Referenced Documents
relative standard deviation, RSD.
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2.1 ASTM Standards:
3.1.4 confidence bound, n—see confidence limit.
E178 Practice for Dealing With Outlying Observations
E456 Terminology Relating to Quality and Statistics 3.1.5 confidence coeffıcient, n—see confidence level.
E2234 Practice for Sampling a Stream of Product by Attri-
3.1.6 confidence interval, n—an interval estimate [L, U]
butes Indexed by AQL
with the statistics L and U as limits for the parameter θ and
E2282 Guide for Defining the Test Result of a Test Method
with confidence level 1 – α, where Pr(L ≤θ≤ U) ≥1– α.
E3080 Practice for Regression Analysis with a Single Pre-
3.1.6.1 Discussion—The confidence level, 1 – α, reflects the
dictor Variable
proportion of cases that the confidence interval [L, U] would
containorcoverthetrueparametervalueinaseriesofrepeated
1 random samples under identical conditions. Once L and U are
This practice is under the jurisdiction ofASTM Committee E11 on Quality and
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling / given values, the resulting confidence interval either does or
Statistics.
doesnotcontainit.Inthissense“confidence”appliesnottothe
Current edition approved April 1, 2019. Published May 2019. Originally
particular interval but only to the long run proportion of cases
approved in 2007. Last previous edition approved in 2018 as E2586 – 18. DOI:
when repeating the procedure many times.
10.1520/E2586-19E01.
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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
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Standards volume information, refer to the standard’s Document Summary page on Available from American National Standards Institute (ANSI), 25 W. 43rd St.,
the ASTM website. 4th Floor, New York, NY 10036, http://www.ansi.o
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