ASTM E2586-19
(Practice)Standard Practice for Calculating and Using Basic Statistics
Standard Practice for Calculating and Using Basic Statistics
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.
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Designation: E2586 − 19 An American National Standard
Standard Practice for
1
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.
3
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.
3.1.1.1 Discussion—The alternative hypothesis is typically
1.3 This standard does not purport to address all of the
a research hypothesis or a statement that we hope to show is
safety concerns, if any, associated with its use. It is the
more plausible than the null hypothesis using real data.
responsibility of the user of this standard to establish appro-
3.1.2 characteristic, n—a property of items in a sample or
priate safety, health, and environmental practices and deter-
population which, when measured, counted, or otherwise
mine the applicability of regulatory limitations prior to use.
observed, helps to distinguish among the items. E2282
1.4 This international standard was developed in accor-
3.1.3 coeffıcient of variation, CV, n—for a nonnegative
dance with internationally recognized principles on standard-
characteristic, the ratio of the standard deviation to the mean
ization established in the Decision on Principles for the
for a population or sample
Development of International Standards, Guides and Recom-
3.1.3.1 Discussion—The coefficient of variation is often
mendations issued by the World Trade Organization Technical
expressed as a percentage.
Barriers to Trade (TBT) Committee.
3.1.3.2 Discussion—This statistic is also known as the
relative standard deviation, RSD.
2. Referenced Documents
2
3.1.4 confidence bound, n—see confidence limit.
2.1 ASTM Standards:
E178 Practice for Dealing With Outlying Observations
3.1.5 confidence coeffıcient, n—see confidence level.
E456 Terminology Relating to Quality and Statistics
3.1.6 confidence interval, n—an interval estimate [L, U]
E2234 Practice for Sampling a Stream of Product by Attri-
with the statistics L and U as limits for the parameter θ and
butes Indexed by AQL
with confidence level 1 – α, where Pr(L ≤θ≤ U) ≥1– α.
E2282 Guide for Defining the Test Result of a Test Method
3.1.6.1 Discussion—The confidence level, 1 – α, reflects the
E3080 Practice for Regression Analysis
proportion of cases that the confidence interval [L, U] would
containorcoverthetrueparametervalueinaseriesofrepeated
random samples under identical conditions. Once L and U are
1
given values, the resulting confidence interval either does or
This practice is under the jurisdiction ofASTM Committee E11 on Quality and
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling /
doesnotcontainit.Inthissense“confidence”appliesnottothe
Statistics.
particular interval but only to the long run proportion of cases
Current edition approved April 1, 2019. Published May 2019. Originally
when repeating the procedure many times.
approved in 2007. Last previous edition approved in 2018 as E2586 – 18. DOI:
10.1520/E2586-19.
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
3
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.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E2586 − 19
3.1.7 confidence level, n—thevalue,1 – α,oftheprobability 3.1.22 populati
...
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: E2586 − 18 E2586 − 19 An American National Standard
Standard Practice for
1
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.
1. 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.
2. Referenced Documents
2
2.1 ASTM Standards:
E178 Practice for Dealing With Outlying Observations
E456 Terminology Relating to Quality and Statistics
E2234 Practice for Sampling a Stream of Product by Attributes Indexed by AQL
E2282 Guide for Defining the Test Result of a Test Method
E3080 Practice for Regression Analysis
3
2.2 ISO Standards:
ISO 3534-1 Statistics—Vocabulary and Symbols, part 1: Probability and General Statistical Terms
ISO 3534-2 Statistics—Vocabulary and Symbols, part 2: Applied Statistics
3. Terminology
3.1 Definitions—Unless otherwise noted, terms relating to quality and statistics are as defined in Terminology E456.
3.1.1 alternative hypothesis, H , n—a probability distribution or type of probability distribution distinguished from the null
a
hypothesis.
1
This practice 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 May 15, 2018April 1, 2019. Published May 2018May 2019. Originally approved in 2007. Last previous edition approved in 20162018 as
E2586 – 16.E2586 – 18. DOI: 10.1520/E2586-18.10.1520/E2586-19.
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.
3
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
3.1.1.1 Discussion—
The alternative hypothesis is typically a research hypothesis or a statement that we hope to show is more plausible than the null
hypothesis using real data.
3.1.2 characteristic, n—a property of items in a sample or population which, when measured, counted, or otherwise observed,
helps to distinguish among the items. E2282
3.1.3 coeffıcient of variation, CV, n—for a nonnegative characteristic, the ratio of the standard deviation to the mean for a
population or sample
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E2586 − 19
3.1.3.1 Discussion—
The coefficient of variation is often expressed as a percentage.
3.1.3.2 Discussion—
This statistic is also known as the relative standard deviation, RSD.
3.1.4 confidence bound, n—see confidence limit.
3.1.5 confidence coeffıcient, n—see confidence level.
3.1.6 confidence interval, n—an interval estimate [L, U] with the statistics L and U as limits for the parameter θ and with
confidence level 1 – α, where Pr(L ≤ θ ≤ U) ≥ 1 – α.
3.1.6.1 Discussion—
The confidence level, 1 – α, reflects the proportion of cases that the confidence interval [L, U] would contain or cover the true
parameter value in a series of repeated random
...
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