ASTM E2586-14
(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 descriptive statistics using a set of sample data containing a single variable or two variables. This practice includes simple descriptive statistics for variable data, tabular and graphical methods for variable data, and methods for summarizing simple attribute 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 and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: E2586 − 14 AnAmerican 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 3.1.1 Unless otherwise noted, terms relating to quality and
statistics are as defined in Terminology E456.
1.1 This practice covers methods and equations for comput-
3.1.2 characteristic, n—a property of items in a sample or
ing and presenting basic descriptive statistics using a set of
population which, when measured, counted, or otherwise
sample data containing a single variable or two variables. This
observed, helps to distinguish among the items. E2282
practice includes simple descriptive statistics for variable data,
tabular and graphical methods for variable data, and methods
3.1.3 coeffıcient of determination, n—square of the correla-
for summarizing simple attribute data. Some interpretation and tion coefficient, r.
guidance for use is also included.
3.1.4 coeffıcient of variation, CV, n—for a nonnegative
1.2 The system of units for this practice is not specified. characteristic, the ratio of the standard deviation to the mean
Dimensional quantities in the practice are presented only as
for a population or sample
illustrations of calculation methods. The examples are not
3.1.4.1 Discussion—The coefficient of variation is often
binding on products or test methods treated.
expressed as a percentage.
3.1.4.2 Discussion—This statistic is also known as the
1.3 This standard does not purport to address all of the
relative standard deviation, RSD.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
3.1.5 confidence bound, n—see confidence limit.
priate safety and health practices and determine the applica-
3.1.6 confidence coeffıcient, n—see confidence level.
bility of regulatory limitations prior to use.
3.1.7 confidence interval, n—an interval estimate [L, U]
2. Referenced Documents with the statistics L and U as limits for the parameter θ and
2 with confidence level 1 – α, where Pr(L ≤θ≤ U) ≥1– α.
2.1 ASTM Standards:
3.1.7.1 Discussion—The confidence level, 1 – α, reflects the
E178 Practice for Dealing With Outlying Observations
proportion of cases that the confidence interval [L, U] would
E456 Terminology Relating to Quality and Statistics
containorcoverthetrueparametervalueinaseriesofrepeated
E2282 Guide for Defining the Test Result of a Test Method
random samples under identical conditions. Once L and U are
3
2.2 ISO Standards:
given values, the resulting confidence interval either does or
ISO 3534-1 Statistics—Vocabulary and Symbols, part 1:
does not contain it. In this sense "confidence" applies not to the
Probability and General Statistical Terms
particular interval but only to the long run proportion of cases
ISO 3534-2 Statistics—Vocabulary and Symbols, part 2:
when repeating the procedure many times.
Applied Statistics
3.1.8 confidence level, n—thevalue,1 – α,oftheprobability
associated with a confidence interval, often expressed as a
3. Terminology
percentage.
3.1 Definitions:
3.1.8.1 Discussion—α is generally a small number. Confi-
dence level is often 95 % or 99 %.
1
This practice is under the jurisdiction ofASTM Committee E11 on Quality and 3.1.9 confidence limit, n—each of the limits, L and U, of a
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling /
confidence interval, or the limit of a one-sided confidence
Statistics.
interval.
Current edition approved June 1, 2014. Published January 2015. Originally
approved in 2007. Last previous edition approved in 2014 as E2586 – 13. DOI:
3.1.10 correlation coeffecient, n—for a population, ρ,a
10.1520/E2586-14.
demensionlessmeasureofassociationbetweentwovariablesX
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
and Y, equal to the covariance divided by the product of σ
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM X
Standards volume information, refer to the standard’s Document Summary page on times σ .
Y
the ASTM website.
3
3.1.11 correlation coeffecient, n—for a sample, r, the quan-
Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
4th Floor, New York, NY 10036, http://www.ansi.org. tity:
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E2586 − 14
Σ x 2 x¯ y 2 y¯ 3.1.29 prediction interval, n—an interval for a future value
~ !~ !
...
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 − 13 E2586 − 14 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 descriptive statistics using a set of sample
data containing a single variable or two variables. This practice includes simple descriptive statistics for variable data, tabular and
graphical methods for variable data, and methods for summarizing simple attribute 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 and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2
2.1 ASTM Standards:
E178 Practice for Dealing With Outlying Observations
E456 Terminology Relating to Quality and Statistics
E2282 Guide for Defining the Test Result of a Test Method
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:
3.1.1 Unless otherwise noted, terms relating to quality and statistics are as defined in Terminology E456.
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 determination, n—square of the correlation coefficient, r.
3.1.4 coeffıcient of variation, CV, n—for a nonnegative characteristic, the ratio of the standard deviation to the mean for a
population or sample
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 Oct. 1, 2013June 1, 2014. Published October 2013January 2015. Originally approved in 2007. Last previous edition approved in 20122014 as
E2586 – 12b.E2586 – 13. DOI: 10.1520/E2586-13.10.1520/E2586-14.
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.
3.1.4.1 Discussion—
The coefficient of variation is often expressed as a percentage.
3.1.4.2 Discussion—
This statistic is also known as the relative standard deviation, RSD.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1
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E2586 − 14
3.1.5 confidence bound, n—see confidence limit.
3.1.6 confidence coeffıcient, n—see confidence level.
3.1.7 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.
3.1.7.1 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 samples under identical conditions. Once L and U are given values, the resulting
confidence interval either does or does not contain it. In this sense "confidence" applies not to the particular interval but only to
the long run proportion of cases when repeating the procedure many times.
3.1.8 confidence level, n—the value, 1 – α, of the probability associated with a confidence interval, often expressed as a
percentage.
3.1.8.1 Discussion—
α is generally a small number. Confidence level is often 95 % or 99 %.
3.1.9 confidence limit, n—each of the limits, L and U, of a confidence interval, or the limit of a
...
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