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ASTM E178-16

(Practice)

Standard Practice for Dealing With Outlying Observations

Standard Practice for Dealing With Outlying Observations

ABSTRACT
This practice covers outlying observations in samples and how to test the statistical significance of them. An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs. In this connection, the following two alternatives are of interest: (i) an outlying observation may be merely an extreme manifestation of the random variability inherent in the data. If this is true, the value should be retained and processed in the same manner as the other observations in the sample. (ii) An outlying observation may be the result of gross deviation from prescribed experimental procedure or an error in calculating or recording the numerical value. In such cases, it may be desirable to institute an investigation to ascertain the reason for the aberrant value. The observation may even actually be rejected as a result of the investigation, though not necessarily so. At any rate, in subsequent data analysis, the outlier or outliers will be recognized as probably being from a different population than that of the other sample values. Recommended criteria and illustrations for single samples including the Dixon criteria which are based entirely on ratios of differences between the observations, criterion using independent standard deviation, and criterion for known standard deviation are presented.
SCOPE
1.1 This practice covers outlying observations in samples and how to test the statistical significance of outliers.  
1.2 The system of units for this standard is not specified. Dimensional quantities in the standard 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 requirements prior to use.

General Information

Status
Historical
Publication Date
31-May-2016
ICS
03.120.30 - Application of statistical methods
Technical Committee
E11 - Quality and Statistics
Drafting Committee
E11.10 - Sampling / Statistics
Current Stage
Ref Project

Relations

Replaces
ASTM E178-08 - Standard Practice for Dealing With Outlying Observations
Effective Date
01-Jun-2016
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ASTM D8271-21 - Standard Test Method for the Direct Measurement of Surface Profile of Prepared Concrete
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ASTM D7363-13A(2021)e1 - Standard Test Method for Determination of Parent and Alkyl Polycyclic Aromatics in Sediment Pore Water Using Solid-Phase Microextraction and Gas Chromatography/Mass Spectrometry in Selected Ion Monitoring Mode
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ASTM E456-13a(2022) - Standard Terminology Relating to Quality and Statistics
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ASTM E2891-20 - Standard Guide for Multivariate Data Analysis in Pharmaceutical Development and Manufacturing Applications
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Standards Content (Sample)

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: E178 − 16 AnAmerican National Standard
Standard Practice for
1
Dealing With Outlying Observations
This standard is issued under the fixed designation E178; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 4. Significance and Use
1.1 This practice covers outlying observations in samples 4.1 An outlying observation, or “outlier,” is an extreme one
and how to test the statistical significance of outliers. in either direction that appears to deviate markedly from other
members of the sample in which it occurs.
1.2 The system of units for this standard is not specified.
4.2 Statistical rules test the null hypothesis of no outliers
Dimensional quantities in the standard are presented only as
illustrations of calculation methods. The examples are not against the alternative of one or more actual outliers. The
procedures covered were developed primarily to apply to the
binding on products or test methods treated.
simplest kind of experimental data, that is, replicate measure-
1.3 This standard does not purport to address all of the
ments of some property of a given material or observations in
safety concerns, if any, associated with its use. It is the
a supposedly random sample.
responsibility of the user of this standard to establish appro-
priate safety and health practices and determine the applica- 4.3 Astatistical test may be used to support a judgment that
bility of regulatory requirements prior to use. a physical reason does actually exist for an outlier, or the
statistical criterion may be used routinely as a basis to initiate
action to find a physical cause.
2. Referenced Documents
2
2.1 ASTM Standards:
5. Procedure
E456Terminology Relating to Quality and Statistics
E2586Practice for Calculating and Using Basic Statistics 5.1 In dealing with an outlier, the following alternatives
should be considered:
3. Terminology
5.1.1 An outlying observation might be the result of gross
deviation from prescribed experimental procedure or an error
3.1 Definitions: The terminology defined in Terminology
in calculating or recording the numerical value. When the
E456 applies to this standard unless modified herein.
experimenter is clearly aware that a deviation from prescribed
3.1.1 order statistic x ,n—value of the kth observed value
(k)
experimental procedure has taken place, the resultant observa-
in a sample after sorting by order of magnitude. (Practice
tion should be discarded, whether or not it agrees with the rest
E2586.)
of the data and without recourse to statistical tests for outliers.
3.1.1.1 Discussion—In this Practice, x is used to denote
k
If a reliable correction procedure is available, the observation
order statistics in place of x , to simplify the notation.
(k)
may sometimes be corrected and retained.
3.1.2 outlier—see outlying observation.
5.1.2 An outlying observation might be merely an extreme
manifestation of the random variability inherent in the data. If
3.1.3 outlying observation, n—an extreme observation in
this is true, the value should be retained and processed in the
either direction that appears to deviate markedly in value from
same manner as the other observations in the sample. Trans-
other members of the sample in which it appears.
formation of data or using methods of data analysis designed
for a non-normal distribution might be appropriate.
5.1.3 Test units that give outlying observations might be of
1
ThispracticeisunderthejurisdictionofASTMCommitteeE11onQualityand
special interest. If this is true, once identified they should be
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling /
Statistics. segregated for more detailed study.
Current edition approved June 1, 2016. Published June 2016. Originally
5.2 In many cases, evidence for deviation from prescribed
approved in 1961. Last previous edition approved in 2008 as E178–08. DOI:
10.1520/E0178-16.
procedure will consist primarily of the discordant value itself.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Insuchcasesitisadvisabletoadoptacautiousattitude.Useof
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
one of the criteria discussed below will sometimes permit a
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. clearcut decision to be made.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
E178 − 16
5.2.1 When the experimenter cannot identify abnormal 6.3 Although
...

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: E178 − 08 E178 − 16 An American National Standard
Standard Practice for
1
Dealing With Outlying Observations
This standard is issued under the fixed designation E178; 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 outlying observations in samples and how to test the statistical significance of them. An outlying
observation, or “outlier,” is one that appears to deviate markedly from other members of the sample in which it occurs. In this
connection, the following two alternatives are of interest:outliers.
1.1.1 An outlying observation may be merely an extreme manifestation of the random variability inherent in the data. If this
is true, the value should be retained and processed in the same manner as the other observations in the sample.
1.1.2 On the other hand, an outlying observation may be the result of gross deviation from prescribed experimental procedure
or an error in calculating or recording the numerical value. In such cases, it may be desirable to institute an investigation to
ascertain the reason for the aberrant value. The observation may even actually be rejected as a result of the investigation, though
not necessarily so. At any rate, in subsequent data analysis the outlier or outliers will be recognized as probably being from a
different population than that of the other sample values.
1.2 It is our purpose here to provide statistical rules that will lead the experimenter almost unerringly to look for causes of
outliers when they really exist, and hence to decide whether alternative The system of units for this standard 1.1.1 above, is not
the more plausible hypothesis to accept, as compared to alternative is not specified. Dimensional quantities 1.1.2, in order that the
most appropriate action in further data analysis may be taken. The procedures covered herein apply primarily to the simplest kind
of experimental data, that is, replicate measurements of some property of a given material, or observations in a supposedly single
random sample. Nevertheless, the tests suggested do cover a wide enough range of cases in practice to have broad utility.the
standard 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
requirements prior to use.
2. Referenced Documents
2
2.1 ASTM Standards:
E456 Terminology Relating to Quality and Statistics
E2586 Practice for Calculating and Using Basic Statistics
3. Terminology
3.1 Definitions: The terminology defined in Terminology E456 applies to this standard unless modified herein.
3.1.1 order statistic x , n—value of the kth observed value in a sample after sorting by order of magnitude. (Practice E2586.)
(k)
1
This practice is under the jurisdiction of ASTM Committee D19E11 on WaterQuality and Statistics and is the direct responsibility of Subcommittee D19.05E11.10 on
Inorganic Constituents in WaterSampling / Statistics.
Current edition approved June 1, 2016. Published November 2008June 2016. Originally approved in 1961. Last previous edition approved in 20022008 as
E178 – 02.E178 – 08. DOI: 10.1520/E0178-08.10.1520/E0178-16.
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.
3.1.1.1 Discussion—
In this Practice, x is used to denote order statistics in place of x , to simplify the notation.
k (k)
3.1.2 outlier—see outlying observation.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
E178 − 16
3.1.3 outlying observation, n—an observation extreme observation in either direction that appears to deviate markedly in value
from other members of the sample in which it appears.
4. Significance and Use
4.1 When the experimenter is clearly aware that a gross deviation from prescribed experimental procedu
...

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ASTM
ASTM E122-17(2022)(Practice)
Standard Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process

ABSTRACT
This practice covers simple methods for calculating how many units to include in a random sample in order to estimate with a specified precision, a measure of quality for all the units of a lot of material or produced by a process. It also treats the common situation where the sampling units can be considered to exhibit a single source of variability; it does not treat multi-level sources of variability.
SIGNIFICANCE AND USE
4.1 This practice is intended for use in determining the sample size required to estimate, with specified precision, a measure of quality of a lot or process. The practice applies when quality is expressed as either the lot average for a given property, or as the lot fraction not conforming to prescribed standards. The level of a characteristic may often be taken as an indication of the quality of a material. If so, an estimate of the average value of that characteristic or of the fraction of the observed values that do not conform to a specification for that characteristic becomes a measure of quality with respect to that characteristic. This practice is intended for use in determining the sample size required to estimate, with specified precision, such a measure of the quality of a lot or process either as an average value or as a fraction not conforming to a specified value.
SCOPE
1.1 This practice covers simple methods for calculating how many units to include in a random sample in order to estimate with a specified precision, a measure of quality for all the units of a lot of material, or produced by a process. This practice will clearly indicate the sample size required to estimate the average value of some property or the fraction of nonconforming items produced by a production process during the time interval covered by the random sample. If the process is not in a state of statistical control, the result will not have predictive value for immediate (future) production. The practice treats the common situation where the sampling units can be considered to exhibit a single (overall) source of variability; it does not treat multi-level sources of variability.  
1.2 The system of units for this standard is not specified. Dimensional quantities in the standard are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.3 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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ASTM
ASTM E2587-16(2021)e1(Practice)
Standard Practice for Use of Control Charts in Statistical Process Control

ABSTRACT
This guide covers fundamental concepts, applications, and mathematical relationships associated with reliability as used in industrial areas and as applied to simple components, processes, and systems or complex final products. This guide summarizes selected concepts, terminology, formulas, and methods associated with reliability and its application to products and processes.
SIGNIFICANCE AND USE
4.1 This practice describes the use of control charts as a tool for use in statistical process control (SPC). Control charts were developed by Shewhart (2)3 in the 1920s and are still in wide use today. SPC is a branch of statistical quality control (3, 4), which also encompasses process capability analysis and acceptance sampling inspection. Process capability analysis, as described in Practice E2281, requires the use of SPC in some of its procedures. Acceptance sampling inspection, described in Practices E1994, E2234, and E2762, requires the use of SPC to minimize rejection of product.  
4.2 Principles of SPC—A process may be defined as a set of interrelated activities that convert inputs into outputs. SPC uses various statistical methodologies to improve the quality of a process by reducing the variability of one or more of its outputs, for example, a quality characteristic of a product or service.  
4.2.1 A certain amount of variability will exist in all process outputs regardless of how well the process is designed or maintained. A process operating with only this inherent variability is said to be in a state of statistical control, with its output variability subject only to chance, or common, causes.  
4.2.2 Process upsets, said to be due to assignable, or special causes, are manifested by changes in the output level, such as a spike, shift, trend, or by changes in the variability of an output. The control chart is the basic analytical tool in SPC and is used to detect the occurrence of special causes operating on the process.  
4.2.3 When the control chart signals the presence of a special cause, other SPC tools, such as flow charts, brainstorming, cause-and-effect diagrams, or Pareto analysis, described in various references (4-8), are used to identify the special cause. Special causes, when identified, are either eliminated or controlled. When special cause variation is eliminated, process variability is reduced to its inherent variability, and control...
SCOPE
1.1 This practice provides guidance for the use of control charts in statistical process control programs, which improve process quality through reducing variation by identifying and eliminating the effect of special causes of variation.  
1.2 Control charts are used to continually monitor product or process characteristics to determine whether or not a process is in a state of statistical control. When this state is attained, the process characteristic will, at least approximately, vary within certain limits at a given probability.  
1.3 This practice applies to variables data (characteristics measured on a continuous numerical scale) and to attributes data (characteristics measured as percentages, fractions, or counts of occurrences in a defined interval of time or space).  
1.4 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.  
1.5 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.  
1.6 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...

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ASTM
ASTM E2819-11(2021)(Practice)
Standard Practice for Single- and Multi-Level Continuous Sampling of a Stream of Product by Attributes Indexed by AQL

ABSTRACT
This practice establishes tables and procedures for applying five different types of continuous sampling plans for inspection by attributes using MIL-STD-1235B as a basis for sampling a steady stream of lots indexed by AQL. This practice represents a conversion of MIL-STD1235B to an ASTM-supported standard.
SIGNIFICANCE AND USE
4.1 The reason for preserving military sampling standards is that many organizations throughout the world still use these standards in their current form. MIL-STD-1235B is no longer supported by the U.S. Department of Defense as of the mid-1990s and is out of print, but does exist in the public domain. This practice represents a conversion of MIL-STD-1235B to an ASTM-supported standard.  
4.2 This practice provides the tables and procedures for applying five different types of continuous sampling plans for inspection by attributes. These continuous sampling plans are discussed in Sections 6 – 10 of this practice and each section includes information on:
(1) Initiation of 100 % inspection in use.
(2) Requirements on when to switch to sampling inspection.
(3) Conditions warranting a return to 100 % inspection.
(4) When a change in Code Letter, if desired, can be made.
(5) What to do when the checking inspector finds a defect that was originally found conforming by the screening inspector(s), that is, ineffective screening.
(6) Situations where a defect is found before the switch to 100 % inspection causing excessive periods of 100 % inspection so action must be taken, that is, long periods of screening.  
4.2.1 Section 6 (Section 2 in MIL-STD-1235B) describes specific procedures and applications of the CSP-1 sampling plans – a single-level continuous sampling procedure which provides for alternating between sequences of 100 % inspection and sampling inspection.  
4.2.2 Section 7 (Section 3 in MIL-STD-1235B) describes specific procedures and applications of the CSP-F sampling plans – a variation of the CSP-1 plans in that CSP-F plans are applied to a relatively short run of product, thereby permitting smaller clearance numbers to be used.  
4.2.3 Section 8 (Section 4 in MIL-STD-1235B) describes specific procedures and applications of the CSP-2 sampling plans – a modification of CSP-1 in that 100 % inspection resumes only after a prescribed number of def...
SCOPE
1.1 This practice establishes tables and procedures for applying five different types of continuous sampling plans for inspection by attributes using MIL-STD-1235B as a basis for sampling a steady stream of lots indexed by AQL.  
1.2 This practice provides the sampling plans of MIL-STD-1235B in ASTM format for use by ASTM committees and others. It recognizes the continuing usage of MIL-STD-1235B in industries supported by ASTM. Most of the original text in MIL-STD-1235B is preserved in Sections 6 – 10 of this practice.  
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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ASTM
ASTM E178-21(Practice)
Standard Practice for Dealing With Outlying Observations

ABSTRACT
This practice covers outlying observations in samples and how to test the statistical significance of outliers. The procedures in this practice were developed primarily to apply to the simplest kind of experimental data, that is, replicate measurements of some property of a given material or observations in a supposedly random sample.
SCOPE
1.1 This practice covers outlying observations in samples and how to test the statistical significance of outliers.  
1.2 The system of units for this standard is not specified. Dimensional quantities in the standard 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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ASTM
ASTM E2935-21(Practice)
Standard Practice for Evaluating Equivalence of Two Testing Processes

ABSTRACT
This practice provides statistical methodology for conducting equivalence testing on numerical data from two sources to determine if their true means or variances differ by no more than predetermined limits. This standard provides guidance on experiments and statistical methods needed to demonstrate that the test results from a modified testing process are equivalent to those from the current testing process, where equivalence is defined as agreement within a prescribed limit, termed an equivalence limit.
SIGNIFICANCE AND USE
4.1 Laboratories conducting routine testing have a continuing need to make improvements in their testing processes. In these situations it must be demonstrated that any changes will neither cause an undesirable shift in the test results from the current testing process nor substantially affect a performance characteristic of the test method. This standard provides guidance on experiments and statistical methods needed to demonstrate that the test results from a modified testing process are equivalent to those from the current testing process, where equivalence is defined as agreement within a prescribed limit, termed an equivalence limit.  
4.1.1 The equivalence limit, which represents a worst-case difference or ratio, is determined prior to the equivalence test and its value is usually set by consensus among subject-matter experts.  
4.1.2 Examples of modifications to the testing process include, but are not limited, to the following:  
(1) Changes to operating levels in the steps of the test method procedure,
(2) Installation of new instruments, apparatus, or sources of reagents and test materials,
(3) Evaluation of new personnel performing the testing, and
(4) Transfer of testing to a new location.  
4.1.3 Examples of performance characteristics directly applicable to the test method include bias, precision, sensitivity, specificity, linearity, and range. Additional characteristics are test cost and elapsed time needed to conduct the test procedure.  
4.2 Equivalence studies are performed by a designed experiment that generates test results from the modified and current testing procedures on the same types of materials that are routinely tested. The design of the experiment depends on the type of equivalence needed as discussed below. Experiment design and execution for various objectives is discussed in Section 5.  
4.2.1 Means equivalence is concerned with a potential shift in the mean test result in either direction due to a modification in the te...
SCOPE
1.1 This practice provides statistical methodology for conducting equivalence studies on numerical data from two sources of test results to determine if their true means, variances, or other parameters differ by no more than predetermined limits.  
1.2 Applications include (1) equivalence studies for bias against an accepted reference value, (2) determining means equivalence of two test methods, test apparatus, instruments, reagent sources, or operators within a laboratory or equivalence of two laboratories in a method transfer, and (3) determining non-inferiority of a modified test procedure versus a current test procedure with respect to a performance characteristic.  
1.3 The guidance in this standard applies to experiments conducted either on a single material at a given level of the test result or on multiple materials covering a selected range of test results.  
1.4 Guidance is given for determining the amount of data required for an equivalence study. The control of risks associated with the equivalence decision is discussed.  
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.6 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 t...

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