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ASTM E178-21

(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 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.

General Information

Status
Published
Publication Date
31-May-2021
ICS
03.120.30 - Application of statistical methods
Technical Committee
E11 - Quality and Statistics
Drafting Committee
E11.10 - Sampling / Statistics
Current Stage
Ref Project

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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.
Designation: E178 − 21 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.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3.1.2.1 Discussion—In this practice, x is used to denote
k
order statistics in place of x , to simplify the notation.
(k)
1.1 This practice covers outlying observations in samples
3.1.3 outlier—see outlying observation.
and how to test the statistical significance of outliers.
3.1.4 outlying observation, n—an extreme observation in
1.2 The system of units for this standard is not specified.
either direction that appears to deviate markedly in value from
Dimensional quantities in the standard are presented only as
other members of the sample in which it appears.
illustrations of calculation methods. The examples are not
binding on products or test methods treated.
3.1.4.1 Discussion—The identification of a value as
1.3 This standard does not purport to address all of the
outlying, and therefore a doubtful observation, is a judgement
safety concerns, if any, associated with its use. It is the
of the analyst and can be made before any statistical test.
responsibility of the user of this standard to establish appro-
4. Significance and Use
priate safety, health, and environmental practices and deter-
mine the applicability of regulatory limitations prior to use. 4.1 An outlying observation, or “outlier,” is an extreme one
in either direction that appears to deviate markedly from other
1.4 This international standard was developed in accor-
dance with internationally recognized principles on standard- members of the sample in which it occurs.
ization established in the Decision on Principles for the
4.2 Statistical rules test the null hypothesis of no outliers
Development of International Standards, Guides and Recom-
against the alternative of one or more actual outliers. The
mendations issued by the World Trade Organization Technical
procedures covered were developed primarily to apply to the
Barriers to Trade (TBT) Committee.
simplest kind of experimental data, that is, replicate measure-
ments of some property of a given material or observations in
2. Referenced Documents
a supposedly random sample.
2
2.1 ASTM Standards:
4.3 Astatistical test may be used to support a judgment that
E456Terminology Relating to Quality and Statistics
a physical reason does actually exist for an outlier, or the
E2586Practice for Calculating and Using Basic Statistics
statistical criterion may be used routinely as a basis to initiate
3. Terminology action to find a physical cause.
3.1 Definitions—Unlessotherwisenotedinthisstandard,all
5. Procedure
terms relating to quality and statistics are defined in Terminol-
5.1 In dealing with an outlier, the following alternatives
ogy E456.
should be considered:
3.1.1 null hypothesis, H ,n—astatementaboutaparameter
0
5.1.1 An outlying observation might be the result of gross
of a probability distribution or about the type of probability
deviation from prescribed experimental procedure or an error
distribution, tentatively regarded as true until rejected using a
in calculating or recording the numerical value. When the
statistical hypothesis test. E2586
experimenter is clearly aware that a deviation from prescribed
3.1.2 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. E2586
tion should be discarded, whether or not it agrees with the rest
of the data and without recourse to statistical tests for outliers.
1
ThispracticeisunderthejurisdictionofASTMCommitteeE11onQualityand
If a reliable correction procedure is available, the observation
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling /
may sometimes be corrected and retained.
Statistics.
5.1.2 An outlying observation might be merely an extreme
Current edition approved June 1, 2021. Published June 2021. Originally
manifestation of the random variability inherent in the data. If
approved in 1961. Last previous edition approved in 2016 as E178–16a. DOI:
10.1520/E0178-21.
this is true, the value should be retained and processed in the
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
same manner as the other observations in the sample. Trans-
contact ASTM Customer Service at service@astm.org. For Annu
...

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 − 16a E178 − 21 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.
Note—Corrections were made to Table 2 and the year date was changed on Sept. 7, 2016.
1. 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 safety, health, and healthenvironmental practices and determine the
applicability of regulatory requirementslimitations 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:
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—Unless otherwise noted in this E456 applies to this standard unless
modified herein.standard, all terms relating to quality and statistics are defined in Terminology E456.
3.1.1 null hypothesis, H , n—a statement about a parameter of a probability distribution or about the type of probability
0
distribution, tentatively regarded as true until rejected using a statistical hypothesis test. E2586
3.1.2 order statistic x , n—value of the kth observed value in a sample after sorting by order of magnitude. E2586
(k)
3.1.2.1 Discussion—
In this practice, x is used to denote order statistics in place of x , to simplify the notation.
k (k)
3.1.3 outlier—see outlying observation.
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 Sept. 7, 2016June 1, 2021. Published September 2016June 2021. Originally approved in 1961. Last previous edition approved in 2016 as
E178 – 16.E178 – 16a. DOI: 10.1520/E0178-16A.10.1520/E0178-21.
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.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
E178 − 21
3.1.4 outlying observation, n—an extreme observation in either direction that appears to deviate markedly in value from other
members of the sample in which it appears.
3.1.4.1 Discussion—
The identification of a value as outlying, and therefore a doubtful observation, is a judgement of the analyst and can be made before
any statistical test.
4. Significance and Use
4.1 An outlying observation, or “outlier,” is an extreme one in either direction that appears to deviate markedly from other
members of the sample in which it occurs.
4.2 Statistical rules test the null hypothesis of no outliers against the alternative of one or more actual outliers. The procedures
covered 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.
4.3 A statistical test may be used to support a judgment that 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.
5. Procedure
5.1 In dealing with an outlier, the following alternatives should be considered:
5.1.1 An outlying observation might be the result of gross deviation from prescri
...

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This practice is primarily a statement of principals for the guidance of ASTM technical committees and others in the use of average outgoing quality limit, AOQL, and lot tolerance percent defective, LTPD, sampling plans for determining acceptable of lots of product. Two general types of tables are given, one based on the concept of lot tolerance, LTPD, and the other on AOQL. For each of the types, tables are provided both for single sampling and for double sampling. Each of the individual tables constitutes a collection of solutions to the problem of minimizing the over-all amount of inspection.
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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.
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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.
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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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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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ASTM
ASTM E2862-23(Practice)
Standard Practice for Probability of Detection Analysis for Hit/Miss Data

SIGNIFICANCE AND USE
5.1 The POD analysis method described herein is based on a well-known and well established statistical regression method. It shall be used to quantify the demonstrated POD for a specific set of examination parameters and known range of discontinuity sizes under the following conditions.  
5.1.1 The initial response from a nondestructive evaluation inspection system is ultimately binary in nature (that is, hit or miss).  
5.1.2 Discontinuity size is the predictor variable and can be accurately quantified.  
5.1.3 A relationship between discontinuity size and POD exists and is best described by a generalized linear model with the appropriate link function for binary outcomes.  
5.2 This practice does not limit the use of a generalized linear model with more than one predictor variable or other types of statistical models if justified as more appropriate for the hit/miss data.  
5.3 If the initial response from a nondestructive evaluation inspection system is measurable and can be classified as a continuous variable (for example, data collected from an Eddy Current inspection system), then Practice E3023 may be more appropriate.  
5.4 Prior to performing the analysis it is assumed that the discontinuity of interest is clearly defined; the number and distribution of induced discontinuity sizes in the POD specimen set is known and well-documented; discontinuities in the POD specimen set are unobstructed; and the POD examination administration procedure (including data collection method) is well-designed, well-defined, under control, and unbiased. The analysis results are only valid if convergence is achieved and the model adequately represents the data.  
5.5 The POD analysis method described herein is consistent with the analysis method for binary data described in MIL-HDBK-1823A, and is included in several widely utilized POD software packages to perform a POD analysis on hit/miss data. It is also found in statistical software packages that have generalized line...
SCOPE
1.1 This practice covers the procedure for performing a statistical analysis on nondestructive testing hit/miss data to determine the demonstrated probability of detection (POD) for a specific set of examination parameters. Topics covered include the standard hit/miss POD curve formulation, validation techniques, and correct interpretation of results.  
1.2 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard.  
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 D6299-23e1(Practice)
Standard Practice for Applying Statistical Quality Assurance and Control Charting Techniques to Evaluate Analytical Measurement System Performance

SIGNIFICANCE AND USE
5.1 This practice may be used to continuously demonstrate the proficiency of analytical measurement systems that are used for establishing and ensuring the quality of petroleum and petroleum products.  
5.2 Data accrued, using the techniques included in this practice, provide the ability to monitor analytical measurement system precision and bias.  
5.3 These data are useful for updating test methods as well as for indicating areas of potential measurement system improvement.  
5.4 Control chart statistics can be used to compute limits that the signed difference (Δ) between two single results for the same sample obtained under site precision conditions is expected to fall outside of about 5 % of the time, when each result is obtained using a different measurement system in the same laboratory executing the same test method, and both systems are in a state of statistical control.
SCOPE
1.1 This practice covers information for the design and operation of a program to monitor and control ongoing stability and precision and bias performance of selected analytical measurement systems using a collection of generally accepted statistical quality control (SQC) procedures and tools.  
Note 1: A complete list of criteria for selecting measurement systems to which this practice should be applied and for determining the frequency at which it should be applied is beyond the scope of this practice. However, some factors to be considered include (1) frequency of use of the analytical measurement system, (2) criticality of the parameter being measured, (3) system stability and precision performance based on historical data, (4) business economics, and (5) regulatory, contractual, or test method requirements.  
1.2 This practice is applicable to stable analytical measurement systems that produce results on a continuous numerical scale.  
1.3 This practice is applicable to laboratory test methods.  
1.4 This practice is applicable to validated process stream analyzers.  
1.5 This practice is applicable to monitoring the differences between two analytical measurement systems that purport to measure the same property provided that both systems have been assessed in accordance with the statistical methodology in Practice D6708 and the appropriate bias applied.
Note 2: For validation of univariate process stream analyzers, see also Practice D3764.
Note 3: One or both of the analytical systems in 1.5 may be laboratory test methods or validated process stream analyzers.  
1.6 This practice assumes that the normal (Gaussian) model is adequate for the description and prediction of measurement system behavior when it is in a state of statistical control.  
Note 4: For non-Gaussian processes, transformations of test results may permit proper application of these tools. Consult a statistician for further guidance and information.  
1.7 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 E2709-19(2023)(Practice)
Standard Practice for Demonstrating Capability to Comply with an Acceptance Procedure

ABSTRACT
This practice provides a general methodology for evaluating single-stage or multiple-stage acceptance procedures which involve a quality characteristic measured on a numerical scale. This methodology computes, at a prescribed confidence level, a lower bound on the probability of passing an acceptance procedure, using estimates of the parameters of the distribution of test results from a sampled population.
SIGNIFICANCE AND USE
4.1 This practice considers inspection procedures that may involve multiple-stage sampling, where at each stage one can decide to accept or to continue sampling, and the decision to reject is deferred until the last stage.  
4.1.1 At each stage there are one or more acceptance criteria on the test results; for example, limits on each individual test result, or limits on statistics based on the sample of test results, such as the average, standard deviation, or coefficient of variation (relative standard deviation).  
4.2 The methodology in this practice defines an acceptance region for a set of test results from the sampled population such that, at a prescribed confidence level, the probability that a sample from the population will pass the acceptance procedure is greater than or equal to a prespecified lower bound.  
4.2.1 Having test results fall in the acceptance region is not equivalent to passing the acceptance procedure, but provides assurance that a sample would pass the acceptance procedure with a specified probability.  
4.2.2 This information can be used for process demonstration, validation of test methods, and qualification of instruments, processes, and materials.  
4.2.3 This information can be used for lot release (acceptance), but the lower bound may be conservative in some cases.  
4.2.4 If the results are to be applied to future test results from the same process, then it is assumed that the process is stable and predictable. If this is not the case then there can be no guarantee that the probability estimates would be valid predictions of future process performance.  
4.3 This methodology was originally developed (1-4)3 for use in two specific quality characteristics of drug products in the pharmaceutical industry but will be applicable for acceptance procedures in all industries.  
4.4 Mathematical derivations would be required that are specific to the individual criteria of each test.
SCOPE
1.1 This practice provides a general methodology for evaluating single-stage or multiple-stage acceptance procedures which involve a quality characteristic measured on a numerical scale. This methodology computes, at a prescribed confidence level, a lower bound on the probability of passing an acceptance procedure, using estimates of the parameters of the distribution of test results from a sampled population.  
1.2 For a prescribed lower probability bound, the methodology can also generate an acceptance limit table, which defines a set of test method outcomes (for example, sample averages and standard deviations) that would pass the acceptance procedure at a prescribed confidence level.  
1.3 This approach may be used for demonstrating compliance with in-process, validation, or lot-release specifications.  
1.4 The system of units for this practice is not specified.  
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 issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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