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ASTM E2586-16

(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. 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.

General Information

Status
Historical
Publication Date
31-Oct-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

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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: E2586 − 16 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 ISO 3534-2 Statistics—Vocabulary and Symbols, part 2:
Applied Statistics
1.1 This practice covers methods and equations for comput-
ing and presenting basic descriptive statistics using a set of
3. Terminology
sample data containing a single variable.This practice includes
simple descriptive statistics for variable data, tabular and 3.1 Definitions—Unless otherwise noted, terms relating to
graphical methods for variable data, and methods for summa- quality and statistics are as defined in Terminology E456.
rizing simple attribute data. Some interpretation and guidance 3.1.1 characteristic, n—a property of items in a sample or
for use is also included. population which, when measured, counted, or otherwise
observed, helps to distinguish among the items. E2282
1.2 The system of units for this practice is not specified.
3.1.2 coeffıcient of variation, CV, n—for a nonnegative
Dimensional quantities in the practice are presented only as
characteristic, the ratio of the standard deviation to the mean
illustrations of calculation methods. The examples are not
for a population or sample
binding on products or test methods treated.
3.1.2.1 Discussion—The coefficient of variation is often
1.3 This standard does not purport to address all of the
expressed as a percentage.
safety concerns, if any, associated with its use. It is the
3.1.2.2 Discussion—This statistic is also known as the
responsibility of the user of this standard to establish appro-
relative standard deviation, RSD.
priate safety, health, and environmental practices and deter-
3.1.3 confidence bound, n—see confidence limit.
mine the applicability of regulatory limitations prior to use.
1.4 This international standard was developed in accor-
3.1.4 confidence coeffıcient, n—see confidence level.
dance with internationally recognized principles on standard-
3.1.5 confidence interval, n—an interval estimate [L, U]
ization established in the Decision on Principles for the
with the statistics L and U as limits for the parameter θ and
Development of International Standards, Guides and Recom-
with confidence level 1 – α, where Pr(L ≤θ≤ U) ≥1– α.
mendations issued by the World Trade Organization Technical
3.1.5.1 Discussion—The confidence level, 1 – α, reflects the
Barriers to Trade (TBT) Committee.
proportion of cases that the confidence interval [L, U] would
containorcoverthetrueparametervalueinaseriesofrepeated
2. Referenced Documents
random samples under identical conditions. Once L and U are
2
2.1 ASTM Standards:
given values, the resulting confidence interval either does or
E178 Practice for Dealing With Outlying Observations
doesnotcontainit.Inthissense“confidence”appliesnottothe
E456 Terminology Relating to Quality and Statistics
particular interval but only to the long run proportion of cases
E2282 Guide for Defining the Test Result of a Test Method
when repeating the procedure many times.
E3080 Practice for Regression Analysis
3
3.1.6 confidence level, n—thevalue,1 – α,oftheprobability
2.2 ISO Standards:
associated with a confidence interval, often expressed as a
ISO 3534-1 Statistics—Vocabulary and Symbols, part 1:
percentage.
Probability and General Statistical Terms
3.1.6.1 Discussion—α is generally a small number. Confi-
1 dence level is often 95 % or 99 %.
This practice is under the jurisdiction ofASTM Committee E11 on Quality and
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling /
3.1.7 confidence limit, n—each of the limits, L and U, of a
Statistics.
confidence interval, or the limit of a one-sided confidence
Current edition approved Nov. 1, 2016. Published November 2016. Originally
approved in 2007. Last previous edition approved in 2014 as E2586 – 14. DOI: interval.
10.1520/E2586-16.
3.1.8 degrees of freedom, n—the number of independent
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
data points minus the number of parameters that have to be
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
estimated before calculating the variance.
the ASTM website.
3 3.1.9 estimate, n—sample statistic used to approximate a
Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
4th Floor, New York, NY 10036, http://www.ansi.org. population parameter.
Copyright © AST
...

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 − 14 E2586 − 16 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. variable. 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:Definitions
3.1.1 Unless otherwise noted, terms relating to quality and statistics are as defined in Terminology E456.—Unless otherwise
noted, terms relating to quality and statistics are as defined in Terminology E456.
3.1.1 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.
3.1.2 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 June 1, 2014Nov. 1, 2016. Published January 2015November 2016. Originally approved in 2007. Last previous edition approved in 2014 as
E2586 – 13.E2586 – 14. DOI: 10.1520/E2586-14.10.1520/E2586-16.
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
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
3.1.2.1 Discussion—
The coefficient of variation is often expressed as a percentage.
3.1.2.2 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

---------------------- Page: 1 ----------------------
E2586 − 16
3.1.3 confidence bound, n—see confidence limit.
3.1.4 confidence coeffıcient, n—see confidence level.
3.1.5 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.
3.1.5.1 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"“confidence” applies not to the particular interval
but only to the long run proportion of cases when repeating the procedure many times.
3.1.6 confidence level, n—the value, 1 – α, of the probability associated with a confidence interval, often expressed as a
percentage.
3.1.6.1 Discussion—
α is generally a small number. Confidenc
...

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Standard Practice for Acceptance of Evidence Based on the Results of Probability Sampling

ABSTRACT
This practice presents rules for accepting or rejecting evidence based on a sample. Statistical evidence for this practice is in the form of an estimate of a proportion, an average, a total, or other numerical characteristic of a finite population or lot. This practice is an estimate of the result which would have been obtained by investigating the entire lot or population under the same rules and with the same care as was used for the sample. One purpose of this practice is to describe straightforward sample selection and data calculation procedures so that courts, commissions, etc. will be able to verify whether such procedures have been applied.
SIGNIFICANCE AND USE
4.1 This practice is designed to permit users of sample survey data to judge the trustworthiness of results from such surveys. Practice E105 provides a statement of principles for guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material. Guide E1402 describes the principal types of sampling designs. Practice E122 aids in deciding on the required sample size.  
4.2 Section 5 gives extended definitions of the concepts basic to survey sampling and the user should verify that such concepts were indeed used and understood by those who conducted the survey. What was the frame? How large (exactly) was the quantity N? How was the parameter θ estimated and its standard error calculated? If replicate subsamples were not used, why not? Adequate answers should be given for all questions. There are many acceptable answers to the last question.  
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4.5 Refer to Section 7 to guide in the interpretation of the uncertainty in the reported value of the parameter estimate, θ^, that is, the value of its standard error, se(θ^). The quantity se(θ^) should be reviewed to verify that the risks it entails are commensurate with the size of the sample.  
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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
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SCOPE
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SCOPE
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ABSTRACT
This practice presents methodology for the setting of an upper confidence bound regarding an unknown fraction or quantity non-conforming, or a rate of occurrence for nonconformities, in cases where the method of attributes is used and there is a zero response in a sample. Three cases are considered. In Case 1, the sample is selected from a process or a very large population of interest. In Case 2, a sample of n items is selected at random from a finite lot of N items. In Case 3, there is a process, but the output is a continuum, such as area (for example, a roll of paper or other material, a field of crop), volume (for example, a volume of liquid or gas), or time (for example, hours, days, quarterly, etc.) The sample size is defined as that portion of the �continuum� sampled, and the defined attribute may occur any number of times over the sampled portion.
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4.1 In Case 1, the sample is selected from a process or a very large population of interest. The population is essentially unlimited, and each item either has or has not the defined attribute. The population (process) has an unknown fraction of items p (long run average process non-conforming) having the attribute. The sample is a group of n discrete items selected at random from the process or population under consideration, and the attribute is not exhibited in the sample. The objective is to determine an upper confidence bound, pu, for the unknown fraction p whereby one can claim that p ≤ pu with some confidence coefficient (probability) C. The binomial distribution is the sampling distribution in this case.  
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SCOPE
1.1 This practice presents methodology for the setting of an upper confidence bound regarding a unknown fraction or quantity non-conforming, or a rate of occurrence for nonconformities, in cases where the method of attributes is used and there is a zero response in a sample. Three cases are considered.  
1.1.1 The sample is selected from a process or a very large population of discrete items, and the number of non-conforming items in the sample is zero.  
1.1.2 A sample of items is selected at random from a finite lot of discrete items, and the number of non-conforming items in the sample is zero.  
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1.3 The values stated in inch-pound units are to be regarded as standard. No other units of measurement are included in this standard.  
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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 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 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 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 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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