E11.10 - Sampling / Statistics

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.  
4.3 If the sample design was relatively simple, such as simple random or stratified, then fully valid estimates of sampling variance are easily available. If a more complex design was used then methods such as discussed in Ref (1)3 or in Guide E1402 may be acceptable. Use of replicate subsamples is the most straightforward way to estimate sampling variances when the survey design is complex.  
4.4 Once the survey procedures that were used satisfy Section 5, see if any increase in sample size is needed. The calculations for making it objectively are described in Section 6.  
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.  
4.6 When the audit subsample shows that there was reasonable conformity with prescribed procedures and when the known instances of departures from the survey plan can be shown to have no appreciable effect on the est...
SCOPE
1.1 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. It 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.  
1.2 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. The methods may not give least uncertainty at least cost, they should however furnish a reasonable estimate with calculable uncertainty.  
1.3 This practice is primarily intended for one-of-a-kind studies. Repetitive surveys allow estimates of sampling uncertainties to be pooled; the emphasis of this practice is on estimation of sampling uncertainty from the sample itself. The parameter of interest for this practice is effectively a constant. Thus, the principal inference is a simple point estimate to be used as if it were the unknown constant, rather than, for example, a forecast or prediction interval or distribution...

ABSTRACT
This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards. This guide also describes the principal types of sampling designs and provides formulas for estimating population means and standard errors of the estimates.
SIGNIFICANCE AND USE
4.1 This guide describes the principal types of sampling designs and provides formulas for estimating population means and standard errors of the estimates. Practice E105 provides principles for designing probability sampling plans in relation to the objectives of study, costs, and practical constraints. Practice E122 aids in specifying the required sample size. Practice E141 describes conditions to ensure validity of the results of sampling. Further description of the designs and formulas in this guide, and beyond it, can be found in textbooks (1-10).3  
4.2 Sampling, both discrete and bulk, is a clerical and physical operation. It generally involves training enumerators and technicians to use maps, directories and stop watches so as to locate designated sampling units. Once a sampling unit is located at its address, discrete sampling and area sampling enumeration proceeds to a measurement. For bulk sampling, material is extracted into a composite.  
4.3 A sampling plan consists of instructions telling how to list addresses and how to select the addresses to be measured or extracted. A frame is a listing of addresses each of which is indexed by a single integer or by an n-tuple (several integer) number. The sampled population consists of all addresses in the frame that can actually be selected and measured. It is sometimes different from a targeted population that the user would have preferred to be covered.  
4.4 A selection scheme designates which indexes constitute the sample. If certified random numbers completely control the selection scheme the sample is called a probability sample. Certified random numbers are those generated either from a table (for example, Ref (11)) that has been tested for equal digit frequencies and for serial independence, from a computer program that was checked to have a long cycle length, or from a random physical method such as tossing of a coin or a casino-quality spinner.  
4.5 The objective of sampling is often to estimate t...
SCOPE
1.1 This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards.  
1.2 Sampling may be done for the purpose of estimation, of comparison between parts of a sampled population, or for acceptance of lots. Sampling is also used for the purpose of auditing information obtained from complete enumeration of the population.  
1.3 No system of units is specified in this standard.  
1.4 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.  
1.5 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.

ABSTRACT
This practice covers regression analysis of a set of data to define the statistical relationship between two numerical variables for use in predicting one variable from the other. This practice is restricted in scope to consider only a single numerical response variable and a single numerical predictor variable. The objective is to obtain a regression model for use in predicting the value of the response variable Y for given values of the predictor variable X.
SIGNIFICANCE AND USE
4.1 Regression analysis is a procedure that uses data to study the statistical relationships between two or more variables (1, 2).3 This practice is restricted in scope to consider only a single numerical response variable and a single numerical predictor variable. The objective is to obtain a regression model for use in predicting the value of the response variable Y for given values of the predictor variable X.  
4.2 A regression model consists of: (1) a regression function that relates the mean values of the response variable distribution to fixed values of the predictor variable, and (2) a statistical distribution that describes the variability in the response variable values at a fixed value of the predictor variable.  
4.2.1 The regression analysis utilizes either experimental or observational data to estimate the parameters defining a regression model and their precision. Diagnostic procedures are utilized to assess the resulting model fit and can suggest other models for improved prediction performance.  
4.3 The information in this practice is arranged as follows.  
4.3.1 Section 5 gives a general outline of the steps in the regression analysis procedure. The subsequent sections cover procedures for estimation of specific regression models.  
4.3.2 Section 6 assumes a straight line relationship between the two variables. This is also known as the simple linear regression model or a first order model. This model should be used as a starting point for understanding the XY relationship and ultimately defining the best fitting model to the data.  
4.3.3 Section 7 considers a proportional relationship between the variables, where the ratio of one variable to the other is constant. The intercept is constrained to be zero. This model is useful for single point calibration, where a reference material is run periodically as a standard during routine testing to correct for drift in instrument performance over a given range of test results.  
4.3.4 Section 8 di...
SCOPE
1.1 This practice covers regression analysis of a set of data to define the statistical relationship between two numerical variables for use in predicting one variable from the other.  
1.2 The regression analysis provides graphical and calculational procedures for selecting the best statistical model that describes the relationship and for evaluation of the fit of the data to the selected model.  
1.3 The resulting regression model can be useful for developing process knowledge through description of the variable relationship, in making predictions of future values, in relating the precision of a test method to the value of the characteristic being measured, and in developing control methods for the process generating values of the variables.  
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 ...

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.

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.

ABSTRACT
This practice is primarily a statement of principles for the guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material. The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, the percentage of some constituent, the fraction of the items that fail to meet (or meet) a specified requirement, the average characteristic or quality of an item, the total weight of the shipment, or the probable maximum or minimum content of some chemical. A probability sampling plan will possess an objective procedure for the selection of the sample with the use of random numbers and a definite formula for the estimate and standard error of any estimate.
SIGNIFICANCE AND USE
4.1 The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, the percentage of some constituent, the fraction of the items that fail to meet (or meet) a specified requirement, the average characteristic or quality of an item, the total weight of the shipment, or the probable maximum or minimum content of, say, some chemical.  
4.2 The purpose may be the rational disposition of a lot or shipment without the intermediate step of the formation of an estimate.  
4.3 The purpose may be to provide aid toward rational action concerning the production process that generated the lot, pile or shipment.  
4.4 Whatever the purpose of the sample, adhering to the principles of probability sampling will allow the uncertainties, such as bias and variance of estimates or the risks of the rational disposition or action, to be calculated objectively and validly from the theory of combinatorial probabilities. This assumes, of course, that the sampling operations themselves were carried out properly, as well. Proper sampling requires that any random numbers were generated properly, the units to be sampled from were correctly identified, located, and drawn, and the measurements were made with measurement error at a level not exceeding the required purposes.  
4.5 Determination of bias and variance and of risks can be calculated when the selection was only partially determined by random numbers and a frame, but they then require suppositions and assumptions which may be more or less mistaken or require additional data which may introduce experimental error.
SCOPE
1.1 This guide is primarily a statement of principles for the guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material.  
1.2 A system of units is not specified in this 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.

ABSTRACT
This standard includes those statistical items related to the area of design of experiments for which standard definitions appear desirable. It provides definitions, descriptions, discussion, and comparison of terms.
SIGNIFICANCE AND USE
3.1 This standard is a subsidiary to Terminology E456.  
3.2 It provides definitions, descriptions, discussion, and comparison of terms.
SCOPE
1.1 This standard includes those statistical items related to the area of design of experiments for which standard definitions appear desirable.  
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
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.

ABSTRACT
This practice covers methods and equations for computing and presenting basic statistics. This practice includes simple descriptive statistics for variable and attribute data, elementary methods of statistical inference, and tabular and graphical methods for variable data. Some interpretation and guidance for use is also included.
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.
SIGNIFICANCE AND USE
4.1 This practice provides approaches for characterizing a sample of n observations that arrive in the form of a data set. Large data sets from organizations, businesses, and governmental agencies exist in the form of records and other empirical observations. Research institutions and laboratories at universities, government agencies, and the private sector also generate considerable amounts of empirical data.  
4.1.1 A data set containing a single variable usually consists of a column of numbers. Each row is a separate observation or instance of measurement of the variable. The numbers themselves are the result of applying the measurement process to the variable being studied or observed. We may refer to each observation of a variable as an item in the data set. In many situations, there may be several variables defined for study.  
4.1.2 The sample is selected from a larger set called the population. The population can be a finite set of items, a very large or essentially unlimited set of items, or a process. In a process, the items originate over time and the population is dynamic, continuing to emerge and possibly change over time. Sample data serve as representatives of the population from which the sample originates. It is the population that is of primary interest in any particular study.  
4.2 The data (measurements and observations) may be of the variable type or the simple attribute type. In the case of attributes, the data may be either binary trials or a count of a defined event over some interval (time, space, volume, weight, or area). Binary trials consist of a sequence of 0s and 1s in which a “1” indicates that the inspected item exhibited the attribute being studied and a “0” indicates the item did not exhibit the attribute. Each inspection item is assigned either a “0” or a “1.” Such data are often governed by the binomial distribution. For a count of events over some interval, the number of times the event is observed on the inspection interval ...
SCOPE
1.1 This practice covers methods and equations for computing and presenting basic statistics. This practice includes simple descriptive statistics for variable and attribute data, elementary methods of statistical inference, and tabular and graphical methods for variable data. Some interpretation and guidance for use is also included.  
1.2 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This practice covers regression analysis of a set of data to define the statistical relationship between two numerical variables for use in predicting one variable from the other. This practice is restricted in scope to consider only a single numerical response variable and a single numerical predictor variable. The objective is to obtain a regression model for use in predicting the value of the response variable Y for given values of the predictor variable X.
SIGNIFICANCE AND USE
4.1 Regression analysis is a procedure that uses data to study the statistical relationships between two or more variables (1, 2).3 This practice is restricted in scope to consider only a single numerical response variable and a single numerical predictor variable. The objective is to obtain a regression model for use in predicting the value of the response variable Y for given values of the predictor variable X.  
4.2 A regression model consists of: (1) a regression function that relates the mean values of the response variable distribution to fixed values of the predictor variable, and (2) a statistical distribution that describes the variability in the response variable values at a fixed value of the predictor variable.  
4.2.1 The regression analysis utilizes either experimental or observational data to estimate the parameters defining a regression model and their precision. Diagnostic procedures are utilized to assess the resulting model fit and can suggest other models for improved prediction performance.  
4.3 The information in this practice is arranged as follows.  
4.3.1 Section 5 gives a general outline of the steps in the regression analysis procedure. The subsequent sections cover procedures for estimation of specific regression models.  
4.3.2 Section 6 assumes a straight line relationship between the two variables. This is also known as the simple linear regression model or a first order model. This model should be used as a starting point for understanding the XY relationship and ultimately defining the best fitting model to the data.  
4.3.3 Section 7 considers a proportional relationship between the variables, where the ratio of one variable to the other is constant. The intercept is constrained to be zero. This model is useful for single point calibration, where a reference material is run periodically as a standard during routine testing to correct for drift in instrument performance over a given range of test results.  
4.3.4 Section 8 di...
SCOPE
1.1 This practice covers regression analysis of a set of data to define the statistical relationship between two numerical variables for use in predicting one variable from the other.  
1.2 The regression analysis provides graphical and calculational procedures for selecting the best statistical model that describes the relationship and for evaluation of the fit of the data to the selected model.  
1.3 The resulting regression model can be useful for developing process knowledge through description of the variable relationship, in making predictions of future values, in relating the precision of a test method to the value of the characteristic being measured, and in developing control methods for the process generating values of the variables.  
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 ...

SIGNIFICANCE AND USE
4.1 This practice provides approaches for characterizing a sample of n observations that arrive in the form of a data set. Large data sets from organizations, businesses, and governmental agencies exist in the form of records and other empirical observations. Research institutions and laboratories at universities, government agencies, and the private sector also generate considerable amounts of empirical data.  
4.1.1 A data set containing a single variable usually consists of a column of numbers. Each row is a separate observation or instance of measurement of the variable. The numbers themselves are the result of applying the measurement process to the variable being studied or observed. We may refer to each observation of a variable as an item in the data set. In many situations, there may be several variables defined for study.  
4.1.2 The sample is selected from a larger set called the population. The population can be a finite set of items, a very large or essentially unlimited set of items, or a process. In a process, the items originate over time and the population is dynamic, continuing to emerge and possibly change over time. Sample data serve as representatives of the population from which the sample originates. It is the population that is of primary interest in any particular study.  
4.2 The data (measurements and observations) may be of the variable type or the simple attribute type. In the case of attributes, the data may be either binary trials or a count of a defined event over some interval (time, space, volume, weight, or area). Binary trials consist of a sequence of 0s and 1s in which a “1” indicates that the inspected item exhibited the attribute being studied and a “0” indicates the item did not exhibit the attribute. Each inspection item is assigned either a “0” or a “1.” Such data are often governed by the binomial distribution. For a count of events over some interval, the number of times the event is observed on the inspection interval ...
SCOPE
1.1 This practice covers methods and equations for computing and presenting basic statistics. This practice includes simple descriptive statistics for variable and attribute data, elementary methods of statistical inference, and tabular and graphical methods for variable data. Some interpretation and guidance for use is also included.  
1.2 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ABSTRACT
This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards. This guide also describes the principal types of sampling designs and provides formulas for estimating population means and standard errors of the estimates.
Sampling, both discrete and bulk, is a clerical and physical operation. It generally involves training enumerators and technicians to use maps, directories and stop watches so as to locate designated sampling units. Once a sampling unit is located at its address, discrete sampling and area sampling enumeration proceeds to a measurement.
SIGNIFICANCE AND USE
4.1 This guide describes the principal types of sampling designs and provides formulas for estimating population means and standard errors of the estimates. Practice E105 provides principles for designing probability sampling plans in relation to the objectives of study, costs, and practical constraints. Practice E122 aids in specifying the required sample size. Practice E141 describes conditions to ensure validity of the results of sampling. Further description of the designs and formulas in this guide, and beyond it, can be found in textbooks (1-10).3  
4.2 Sampling, both discrete and bulk, is a clerical and physical operation. It generally involves training enumerators and technicians to use maps, directories and stop watches so as to locate designated sampling units. Once a sampling unit is located at its address, discrete sampling and area sampling enumeration proceeds to a measurement. For bulk sampling, material is extracted into a composite.  
4.3 A sampling plan consists of instructions telling how to list addresses and how to select the addresses to be measured or extracted. A frame is a listing of addresses each of which is indexed by a single integer or by an n-tuple (several integer) number. The sampled population consists of all addresses in the frame that can actually be selected and measured. It is sometimes different from a targeted population that the user would have preferred to be covered.  
4.4 A selection scheme designates which indexes constitute the sample. If certified random numbers completely control the selection scheme the sample is called a probability sample. Certified random numbers are those generated either from a table (for example, Ref (11)) that has been tested for equal digit frequencies and for serial independence, from a computer program that was checked to have a long cycle length, or from a random physical method such as tossing of a coin or a casino-quality spinner.  
4.5 The objective of sampling is often to estimate t...
SCOPE
1.1 This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards.  
1.2 Sampling may be done for the purpose of estimation, of comparison between parts of a sampled population, or for acceptance of lots. Sampling is also used for the purpose of auditing information obtained from complete enumeration of the population.  
1.3 No system of units is specified in this standard.  
1.4 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.  
1.5 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.

SIGNIFICANCE AND USE
4.1 This practice provides approaches for characterizing a sample of n observations that arrive in the form of a data set. Large data sets from organizations, businesses, and governmental agencies exist in the form of records and other empirical observations. Research institutions and laboratories at universities, government agencies, and the private sector also generate considerable amounts of empirical data.  
4.1.1 A data set containing a single variable usually consists of a column of numbers. Each row is a separate observation or instance of measurement of the variable. The numbers themselves are the result of applying the measurement process to the variable being studied or observed. We may refer to each observation of a variable as an item in the data set. In many situations, there may be several variables defined for study.  
4.1.2 The sample is selected from a larger set called the population. The population can be a finite set of items, a very large or essentially unlimited set of items, or a process. In a process, the items originate over time and the population is dynamic, continuing to emerge and possibly change over time. Sample data serve as representatives of the population from which the sample originates. It is the population that is of primary interest in any particular study.  
4.2 The data (measurements and observations) may be of the variable type or the simple attribute type. In the case of attributes, the data may be either binary trials or a count of a defined event over some interval (time, space, volume, weight, or area). Binary trials consist of a sequence of 0s and 1s in which a “1” indicates that the inspected item exhibited the attribute being studied and a “0” indicates the item did not exhibit the attribute. Each inspection item is assigned either a “0” or a “1.” Such data are often governed by the binomial distribution. For a count of events over some interval, the number of times the event is observed on the inspection interval ...
SCOPE
1.1 This practice covers methods and equations for computing and presenting basic statistics. This practice includes simple descriptive statistics for variable and attribute data, elementary methods of statistical inference, and tabular and graphical methods for variable data. Some interpretation and guidance for use is also included.  
1.2 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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.
This practice includes the concepts and procedures of sampling. Examples include sampling mineral ore or grain from a conveyor belt or sampling from a list of households along a street. If the systematic sample is obtained by a single random start, the plan is then a probability sampling plan, but it does not permit calculating the standard error as required by this practice.
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.  
4.3 If the sample design was relatively simple, such as simple random or stratified, then fully valid estimates of sampling variance are easily available. If a more complex design was used then methods such as discussed in Ref (1)3 or in Guide E1402 may be acceptable. Use of replicate subsamples is the most straightforward way to estimate sampling variances when the survey design is complex.  
4.4 Once the survey procedures that were used satisfy Section 5, see if any increase in sample size is needed. The calculations for making it objectively are described in Section 6.  
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.  
4.6 When the audit subsample shows that there was reasonable conformity with prescribed procedures and when the known instances of departures from the survey plan can be shown to have no appreciable effect on the est...
SCOPE
1.1 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. It 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.  
1.2 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. The methods may not give least uncertainty at least cost, they should however furnish a reasonable estimate with calculable uncertainty.  
1.3 This practice is primarily intended for one-of-a-kind studies. Repetitive surveys allow estimates of sa...

SIGNIFICANCE AND USE
4.1 Regression analysis is a statistical procedure that studies the statistical relationships between two or more variables Ref. (1, 2).3 In general, one of these variables is designated as a response variable and the rest of the variables are designated as predictor variables. Then the objective of the model is to predict the response from the predictor variables.  
4.1.1 This standard considers a numerical response variable and only a single numerical predictor variable.  
4.1.2 The regression model consists of: (1) a mathematical function that relates the mean values of the response variable distribution to fixed values of the predictor variable, and (2) a description of statistical distribution that describes the variability in the response variable at fixed levels of the predictor variable.  
4.1.3 The regression procedure utilizes experimental or observational data to estimate the parameters defining a regression model and their precision. Diagnostic procedures are utilized to assess the resulting model fit and can suggest other models for improved prediction performance.  
4.1.4 The regression model can be useful for developing process knowledge through description of the variable relationship, in making predictions of future values, and in developing control methods for the process generating values of the variables.  
4.2 Section 5 in this standard deals with the simple linear regression model using a straight line mathematical relationship between the two variables where variability of the response variable over the range of values of the predictor variable is described by a normal distribution with constant variance. Appendix X1 provides supplemental information.
SCOPE
1.1 This practice covers regression analysis methodology for estimating, evaluating, and using the simple linear regression model to define the statistical relationship between two numerical variables.  
1.2 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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.
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. It 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.
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.

SIGNIFICANCE AND USE
4.1 Regression analysis is a statistical procedure that studies the relations between two or more numerical variables and utilizes existing data to determine a model equation for prediction of one variable from another. In this standard, a simple linear regression model, that is, a straight line relationship between two variables, is considered (1, 2).3
SCOPE
1.1 This practice covers regression analysis methodology for estimating, evaluating, and using the simple linear regression model to define the relationship between two numerical variables.  
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.

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.

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.
This practice covers alternatives that should be considered in dealing with an outlier. An outlying observation might be the result of gross deviation from prescribed experimental procedure or an error in calculating or recording the numerical value.
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.

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.

ABSTRACT
This standard includes those statistical items related to the area of design of experiments for which standard definitions appear desirable. It provides definitions, descriptions, discussion, and comparison of terms.
This standard also provides the table of contrast coefficient and table of contrast analysis. The table of contrast coefficient implies that once the contrast coefficients of the main effects (X1, X2, X3 and X4) are filled in, the coefficients for all interaction and other second or higher order effects can be derived as products (Xij = Xi Xi) of the appropriate terms. The table on contrast analysis indicates the measure of experimental error, s, that can be obtained in various ways. If the experiment is replicated, s is the square root of the pooled variances of the pairs for each treatment combination. If some effects were felt to be pseudo-replicates, multiplying the contrast by the regression coefficient of these terms forms a sum of squares (as in analysis of variance) and these would be summed and divided by the number of terms involved to give s².
SIGNIFICANCE AND USE
3.1 This standard is a subsidiary to Terminology E456.  
3.2 It provides definitions, descriptions, discussion, and comparison of terms.
SCOPE
1.1 This standard includes those statistical items related to the area of design of experiments for which standard definitions appear desirable.

ABSTRACT
This practice is primarily a statement of principles for the guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material. The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, the percentage of some constituent, the fraction of the items that fail to meet (or meet) a specified requirement, the average characteristic or quality of an item, the total weight of the shipment, or the probable maximum or minimum content of some chemical. A probability sampling plan will possess an objective procedure for the selection of the sample with the use of random numbers and a definite formula for the estimate and standard error of any estimate.
This practice also covers the minimum standards for a probability sampling plan, selection of sample, sampling of bulk materials, selection of sample, and planning for sampling.
SIGNIFICANCE AND USE
4.1 The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, the percentage of some constituent, the fraction of the items that fail to meet (or meet) a specified requirement, the average characteristic or quality of an item, the total weight of the shipment, or the probable maximum or minimum content of, say, some chemical.  
4.2 The purpose may be the rational disposition of a lot or shipment without the intermediate step of the formation of an estimate.  
4.3 The purpose may be to provide aid toward rational action concerning the production process that generated the lot, pile or shipment.  
4.4 Whatever the purpose of the sample, adhering to the principles of probability sampling will allow the uncertainties, such as bias and variance of estimates or the risks of the rational disposition or action, to be calculated objectively and validly from the theory of combinatorial probabilities. This assumes, of course, that the sampling operations themselves were carried out properly, as well. For example, that any random numbers required were generated properly, the units to be sampled from were correctly identified, located, and drawn, and the measurements were made with measurement error at a level not exceeding the required purposes.  
4.5 Determination of bias and variance and of risks can be calculated when the selection was only partially determined by random numbers and a frame, but they then require suppositions and assumptions which may be more or less mistaken or require additional data which may introduce experimental error.
SCOPE
1.1 This practice is primarily a statement of principles for the guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material.

SIGNIFICANCE AND USE
4.1 This practice provides approaches for characterizing a sample of n observations that arrive in the form of a data set. Large data sets from organizations, businesses, and governmental agencies exist in the form of records and other empirical observations. Research institutions and laboratories at universities, government agencies, and the private sector also generate considerable amounts of empirical data.  
4.1.1 A data set containing a single variable usually consists of a column of numbers. Each row is a separate observation or instance of measurement of the variable. The numbers themselves are the result of applying the measurement process to the variable being studied or observed. We may refer to each observation of a variable as an item in the data set. In many situations, there may be several variables defined for study.  
4.1.2 The sample is selected from a larger set called the population. The population can be a finite set of items, a very large or essentially unlimited set of items, or a process. In a process, the items originate over time and the population is dynamic, continuing to emerge and possibly change over time. Sample data serve as representatives of the population from which the sample originates. It is the population that is of primary interest in any particular study.  
4.2 The data (measurements and observations) may be of the variable type or the simple attribute type. In the case of attributes, the data may be either binary trials or a count of a defined event over some interval (time, space, volume, weight, or area). Binary trials consist of a sequence of 0s and 1s in which a “1” indicates that the inspected item exhibited the attribute being studied and a “0” indicates the item did not exhibit the attribute. Each inspection item is assigned either a “0” or a “1.” Such data are often governed by the binomial distribution. For a count of events over some interval, the number of times the event is observed on the inspection interval ...
SCOPE
1.1 This practice covers methods and equations for computing and presenting basic descriptive statistics using a set of sample data containing a single variable or two variables. This practice includes simple descriptive statistics for variable data, tabular and graphical methods for variable data, and methods for summarizing simple attribute data. Some interpretation and guidance for use is also included.  
1.2 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
4.1 This practice provides approaches for characterizing a sample of n observations that arrive in the form of a data set. Large data sets from organizations, businesses, and governmental agencies exist in the form of records and other empirical observations. Research institutions and laboratories at universities, government agencies, and the private sector also generate considerable amounts of empirical data.  
4.1.1 A data set containing a single variable usually consists of a column of numbers. Each row is a separate observation or instance of measurement of the variable. The numbers themselves are the result of applying the measurement process to the variable being studied or observed. We may refer to each observation of a variable as an item in the data set. In many situations, there may be several variables defined for study.  
4.1.2 The sample is selected from a larger set called the population. The population can be a finite set of items, a very large or essentially unlimited set of items, or a process. In a process, the items originate over time and the population is dynamic, continuing to emerge and possibly change over time. Sample data serve as representatives of the population from which the sample originates. It is the population that is of primary interest in any particular study.  
4.2 The data (measurements and observations) may be of the variable type or the simple attribute type. In the case of attributes, the data may be either binary trials or a count of a defined event over some interval (time, space, volume, weight, or area). Binary trials consist of a sequence of 0s and 1s in which a “1” indicates that the inspected item exhibited the attribute being studied and a “0” indicates the item did not exhibit the attribute. Each inspection item is assigned either a “0” or a “1.” Such data are often governed by the binomial distribution. For a count of events over some interval, the number of times the event is observed on the inspection interval ...
SCOPE
1.1 This practice covers methods and equations for computing and presenting basic descriptive statistics using a set of sample data containing a single variable or two variables. This practice includes simple descriptive statistics for variable data, tabular and graphical methods for variable data, and methods for summarizing simple attribute data. Some interpretation and guidance for use is also included.  
1.2 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
4.1 This guide describes the principal types of sampling designs and provides formulas for estimating population means and standard errors of the estimates. Practice E105 provides principles for designing probability sampling plans in relation to the objectives of study, costs, and practical constraints. Practice E122 aids in specifying the required sample size. Practice E141 describes conditions to ensure validity of the results of sampling. Further description of the designs and formulas in this guide, and beyond it, can be found in textbooks (1-10).3  
4.2 Sampling, both discrete and bulk, is a clerical and physical operation. It generally involves training enumerators and technicians to use maps, directories and stop watches so as to locate designated sampling units. Once a sampling unit is located at its address, discrete sampling and area sampling enumeration proceeds to a measurement. For bulk sampling, material is extracted into a composite.  
4.3 A sampling plan consists of instructions telling how to list addresses and how to select the addresses to be measured or extracted. A frame is a listing of addresses each of which is indexed by a single integer or by an n-tuple (several integer) number. The sampled population consists of all addresses in the frame that can actually be selected and measured. It is sometimes different from a targeted population that the user would have preferred to be covered.  
4.4 A selection scheme designates which indexes constitute the sample. If certified random numbers completely control the selection scheme the sample is called a probability sample. Certified random numbers are those generated either from a table (for example, Ref (11)) that has been tested for equal digit frequencies and for serial independence, from a computer program that was checked to have a long cycle length, or from a random physical method such as tossing of a coin or a casino-quality spinner.  
4.5 The objective of sampling is often to estimate...
SCOPE
1.1 This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards.  
1.2 Sampling may be done for the purpose of estimation, of comparison between parts of a sampled population, or for acceptance of lots. Sampling is also used for the purpose of auditing information obtained from complete enumeration of the population.  
1.3 No system of units is specified in this standard.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use.

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.

SIGNIFICANCE AND USE
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.
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.
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.
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 is recorded for each of...
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.

SIGNIFICANCE AND USE
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.
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.
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.
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 is recorded for each of...
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.

SIGNIFICANCE AND USE
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.

SIGNIFICANCE AND USE
The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, the percentage of some constituent, the fraction of the items that fail to meet (or meet) a specified requirement, the average characteristic or quality of an item, the total weight of the shipment, or the probable maximum or minimum content of, say, some chemical.
The purpose may be the rational disposition of a lot or shipment without the intermediate step of the formation of an estimate.
The purpose may be to provide aid toward rational action concerning the production process that generated the lot, pile or shipment.
Whatever the purpose of the sample, adhering to the principles of probability sampling will allow the uncertainties, such as bias and variance of estimates or the risks of the rational disposition or action, to be calculated objectively and validly from the theory of combinatorial probabilities. This assumes, of course, that the sampling operations themselves were carried out properly, as well. For example, that any random numbers required were generated properly, the units to be sampled from were correctly identified, located, and drawn, and the measurements were made with measurement error at a level not exceeding the required purposes.
Determination of bias and variance and of risks can be calculated when the selection was only partially determined by random numbers and a frame, but they then require suppositions and assumptions which may be more or less mistaken or require additional data which may introduce experimental error.
SCOPE
1.1 This practice is primarily a statement of principles for the guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material.

SIGNIFICANCE AND USE
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.
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.
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.
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 is recorded for each of...
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.

SIGNIFICANCE AND USE
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.
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1.1 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. It 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.
1.2 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. The methods may not give least uncertainty at least cost, they should however furnish a reasonable estimate with calculable uncertainty.
1.3 This practice is primarily intended for one-of-a-kind studies. Repetitive surveys allow estimates of sampling uncertainties to be pooled; the emphasis of this practice is on estimation of sampling uncertainty from the sample itself. The parameter of interest for this practice is effectively a constant. Thus, the principal inference is a simple point estimate to be used as if it were the unknown constant, rather than, for example, a forecast or prediction interval or distribution devised to match a random quantity of interest.
1.4 A system of units is not specified in this standard.
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 and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
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.
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.
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.
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 is recorded for each of...
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1.1 This practice covers methods and formulas 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.

SIGNIFICANCE AND USE
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.
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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.

SIGNIFICANCE AND USE
This guide describes the principal types of sampling designs and provides formulas for estimating population means and standard errors of the estimates. Practice E105 provides principles for designing probability sampling plans in relation to the objectives of study, costs, and practical constraints. Practice E122 aids in specifying the required sample size. Practice E141 describes conditions to ensure validity of the results of sampling. Further description of the designs and formulas in this guide, and beyond it, can be found in textbooks (1-10).  
Sampling, both discrete and bulk, is a clerical and physical operation. It generally involves training enumerators and technicians to use maps, directories and stop watches so as to locate designated sampling units. Once a sampling unit is located at its address, discrete sampling and area sampling enumeration proceeds to a measurement. For bulk sampling, material is extracted into a composite.  
A sampling plan consists of instructions telling how to list addresses and how to select the addresses to be measured or extracted. A frame is a listing of addresses each of which is indexed by a single integer or by an n-tuple (several integer) number. The sampled population consists of all addresses in the frame that can actually be selected and measured. It is sometimes different from a targeted population that the user would have preferred to be covered.
A selection scheme designates which indexes constitute the sample. If certified random numbers completely control the selection scheme the sample is called a probability sample. Certified random numbers are those generated either from a table (for example, Ref (11)) that has been tested for equal digit frequencies and for serial independence, from a computer program that was checked to have a long cycle length, or from a random physical method such as tossing of a coin or a casino-quality spinner.  
The objective of sampling is often to estimate the mean of the populat...
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1.1 This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards.
1.2 Sampling may be done for the purpose of estimation, of comparison between parts of a sampled population, or for acceptance of lots. Sampling is also used for the purpose of auditing information obtained from complete enumeration of the population.  
1.3 No system of units is specified in this standard.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use.

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.
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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:
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 1.1.1 above, is not the more plausible hypothesis to accept, as compared to alternative 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.

SIGNIFICANCE AND USE
This guide describes the principal types of sampling designs and provides formulas for estimating population means and standard errors of the estimates. Practice E 105 provides principles for designing probability sampling plans in relation to the objectives of study, costs, and practical constraints. Practice E 122 aids in specifying the required sample size. Practice E 141 describes conditions to ensure validity of the results of sampling. Further description of the designs and formulas in this guide, and beyond it, can be found in textbooks (1-10 ).
Sampling, both discrete and bulk, is a clerical and physical operation. It generally involves training enumerators and technicians to use maps, directories and stop watches so as to locate designated sampling units. Once a sampling unit is located at its address, discrete sampling and area sampling enumeration proceeds to a measurement. For bulk sampling, material is extracted into a composite.  
A sampling plan consists of instructions telling how to list addresses and how to select the addresses to be measured or extracted. A frame is a listing of addresses each of which is indexed by a single integer or by an n-tuple (several integer) number. The sampled population consists of all addresses in the frame that can actually be selected and measured. It is sometimes different from a targeted population that the user would have preferred to be covered.
A selection scheme designates which indexes constitute the sample. If certified random numbers completely control the selection scheme the sample is called a probability sample. Certified random numbers are those generated either from a table (e.g., (11)) that has been tested for equal digit frequencies and for serial independence, from a computer program that was checked to have a long cycle length, or from a random physical method such as tossing of a coin or a casino-quality spinner.  
The objective of sampling is often to estimate the mean of the population for ...
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1.1 This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards.
1.2 Sampling may be done for the purpose of estimation, of comparison between parts of a sampled population, or for acceptance of lots. Sampling is also used for the purpose of auditing information obtained from complete enumeration of the population.  
1.3 No system of units is specified in this standard.
1.4 This guide defines terms and introduces basic methods for probability sampling of discrete populations, areas, and bulk materials. It provides an overview of common probability sampling methods employed by users of ASTM standards. This standard does not purport to address all of the safety concerns, if any, associated with its use.

SIGNIFICANCE AND USE
This standard is a subsidiary to Terminology E 456.
It provides definitions, descriptions, discussion, and comparison of terms.
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1.1 This standard includes those statistical items related to the area of design of experiments for which standard definitions appears desirable.

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.

SCOPE
1.1 This practice covers methods and formulas 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.
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.

SIGNIFICANCE AND USE
The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, the percentage of some constituent, the fraction of the items that fail to meet (or meet) a specified requirement, the average characteristic or quality of an item, the total weight of the shipment, or the probable maximum or minimum content of, say, some chemical.
The purpose may be the rational disposition of a lot or shipment without the intermediate step of the formation of an estimate.
The purpose may to provide aid toward rational action concerning the production process that generated the lot, pile or shipment.
Whatever the purpose of the sample, adhering to the principles of probability sampling will allow the uncertainties, such as bias and variance of estimates or the risks of the rational disposition or action, to be calculated objectively and validly from the theory of combinatorial probabilities. This assumes, of course, that the sampling operations themselves ere carried out properly, as well. For example, that any random numbers required were generated properly, the units to be sampled from were correctly identified, located, and drawn, and the measurements were made with measurement error at a level not exceeding the required purposes.
Determination of bias and variance and of risks can be calculated when the selection was only partially determined by random numbers and a frame, but they then require suppositions and assumptions which may be more or less mistaken or require additional data which may introduce experimental error.
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1.1 This practice is primarily a statement of principles for the guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material.

SIGNIFICANCE AND USE
This practice is designed to permit users of sample survey data to judge the trustworthiness of results from such surveys. 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. If the sample design was relatively simple, such as simple random or stratified, then good estimates of sampling variance are easily available. If a more complex design was used then methods such as discussed in [1] may be acceptable. Replicate subsamples is the most straightforward way to estimate sampling variances when the survey design is complex.
Once the survey procedures that were used satisfy Section 5, consult Section 4 to see if any increase in sample size is needed. The calculations for making it are objectively described in Section 4.
Refer to Section 6 to guide in the interpretation of the uncertainty in the reported value of the parameter estimate, θ, i.e. 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.
SCOPE
1.1 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. It 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.
1.2 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. The methods may not give least uncertainty at least cost, they should however furnish a reasonable estimate with calculable uncertainty.
1.3 This practice is primarily intended for one-of-a-kind studies. Repetitive surveys allow estimates of sampling uncertainties to be pooled; the emphasis of this practice is on estimation of sampling uncertainty from the sample itself. The parameter of interest for this practice is effectively a constant. Thus, the principal inference is a simple point estimate to be used as if it were the unknown constant, rather than, for example, a forecast or prediction interval or distribution devised to match a random quantity of interest.
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.

SCOPE
1.1 This standard includes those statistical items related to the area of design of experiments for which standard definitions appears desirable.

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.
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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:  
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 1.1.1 above, is not the more plausible hypothesis to accept, as compared to alternative 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.

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 prescribed 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.

SIGNIFICANCE AND USE
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 prescribed 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.

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1.1 This guide is intended to help ASTM technical committees determine when it is appropriate to add supplementary requirements (see Section B24 of Form and Style for ASTM Standards )  to ASTM standards so that they can be used directly in government  procurement, to offer different format approaches for including supplementary requirements, and to provide content guidance.  
1.2 This guide covers procurement documents only. Regulatory documents are outside the scope of this guide.

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1.1 This standard includes those items related to statistical aspects of sampling.

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1.1 This practice is intended to assist the various technical committees in the use of uniform methods of indicating the number of digits which are to be considered significant in specification limits, for example, specified maximum values and specified minimum values. Its aim is to outline methods which should aid in clarifying the intended meaning of specification limits with which observed values or calculated test results are compared in determining conformance with specifications. Reference to this practice is valid only when a choice of method has been indicated, that is, either absolute method or rounding method .
1.2 This practice is intended to be used in determining conformance with specifications when the applicable ASTM specifications or standards make direct reference to this practice.
1.3 This practice describes two commonly accepted methods of rounding data, identified as the Absolute Method and the Rounding Method. In the application of this practice to a specific material or materials it is essential to specify which method is intended to apply. In the absence of such specification, reference to this practice, which expresses no preference as to which method should apply, would be meaningless. The choice of method is arbitrary, depending upon the current practice of the particular branch of industry or technology concerned, and should therefore be specified in the prime publication.
1.4 Section 7 of this practice gives guidelines for use in recording, calculating, and reporting the final result for test data.

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1.1 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.