D04.94 - Statistical Procedures and Evaluation of Data

SIGNIFICANCE AND USE
4.1 Precision statements for calculated values can be developed using this approach. Users can also evaluate how an individual test method’s precision influences the variability of calculated values.  
4.2 The standard deviation of a calculated value that is the sum, difference, product, or quotient of two or more test method results, each with their own precision statement, can be calculated so long as the individual variables (that is, test results) are independent and the standard deviations are small relative to their mean values. These restrictions are usually met in ASTM methods. In those cases where these restrictions are not met, other methods can be used. Only cases complying with the restrictions are covered in this standard.
SCOPE
1.1 Material and mixture properties such as air voids and voids in mineral aggregates (VMA) are calculated from two or three test results, combined in simple mathematical relationships. The standard deviation equations for these calculated values can be developed using a mathematical process called “propagation of errors” (also called “propagation of uncertainty”). This practice includes uncertainty equations for four forms or material and mixture equations: when two test results are (1) added or subtracted, (2) multiplied together, (3) one divided by the other, and (4) two test results divided by a third.  
1.2 This approach to calculating standard deviation equations is only valid when the distributions of the test results from the two standards are independent (that is, not correlated).  
1.3 The accuracy of a calculated standard deviation is dependent on the accuracy of the standard deviations used for the individual test result methods.  
1.4 Values for the mean and standard deviation for each test method are needed to determine the standard deviation for a calculated value.  
1.5 Examples of how to use these equations are shown in Appendix X1.  
1.6 A brief explanation of how standard deviation equations are derived for more complicated material and mixture equations is also included.  
1.7 The text of this standard references notes and footnotes which provide explanatory material. These notes and footnotes (excluding those in tables and figures) shall not be considered as requirements of the standard.  
1.8 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.  
1.9 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 Each test method has a limited precision. Even if a test is performed as carefully and as correctly as possible on a material which is as homogeneous as can be obtained, the test will still vary from one to another. A widely used measure of the variation of the test results from a test method is the standard deviation (σ). In an ASTM standard test method, the standard deviation of the test method can be found in the Precision and Bias statement for the test. The “Blue Book,” Form and Style for ASTM Standards, requires that all test methods include Precision and Bias statements. Practices C670 and C802 provide guidance for determination of these values.  
4.2 If the precision of a test method is low and the precision of the test has not been properly considered in a material specification, a uniform material with the right quality may still be rejected most of the time because of the wide variation of the test results. In order to have rational specification limits, the precision of the test used should be properly included in a specification.  
4.3 This practice provides a guideline for proper inclusion of precision of the test method in a rational specification.
SCOPE
1.1 This practice covers a method of determining rational specification limits by inclusion of the precision of the test method used in the specification.  
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 The text of this standard references notes and footnotes which provide explanatory material. These notes and footnotes (excluding those in tables and figures) shall not be considered as requirements of the 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 Precision statements for calculated values can be developed using this approach. Users can also evaluate how an individual test method’s precision influences the variability of calculated values.  
4.2 The standard deviation of a calculated value that is the sum, difference, product, or quotient of two or more test method results, each with their own precision statement, can be calculated so long as the individual variables (that is, test results) are independent and the standard deviations are small relative to their mean values. These restrictions are usually met in ASTM methods. In those cases where these restrictions are not met, other methods can be used. Only cases complying with the restrictions are covered in this standard.
SCOPE
1.1 Material and mixture properties such as air voids and voids in mineral aggregates (VMA) are calculated from two or three test results, combined in simple mathematical relationships. The standard deviation equations for these calculated values can be developed using a mathematical process called “propagation of errors” (also called “propagation of uncertainty”). This practice includes uncertainty equations for four forms or material and mixture equations: when two test results are (1) added or subtracted, (2) multiplied together, (3) one divided by the other, and (4) two test results divided by a third.  
1.2 This approach to calculating standard deviation equations is only valid when the distributions of the test results from the two standards are independent (that is, not correlated).  
1.3 The accuracy of a calculated standard deviation is dependent on the accuracy of the standard deviations used for the individual test result methods.  
1.4 Values for the mean and standard deviation for each test method are needed to determine the standard deviation for a calculated value.  
1.5 Examples of how to use these equations are shown in Appendix X1.  
1.6 A brief explanation of how standard deviation equations are derived for more complicated material and mixture equations is also included.  
1.7 The text of this standard references notes and footnotes which provide explanatory material. These notes and footnotes (excluding those in tables and figures) shall not be considered as requirements of the standard.  
1.8 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.  
1.9 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 Each test method has a limited precision. Even if a test is performed as carefully and as correctly as possible on a material which is as homogeneous as can be obtained, the test will still vary from one to another. A widely used measure of the variation of the test results from a test method is the standard deviation (σ). In an ASTM standard test, the standard deviation of the test method can be found in the Precision and Bias statement for the test. The “Blue Book,” Form and Style for ASTM Standards, requires that all test methods include Precision and Bias statements. Practice C670 and Practice C802 provide guidance for determination of these values.  
4.2 If the precision of a test method is low and the precision of the test has not been properly considered in a material specification, a uniform material with the right quality may still be rejected most of the time because of the wide variation of the test results. In order to have rational specification limits, the precision of the test used should be properly included in a specification.  
4.3 This practice provides a guideline for proper inclusion of precision of the test method in a rational specification.
SCOPE
1.1 This practice covers a method of determining rational specification limits by inclusion of the precision of the test method used in the specification.  
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 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 Precision limits for a test result that is calculated by addition, subtraction, multiplication, or division of two other test results that have valid precision limits can be calculated directly. This saves the cost and delay of conducting an interlaboratory study.  
4.2 At the heart of statistical theory is the concept of a frequency distribution of a random variable. The precision limit of the random variable is determined by the standard deviation of the variable. The standard deviation of a random variable that is the sum, difference, product, or quotient of two other random variables can be calculated simply so long as the individual variables are independent and the standard deviations are small relative to their mean values. These restrictions are usually met in ASTM methods. In those cases where these restrictions are not met, other methods can be used. Only cases complying with the restrictions are covered in this standard.
SCOPE
1.1 This practice covers techniques for calculating precision limits when values are calculated from two other methods having precision limits.  
1.2 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
Each test method has a limited precision. Even if a test is performed as carefully and as correctly as possible on a material which is as homogeneous as can be obtained, the test will still vary from one to another. A widely used measure of the variation of the test results from a test method is the standard deviation (σ). In an ASTM standard test, the standard deviation of the test method can be found in the Precision and Bias statement for the test. The “Blue Book,” Form and Style for ASTM Standards, requires that all test methods include Precision and Bias statements. Practice C670 and Practice C802 provide guidance for determination of these values.
If the precision of a test method is low and the precision of the test has not been properly considered in a material specification, a uniform material with the right quality may still be rejected most of the time because of the wide variation of the test results. In order to have rational specification limits, the precision of the test used should be properly included in a specification.
This practice provides a guideline for proper inclusion of precision of the test method in a rational specification.
SCOPE
1.1 This practice covers a method of determining rational specification limits by inclusion of the precision of the test method used in the specification.
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 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
Precision limits for a test result that is calculated by addition, subtraction, multiplication, or division of two other test results that have valid precision limits can be calculated directly. This saves the cost and delay of conducting an interlaboratory study.
At the heart of statistical theory is the concept of a frequency distribution of a random variable. The precision limit of the random variable is determined by the standard deviation of the variable. The standard deviation of a random variable that is the sum, difference, product, or quotient of two other random variables can be calculated simply so long as the individual variables are independent and the standard deviations are small relative to their mean values. These restrictions are usually met in ASTM methods. In those cases where these restrictions are not met, other methods can be used. Only cases complying with the restrictions are covered in this standard.
SCOPE
1.1 This practice covers techniques for calculating precision limits when values are calculated from two other methods having precision limits.
1.2 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
Precision limits for a test result that is calculated by addition, subtraction, multiplication, or division of two other test results that have valid precision limits can be calculated directly. This saves the cost and delay of conducting an interlaboratory study.
At the heart of statistical theory is the concept of a frequency distribution of a random variable. The precision limit of the random variable is determined by the standard deviation of the variable. The standard deviation of a random variable that is the sum, difference, product, or quotient of two other random variables can be calculated simply so long as the individual variables are independent and the standard deviations are small relative to their mean values. These restrictions are usually met in ASTM methods. In those cases where these restrictions are not met, other methods can be used. Only cases complying with the restrictions are covered in this standard.
SCOPE
1.1 This practice covers techniques for calculating precision limits when values are calculated from two other methods having precision limits.
1.2 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
Each test method has a limited precision. Even if a test is performed as carefully and as correctly as possible on a material which is as homogeneous as can be obtained, the test will still vary from one to another. A widely used measure of the variation of the test results from a test method is the standard deviation (σ). In an ASTM standard test, the standard deviation of the test method can be found in the Precision and Bias statement for the test. The “Blue Book,” Form and Style for ASTM Standards, requires that all test methods include Precision and Bias statements. Practice C 670 and Practice C 802 provide guidance for determination of these values.
If the precision of a test method is low and the precision of the test has not been properly considered in a material specification, a uniform material with the right quality may still be rejected most of the time because of the wide variation of the test results. In order to have rational specification limits, the precision of the test used should be properly included in a specification.
This practice provides a guideline for proper inclusion of precision of the test method in a rational specification.
SCOPE
1.1 This practice covers a method of determining rational specification limits by inclusion of the precision of the test method used in the specification.
1.2 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for information only.
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.

SCOPE
1.1 This practice describes techniques for calculating precision limits when values are calculated from two other methods having precision limits.
1.2 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 practice presents a method of determining rational specification limits by inclusion of the precision of the test method used in the specification.

SCOPE
1.1 This practice describes techniques for calculating precision limits when values are calculated from two other methods having precision limits.  
1.2 This standard may involve hazardous materials, operations, and equipment. This standard does not purport to address all of the safety problems associated with its use. It is the responsibility of whoever uses this standard to consult and establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use .