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.

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.