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**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.

**1. 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.*

**2. Referenced Documents** *(purchase separately)* The documents listed below are referenced within the subject standard but are not provided as part of the standard.

**ASTM Standards**

D1188 Test Method for Bulk Specific Gravity and Density of Compacted Bituminous Mixtures Using Coated Samples

D2041 Test Method for Theoretical Maximum Specific Gravity and Density of Bituminous Paving Mixtures

D3203 Test Method for Percent Air Voids in Compacted Dense and Open Bituminous Paving Mixtures

E177 Practice for Use of the Terms Precision and Bias in ASTM Test Methods

**ICS Code**

ICS Number Code 93.080.20 (Road construction materials)

**UNSPSC Code**

UNSPSC Code 41110000(Measuring and observing and testing instruments)

**DOI:** 10.1520/D4460-97R15

ASTM International is a member of CrossRef.

**Citation Format**

ASTM D4460-97(2015), Standard Practice for Calculating Precision Limits Where Values are Calculated from Other Test Methods, ASTM International, West Conshohocken, PA, 2015, www.astm.org

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