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**Significance and Use**

The standard deviation, or one of its derivatives, such as relative standard deviation or pooled standard deviation, derived from this practice, provides an estimate of precision in a measured value. Such results are ordinarily expressed as the mean value ± the standard deviation, that is, X ± s.

If the measured values are, in the statistical sense, “normally” distributed about their mean, then the meaning of the standard deviation is that there is a 67 % chance, that is 2 in 3, that a given value will lie within the range of ± one standard deviation of the mean value. Similarly, there is a 95 % chance, that is 19 in 20, that a given value will lie within the range of ± two standard deviations of the mean. The two standard deviation range is sometimes used as a test for outlying measurements.

The calculation of precision in the slope and intercept of a line, derived from experimental data, commonly is required in the determination of kinetic parameters, vapor pressure or enthalpy of vaporization. This practice describes how to obtain these and other statistically derived values associated with measurements by thermal analysis.

**1. Scope**

1.1 This practice details the statistical data treatment used in some thermal analysis methods.

1.2 The method describes the commonly encountered statistical tools of the mean, standard derivation, relative standard deviation, pooled standard deviation, pooled relative standard deviation and the best fit to a straight line, all calculations encountered in thermal analysis methods.

1.3 Some thermal analysis methods derive the analytical value from the slope or intercept of a best fit straight line assigned to three or more sets of data pairs. Such methods may require an estimation of the precision in the determined slope or intercept. The determination of this precision is not a common statistical tool. This practice details the process for obtaining such information about precision.

1.4 There are no ISO methods equivalent to this practice.

**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**

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

E456 Terminology Relating to Quality and Statistics

E691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method

E2161 Terminology Relating to Performance Validation in Thermal Analysis

F1469 Guide for Conducting a Repeatability and Reproducibility Study on Test Equipment for Nondestructive Testing

**ICS Code**

ICS Number Code 03.120.30 (Application of statistical methods); 17.200.10 (Heat. Calorimetry)

**UNSPSC Code**

UNSPSC Code

**DOI:** 10.1520/E1970-11

ASTM International is a member of CrossRef.

**Citation Format**

ASTM E1970-11, Standard Practice for Statistical Treatment of Thermoanalytical Data, ASTM International, West Conshohocken, PA, 2011, www.astm.org

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