ASTM-E1970 › Standard Practice for Statistical Treatment of Thermoanalytical Data
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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, the best fit to a (linear regression of a) straight line, and propagation of uncertainties for all calculations encountered in thermal analysis methods (see Practice ).
1.3 Some thermal analysis methods derive the analytical value from the slope or intercept of a linear regression 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.
Significance and Use
5.1 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.
5.2 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.
5.3 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.
best fit; error; intercept; linear regression; mean; precision; propagation of uncertainties; relative standard deviation; slope; standard deviation; variance; uncertainty;; ICS Number Code 03.120.30 (Application of statistical methods); 17.200.10 (Heat. Calorimetry)
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May 1, 2016