ASTM E1970-23

Standard Practice for Statistical Treatment of Thermoanalytical Data

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.
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, the best fit to a (linear regression of a) straight line (or plane), and propagation of uncertainties for all calculations encountered in thermal analysis methods (see Practice E2586).  
1.3 Some thermal analysis methods derive the analytical value from the slope or intercept of a linear regression straight line (or plane) 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 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.

General Information

• Status: Published
• Publication Date: 31-Dec-2022
• ICS: 03.120.30 - Application of statistical methods
• ICS: 17.200.10 - Heat. Calorimetry
• Technical Committee: E37 - Thermal Measurements
• Drafting Committee: E37.10 - Fundamental, Statistical and Mechanical Properties

Standards Content (Sample)

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.
Designation: E1970 − 23
Standard Practice for
1
Statistical Treatment of Thermoanalytical Data
This standard is issued under the fixed designation E1970; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope* E691 Practice for Conducting an Interlaboratory Study to
Determine the Precision of a Test Method
1.1 This practice details the statistical data treatment used in
E2161 Terminology Relating to Performance Validation in
some thermal analysis methods.
Thermal Analysis and Rheology
1.2 The method describes the commonly encountered sta-
E2586 Practice for Calculating and Using Basic Statistics
tistical tools of the mean, standard derivation, relative standard
F1469 Guide for Conducting a Repeatability and Reproduc-
deviation, pooled standard deviation, pooled relative standard
ibility Study on Test Equipment for Nondestructive Test-
3
deviation, the best fit to a (linear regression of a) straight line
ing (Withdrawn 2018)
(or plane), and propagation of uncertainties for all calculations
encountered in thermal analysis methods (see Practice E2586).
3. Terminology
1.3 Some thermal analysis methods derive the analytical
3.1 Definitions—The technical terms used in this practice
value from the slope or intercept of a linear regression straight
are defined in Practice E177 and Terminologies E456 and
line (or plane) assigned to three or more sets of data pairs. Such
E2161 including precision, relative standard deviation,
methods may require an estimation of the precision in the
repeatability, reproducibility, slope, standard deviation,
determined slope or intercept. The determination of this
thermoanalytical, and variance.
precision is not a common statistical tool. This practice details 4
3.2 Symbols (1):
the process for obtaining such information about precision.
a, c, m = slope
1.4 This standard does not purport to address all of the
b, d = intercept
safety concerns, if any, associated with its use. It is the
n = number of data sets (that is, x , y )
i i
responsibility of the user of this standard to establish appro-
r = correlation coefficient
priate safety, health, and environmental practices and deter-
R = gage reproducibility and repeatability (see Guide
mine the applicability of regulatory limitations prior to use.
F1469) an estimation of the combined variation of
1.5 This international standard was developed in accor-
repeatability and reproducibility (2)
dance with internationally recognized principles on standard-
2
R = coefficient of determination
ization established in the Decision on Principles for the
RSD = relative standard deviation
Development of International Standards, Guides and Recom-
s = standard deviation
mendations issued by the World Trade Organization Technical
s = standard deviation of the line intercept
b
Barriers to Trade (TBT) Committee.
s = standard deviation of the “ith” measurement
i
s = standard deviation of the slope of a line
m
2. Referenced Documents
s = pooled standard deviation
pooled
2
s = within laboratory repeatability standard deviation
2.1 ASTM Standards:
r
(see Practice E691)
E177 Practice for Use of the Terms Precision and Bias in
s = between laboratory repeatability standard devia-
ASTM Test Methods R
tion (see Practice E691)
E456 Terminology Relating to Quality and Statistics
s = standard deviation of Y values
y
X = mean x value
1 x = an individual independent variable observation
This practice is under the jurisdiction of ASTM Committee E37 on Thermal
i
Measurements and is the direct responsibility of Subcommittee E37.10 on Y = mean y value
Fundamental, Statistical and Mechanical Properties.
y = an individual dependent variable observation
i
Current edition approved Jan. 1, 2023. Published February 2023. Originally
approved in 1998. Last previous edition approved in 2021 as E1970 – 16(2021).
DOI: 10.1520/E1970-23.
2 3
For referenced ASTM standards, visit the ASTM website, www.astm.org, or The last approved version of this historical standard is referenced on www.ast-
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM m.org.
4
Standards volume information, refer to the standard’s Document Summary page on The boldface numbers in parentheses refer to a list of references at the end of
the ASTM website. this standard.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E1970 − 16 (Reapproved 2021) E1970 − 23
Standard Practice for
1
Statistical Treatment of Thermoanalytical Data
This standard is issued under the fixed designation E1970; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 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, the best fit to a (linear regression of a) straight line, line (or plane),
and propagation of uncertainties for all calculations encountered in thermal analysis methods (see Practice E2586).
1.3 Some thermal analysis methods derive the analytical value from the slope or intercept of a linear regression straight line (or
plane) 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.
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.
2. Referenced Documents
2
2.1 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 and Rheology
E2586 Practice for Calculating and Using Basic Statistics
F1469 Guide for Conducting a Repeatability and Reproducibility Study on Test Equipment for Nondestructive Testing
3
(Withdrawn 2018)
1
This practice is under the jurisdiction of ASTM Committee E37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.10 on Fundamental,
Statistical and Mechanical Properties.
Current edition approved Oct. 1, 2021Jan. 1, 2023. Published November 2021February 2023. Originally approved in 1998. Last previous edition approved in 20162021
as E1970 – 16.E1970 – 16(2021). DOI: 10.1520/E1970-16R21.10.1520/E1970-23.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
3
The last approved version of this historical standard is referenced on www.astm.org.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
E1970 − 23
3. Terminology
3.1 Definitions—The technical terms used in this practice are defined in Practice E177 and Terminologies E456 and E2161
including precision, relative standard deviation, repeatability, reproducibility, slope, standard deviation, thermoanalytical, and
variance.
4
3.2 Symbols (1):
a, c, m = slope
b = intercept
b, d = intercept
n = number of data sets (that is, x , y )
i i
x = an individual independent variable observation
i
r = correlation coefficient
y = an individual dependent variable observation
i
R = gage reproducibility and repeatability (see Guide F1469) an estimation of the combined variation of repeatability and
reproducibility (2)
Σ = mathematical operation which means “the sum of all” for the term(s) following the operator
2
R = coefficient of determination
X = mean value
s = standard deviation
RSD = relative standard deviation
s = pooled standard deviation
poo
...