ASTM E1970-16(2021)

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, 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 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.  
1.5 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: Historical
• Publication Date: 30-Sep-2021
• 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)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E1970 − 16 (Reapproved 2021)
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 E2586 Practice for Calculating and Using Basic Statistics
F1469 Guide for Conducting a Repeatability and Reproduc-
1.1 This practice details the statistical data treatment used in
ibility Study on Test Equipment for Nondestructive Test-
some thermal analysis methods.
3
ing (Withdrawn 2018)
1.2 The method describes the commonly encountered sta-
3. Terminology
tistical tools of the mean, standard derivation, relative standard
deviation, pooled standard deviation, pooled relative standard
3.1 Definitions—The technical terms used in this practice
deviation, the best fit to a (linear regression of a) straight line,
are defined in Practice E177 and Terminologies E456 and
and propagation of uncertainties for all calculations encoun-
E2161 including precision, relative standard deviation,
tered in thermal analysis methods (see Practice E2586).
repeatability, reproducibility, slope, standard deviation,
thermoanalytical, and variance.
1.3 Some thermal analysis methods derive the analytical
4
value from the slope or intercept of a linear regression straight
3.2 Symbols (1):
line assigned to three or more sets of data pairs. Such methods
may require an estimation of the precision in the determined m = slope
b = intercept
slope or intercept. The determination of this precision is not a
n = number of data sets (that is, x , y )
common statistical tool. This practice details the process for i i
x = an individual independent variable observation
i
obtaining such information about precision.
y = an individual dependent variable observation
i
1.4 There are no ISO methods equivalent to this practice.
Σ = mathematical operation which means “the sum of
1.5 This international standard was developed in accor- all” for the term(s) following the operator
dance with internationally recognized principles on standard- X = mean value
s = standard deviation
ization established in the Decision on Principles for the
s = pooled standard deviation
Development of International Standards, Guides and Recom- pooled
s = standard deviation of the line intercept
mendations issued by the World Trade Organization Technical b
s = standard deviation of the slope of a line
m
Barriers to Trade (TBT) Committee.
s = standard deviation of Y values
y
RSD = relative standard deviation
2. Referenced Documents
δy = variance in y parameter
2 i
2.1 ASTM Standards:
r = correlation coefficient
E177 Practice for Use of the Terms Precision and Bias in
R = gage reproducibility and repeatability (see Guide
ASTM Test Methods
F1469) an estimation of the combined variation of
E456 Terminology Relating to Quality and Statistics
repeatability and reproducibility (2)
E691 Practice for Conducting an Interlaboratory Study to
s = within laboratory repeatability standard deviation
r
Determine the Precision of a Test Method
(see Practice E691)
E2161 Terminology Relating to Performance Validation in
s = between laboratory repeatability standard deviation
R
Thermal Analysis and Rheology
(see Practice E691)
s = standard deviation of the “ith” measurement
i
1
This practice is under the jurisdiction of ASTM Committee E37 on Thermal
4. Summary of Practice
Measurements and is the direct responsibility of Subcommittee E37.10 on
4.1 The result of a series of replicate measurements of a
Fundamental, Statistical and Mechanical Properties.
Current edition approved Oct. 1, 2021. Published November 2021. Originally
value are typically reported as the mean value plus some
approved in 1998. Last previous edition approved in 2016 as E1970 – 16. DOI:
10.1520/E1970-16R21.
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.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
E1970 − 16 (2021)
estimation of the precision in the mean value. The standard the standard deviation is that there is a 67 % chance, that is 2
deviation is the most commonly encountered tool for es
...

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 E1970 − 16 (Reapproved 2021)
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, 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
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.
1.5 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 April 1, 2016Oct. 1, 2021. Published April 2016November 2021. Originally approved in 1998. Last previous edition approved in 20112016 as
E1970 – 11.E1970 – 16. DOI: 10.1520/E1970-16.10.1520/E1970-16R21.
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 − 16 (2021)
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):
m = slope
b = intercept
n = number of data sets (that is, x , y )
i i
x = an individual independent variable observation
i
y = an individual dependent variable observation
i
Σ = mathematical operation which means “the sum of all” for the term(s) following the operator
X = mean value
s = standard deviation
s = pooled standard deviation
pooled
s = standard deviation of the line intercept
b
s = standard deviation of the slope of a line
m
s = standard deviation of Y values
y
RSD = relative standard deviation
δy = variance in y parameter
i
r = correlation coefficient
R = gage reproducibility and repeatability (see Guide F1469) an estimation of the combined variation of repeatability and
reproducibility (2)
s = within laboratory repeatability standard deviation (see Practice E691)
r
s = between laboratory repeatability standard deviation (see Practice E691)
R
s = standard deviation of the “ith” measurement
i
4. Summary of Prac
...