ASTM E1970-16

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.

General Information

• Status: Historical
• Publication Date: 31-Mar-2016
• 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
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* 3. Terminology
3.1 Definitions—The technical terms used in this practice
1.1 This practice details the statistical data treatment used in
are defined in Practice E177 and Terminologies E456 and
some thermal analysis methods.
E2161 including precision, relative standard deviation,
1.2 The method describes the commonly encountered sta-
repeatability, reproducibility, slope, standard deviation,
tistical tools of the mean, standard derivation, relative standard
thermoanalytical, and variance.
deviation, pooled standard deviation, pooled relative standard
3
3.2 Symbols (1):
deviation, the best fit to a (linear regression of a) straight line,
and propagation of uncertainties for all calculations encoun-
m = slope
tered in thermal analysis methods (see Practice E2586).
b = intercept
n = number of data sets (that is, x,y)
i i
1.3 Some thermal analysis methods derive the analytical
x = an individual independent variable observation
i
value from the slope or intercept of a linear regression straight
y = an individual dependent variable observation
i
line assigned to three or more sets of data pairs. Such methods
Σ = mathematical operation which means “the sum of
may require an estimation of the precision in the determined
all” for the term(s) following the operator
slope or intercept. The determination of this precision is not a
X = mean value
common statistical tool. This practice details the process for
s = standard deviation
obtaining such information about precision.
s = pooled standard deviation
pooled
s = standard deviation of the line intercept
b
1.4 There are no ISO methods equivalent to this practice.
s = standard deviation of the slope of a line
m
s = standard deviation of Y values
y
2. Referenced Documents
RSD = relative standard deviation
2
δy = variance in y parameter
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)
E2586 Practice for Calculating and Using Basic Statistics
s = standard deviation of the “ith” measurement
i
F1469 Guide for Conducting a Repeatability and Reproduc-
ibility Study on Test Equipment for Nondestructive Test-
4. Summary of Practice
ing
4.1 The result of a series of replicate measurements of a
value are typically reported as the mean value plus some
estimation of the precision in the mean value. The standard
1
This practice is under the jurisdiction of ASTM Committee E37 on Thermal
deviation is the most commonly encountered tool for estimat-
Measurements and is the direct responsibility of Subcommittee E37.10 on
ing precision, but other tools, such as relative standard devia-
Fundamental, Statistical and Mechanical Properties.
tion or pooled standard deviation, also may be encountered in
Current edition approved April 1, 2016. Published April 2016. Originally
approved in 1998. Last previous edition approved in 2011 as E1970 – 11. DOI:
specific thermoanalytical test methods. This practice describes
10.1520/E1970-16.
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
3
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. United States
1

---------------------- Page: 1 ----------------------
E1970 − 16
the mathematical process of achieving mean value, standard standard deviation range is sometimes used as a test for
deviation, relative standard deviation and pooled standard outlying measurements.
deviation.
5.3 The calculation of precision in the slope and intercept of
4.2
...

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 − 11 E1970 − 16
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 and deviation, the best fit to a straight line, (linear
regression of a) straight line, and propagation of uncertainties for all calculations encountered in thermal analysis methods.methods
(see Practice E2586).
1.3 Some thermal analysis methods derive the analytical value from the slope or intercept of a best fitlinear 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.
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. 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.
3
3.2 Symbols: 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
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 Aug. 1, 2011April 1, 2016. Published August 2011April 2016. Originally approved in 1998. Last previous edition approved in 20062011 as
E1970 – 06.E1970 – 11. DOI: 10.1520/E1970-11.10.1520/E1970-16.
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
Taylor, J.K., Handbook for SRM Users, Publication 260-100, National Institute of Standards and Technology, Gaithersburg, MD, 1993.
4
Measurement System Analysis, third edition, Automotive Industry Action Group, Southfield, MI, 2003, pp. 55, 177–184.
3
Mandel, J., The Statistical Analysis of Experimental Data, Dover Publications, New York, NY, 1964. The boldface numbers in parentheses refer to a list of references
at the end of 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. United States
1

---------------------- Page: 1 ----------------------
E1970 − 16
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
...