ASTM E1970-01

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.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:E1970–01
Standard Practice for
1
Statistical Treatment of Thermoanalytical Data
This standard is issued under the fixed designation E 1970; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope
m = slope
1.1 This practice details the statistical data treatment used in
b = intercept
some thermal analysis methods.
n = number of data sets (that is, x,y)
i i
1.2 The method describes the commonly encountered sta-
x = an individual independent variable observation
i
tistical tools of the mean, standard derivation, relative standard
y = an individual dependent variable observation
i
deviation, pooled standard deviation, pooled relative standard
S = mathematical operation which means “the sum
deviation and the best fit to a straight line, all calculations
of all” for the term(s) following the operator
encountered in thermal analysis methods.
X = mean value
1.3 Some thermal analysis methods derive the analytical
s = standard deviation
value from the slope or intercept of a best fit straight line
s = pooled standard deviation
pooled
assigned to three or more sets of data pairs. Such methods may
s = standard deviation of the line intercept
b
require an estimation of the precision in the determined slope
s = standard deviation of the slope of a line
m
or intercept. The determination of this precision is not a
s = standard deviation of Y values
y
common statistical tool. This practice details the process for
RSD = relative standard deviation
obtaining such information about precision. dy = variance in y parameter
i
r = correlation coefficient
1.4 Computer or electronic-based instruments, techniques
or data treatment equivalent to this practice may also be used.
4. Summary of Practice
NOTE 1—Users of this practice are expressly advised that some such
4.1 The result of a series of replicate measurements of a
instruments or techniques may not be equivalent. It is the responsibility of
value are typically reported as the mean value plus some
the user of this standard to determine the necessary equivalency prior to
estimation of the precision in the mean value. The standard
use.
deviation is the most commonly encountered tool for estimat-
1.5 SI units are the standard.
ing precision, but other tools, such as relative standard devia-
1.6 There are no ISO methods equivalent to this practice.
tion or pooled standard deviation, also may be encountered in
specific thermoanalytical test methods. This practice describes
2. Referenced Documents
the mathematical process of achieving mean value, standard
2.1 ASTM Standards:
deviation, relative standard deviation and pooled standard
E 177 Practice for Use of the Terms Precision and Bias in
deviation.
2
ASTM Test Methods
4.2 In some thermal analysis experiments, a linear or a
2
E 456 Terminology Relating to Quality and Statistics
straight line, response is assumed and desired values are
obtained from the slope or intercept of the straight line through
3. Terminology
the experimental data. In any practical experiment, however,
3.1 Definitions—The technical terms used in this practice
there will be some uncertainty in the data so that results are
are defined in Practice E 177 and Terminology E 456.
3 scattered about such a straight line.The least squares method is
3.2 Symbols:
an objective tool for determining the “best fit” straight line
drawn through a set of experimental results and for obtaining
1
information concerning the precision of determined values.
This practice is under the jurisdiction of ASTM Committee E37 on Thermal
Measurements and is the direct responsibility of Subcommittee E37.01 on Test
4.2.1 For the purposes of this practice, it is assumed that the
Methods and Recommended Practices.
physical behavior, which the experimental results approximate,
Current edition approved Aug. 10, 2001. Published November 2001. Originally
are linear with respect to the controlled value, and may be
published as E 1970 – 98. Last previous edition E 1970 – 00.
2
Annual Book of ASTM Standards, Vol 14.02. represented by the algebraic function:
3
Taylor, J.K., Handbook for SRM Users, Publication 260-100, National Institute
y 5 mx 1 b (1)
of Standards and Technology, Gaithersburg, MD, 1993.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1

---------------------- Page: 1 ----------------------
E1970
2 2 2 1/2
4.2.2 Experimental results are gathered in pairs, that is, for
~ n 2 1 · s ! 1 ~ n 2 1 · s ! 1.1S~ n 2 1 · s !
$ % $ % $ %
1 1 2 2 i i
s 5
F G
p
every corresponding x (controlled) value, there is a
...