Page 794 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Appendix K

Statistical Treatment

of Measurements

In research and product development and control, there exists a variability in the particular value
measured such as percentage yield, melting point, tensile strength, and electrical conductivity as
you repeat the measurement. Accuracy concerns how close to the true value your measured value
is. Unless there is an established value for a particular material, the values you obtain may well
contribute to the “true” value. Precision deals with the closeness of a group of measurement to one
another. Today, most modern instruments making spectral measurements collect many spectra in a
short time and those measurements undergo some type of statistical treatment, such as FT-IR, so that
the statistical treatment of these results has already been completed. In comparison many measure-
ments are done more or less singularly. This is true for most physical testing measurements. Thus,
to evaluate the tensile strength of a polycarbonate plastic sheeting sample “dog-bones” are cut from
several sheets picked at random and tested under an appropriate set of conditions. These results are
then statistically treated and the reported value given along with the variability. Following is a brief
summary of one of the more common statistically treatments for such measurements.

The first step involves calculation of the average value, A, which is simply the summation of the
individual values, A , divided by the number of measurements or observations, n. This is described
i
mathematically as A = (∑ A )/n, where the summation is for all of the “n” values.
i
The most common statistical measure of the variability, dispersion, or scatter is the standard
deviation, s, defi ned as
s = [(∑(A − A) )/n − 1] 1/2
2
i
The smaller the value of “s,” the greater the precision of the measurements. Some testing call for
the precision to be within some “s” value such as one “s” value or two “s” or three “s,” and so on.

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