A problem often arises when the combination of several series of measurements performed under similar conditions is desired to achieve an improved estimate of the imprecision of the process. If it can be assumed that all the series are of the same
precision although their means may differ, the pooled standard deviations
from
series of measurements can be calculated as
The suffices
refer to the different series of measurements. In this case it is assumed that there exists a single underlying
standard deviation
of which the pooled
standard deviation
is a better estimate than the individual calculated standard deviations
,
For the special case where
sets of duplicate measurements are available, the above equation reduces to
Results from various series of measurements can be combined in the following way to give a
pooled relative standard deviation
:
Source:
PAC, 1981, 53, 1805
(Assignment and presentation of uncertainties of the numerical results of thermodynamic measurements (Provisional))
on page 1821
Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A.Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.
doi:10.1351/goldbook.
