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IUPAC - pooled standard deviation
IUPAC :pooled standard deviation
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 sp
from k series of measurements can be calculated as
[math]
s_p=\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2+...+(n_k-1)s_k^2}{n_1+n_2+...+n_k-k}}
[/math]
The suffices 1, 2, ..., k refer to the different series of measurements. In this case it is assumed that there exists a single underlying standard deviation σ of which the pooled standard deviation sp is a ..→
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