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This presentation illustrates two simple semi-quantitative methods for revealing the presence of temporal correlations in measurement data. The examples come from routine measurements in dc voltage metrology. The observations are nearly equally spaced in time. Attention is drawn to an error commonly made in metrology: the assumption that random fluctuations are independent and identically distributed (IID or white noise processes).
When can we characterize the scatter by the standard deviation of the mean?
When can we characterize the scatter in a set of n measurements, having an experimental or sample standard deviation s, by the standard deviation of the mean calculated from the expression sM = s / n1/2?
– The short answer is "rarely", because of correlations between observations.
 Suppose that X1 and X2 are identically distributed random variables whose distribution has a finite mean and a variance  2 and we are interested in knowing the standard deviation of the mean,
 .
In general,
The X's are identically distributed, so
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If, furthermore, X1 and X2 are independent, then
Generalizing to n observations,
and
 ,
which, in the case of white noise, reduces to
How can we check for correlations in measurements?
Make measurements equally spaced in time and treat the measurement data as a time series; analyse it using frequency spectral techniques, the Allan variance, correlation function techniques, ARMA methods, etc. In the following pages, only two simple semi-quantitative methods are used:
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Summary
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