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Figure 11.3: Standard Error Analysis: As the sample size increases, the standard
error of the estimated mean shifts from being dominated by statistical sampling
noise (red line) to being dominated by 1/f drift in the experiments (green line).
The point where the two lines cross gives the maximum sample size that can be
statistically analyzed in a meaningful way without modeling the 1/f noise.
The variances v i are then averaged over the entire dataset to give an estimate of
the standard error:
σ n = √ 1 n
n∑
v i (11.6)
i=1
The resulting σ n ’s as a function of the section size N n
are shown in Figure
11.3. As the section size is increased, the statistical noise in the estimate of S i
1
goes down, leading to the expected √ decrease in σ n . Eventually, the sections
N/n
become large enough for drifts to dominate their internal variance (as defined
by Equation 11.5) and the resulting σ n ’s level off.
If straight lines are fitted
through each of these two regions, their point of intersection gives an estimate of
the maximum acceptable sample size, in this case 1.55 million samples, or about
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