Allan deviation plot for each eclipse. The black line denotes the $1/\sqrt{N}$ trend expected for uncorrelated noise, while the shaded regions denote the 1σ, 2σ and 3σ confidence intervals for each particular binning calculated using 10,000 white noise draws. We note that only 75% of the white noise draws stay within the 2σ intervals for all bin sizes tested. We see that there can be a particularly large range of deviation from $1/\sqrt{N}$ for large bin sizes even for actual white noise.