A concrete example of how statistical noise may impede the detection of linear response breakdown from observations is shown in Figure 7 for an observable A(x) = x. Shown is the observed sample averageĀ (7) as a function of the perturbation size. The error bars are calculated from the standard deviation as calculated for the single available time series, which is the situation for scientists analyzing observations. For insufficient **data** length N = 10 5 a linear response is consistent within the available statistical significance levels (top of Figure 7). Only for significantly larger time series with **data** length N = 10 6 , does the breakdown become detectable in a statistically significant way (bottom of Figure 7).