As seen in Section 4 the non-smoothness of the invariant measure is caused by the rapid displacement of spikes upon perturbation. The smaller and narrower the spike, the faster it moves. This points to an issue of resolution: the faster spikes carry less mass and therefore require a certain amount of **data** to be reliably resolved; the slower spikes carry more mass but their smaller displacement upon perturbation requires sufficient **data** to be resolved. This means that a sufficiently large amount of **data** is needed for the breakdown parameter q to accurately estimate the mismatch Eq, and to determine whether a system obeys linear response or not. This issue of resolving the mismatch Eq is an additional finite size issue to the one discussed in Section 3 whereby N needs to be sufficiently large to assure that the observed p-value is properly estimated (cf. (15)).