Suppose one is willing to accept a 5% probability of observing the "wrong" outcome (i.e., despite pa < pb, we observe ka > kb), for a given experiment budget of 2n (i.e., n trials assigned to each batch). This demarcation corresponds to setting eqn. (1) or eqn. (2) equal to 0.05 and solving for the contour of pb for each input pa values; contours for n = 24, 48, and 96 are shown in Figure . Points outside a given contour line have a <5% chance of giving the "wrong" answer for the given number of trials, and thus the two chemical systems outside the blue n = 24 contour will be "easiest" to verify if the low and high humidity groups have been sampled identically for all other variables, such as composition. To reiterate, this condition is not strictly obeyed for this dataset, as the historical low and high humidity batches were generally sampled using different methods (vide supra). Even so, this analysis allows us to identify possible serendipitous results and rank the difficulty of testing them in subsequent interventional experiments.