According to Fisher, a hypothesis specifying a density function for X is falsi®ed (at the level of signi®cance a) if the realization of X is in the size-a region of lowest densities. However, non-linear transformations of X can map low-density into high-density regions. Apparently, then, falsi®cations can always be turned into corroborations (and vice versa) by looking at suitable transformatio...