In his paper "Ten ironic rules for non-statistical reviewers", Karl Friston includes the following tongue-in-cheek response of a fictional author to a reviewer who complains about the sample size being too low:
“We suspect the reviewer is one of those scientists who would reject our report of a talking dog because our sample size equals one!”
But in all seriousness, how would one formally make the distinction between sample-to-population inference - with its rules relating sample size, power etc - and single-case observations that undeniably prove a conceptual point? Talking dogs aside, this point could be, for instance, a brain lesion patient who nonetheless is still able to perform a cognitive function for which the lesioned brain area used to be thought necessary for. Surely in this case the sample size N=1 would not prevent a strong claim being made from this neuropsychological result?