When logical fallacies of statistics go uncorrected, they are repeated again and again…and again. And so it is with the limb-sawing fallacy I first posted in one of my “Overheard at the Comedy Hour” posts.* It now resides as a comic criticism of significance tests in a paper by Szucs and Ioannidis (posted this week), Here’s their version:

“[P]aradoxically, when we achieve our goal and successfully reject

Hwe will actually be left in complete existential vacuum because during the rejection of_{0 }HNHST ‘_{0 }saws off its own limb’ (Jaynes, 2003; p. 524): If we manage to rejectHthen it follows that pr(data or more extreme data|_{0}H) is useless because_{0}His not true” (p.15)._{0}

Here’s Jaynes (p. 524):

“Suppose we decide that the effect exists; that is, we reject [null hypothesis]

H. Surely, we must also reject probabilities conditional on_{0}H, but then what was the logical justification for the decision? Orthodox logic saws off its own limb.’ “_{0}

*Ha! Ha!* By this reasoning, no hypothetical testing or falsification could ever occur. As soon as *H* is falsified, the grounds for falsifying disappear! If *H*: all swans are white, then if I see a black swan, *H* is falsified. But according to this criticism, we can no longer assume the deduced prediction from *H*! What? Continue reading