Probably So and Probably Not

Lumo has an odd posting on confidence testing. He makes much of the fact that if you multiply a bunch of probabilities close to 1 (say 0.95) times each other you can get a number that's close to zero. This may not be a big shock to those who remember how to multiply. His purported point (I suppose) is that if you have some proposition the truth of which depends on the truth of n independent proposititons each of which is known with probability p, then the we presumably have confidence p^n in the composite proposition.

The question, of course, is who is supposed to have reached such a composite conclusion?

The Lumonator includes a link to a supposed offender but I searched the linked post in vain for any hint that that was the case. My guess is that LM is blowing smoke, as is his wont.

The actual case in climate science is more nearly the opposite of the situation he seems to be implying. There are multiple lines of nearly independent evidence each of which points to anthropogenic global warming. If we could apply Lumo style reasoning to these (and I'm not suggesting that we can) it would work oppositely to Mr. Motl's case. The no AGW null hypotheses, each rejected at the 95% level, would all need to be true for AGW to be rejected, and that involves multiplying a lot of 0.05s together. More to the point is the fact that his implication is backed by no examples of the reasoning he criticizes whatsoever.

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