It would be a good joke to conclude “If Pr(Data we didn’t see | Cause false) is small then Cause is true”, but it isn’t. People believe it. Peers review it. It is a bad idea that refuses to die. You cannot, you simply cannot, talk people out of it.
Video
Links: YouTube * Twitter – X * Rumble * Bitchute * Class Page * Jaynes Book * Uncertainty
HOMEWORK: Given below; see end of lecture.
Lecture
This and next week wrap up the majestic anti-P-value rant.
I have seen comments, here, and, yes, there, with attempts to justify P-values. This is natural. People do not want to give up on their magic tool. Yet give it up they must.
But what I haven’t seen, not anywhere, was anybody making any comment on this:
Pr(What we want to know | All evidence considered).
This is just ignored and the Wee P White Knights charge the field with their itty bitty poles (the weer the better) and offer any and all manner of arguments to save the mighty P.
The P-value, again, is this calculation:
P = Pr(What did not happen | Cause is false)
Or if you don’t like “Cause is false”, then write “null is true”. The “null” is that the cause you think was present, wasn’t.
There is no sound valid or sober logical argument that leads from “My P is wee, therefore ‘Cause is false’ is false”. Which is a long-winded way of saying “My P is wee, therefore Cause is true”. Replace that by ‘Cause is likely true’ or whatever, and it is still a fallacy.
Why, why, why—I’m asking why—do people think they can get at “What we want to know” from “What did not happen”? Why not just go right for “What we want to know”?
No, I’m asking.
I am lost for how to talk people out of P-values. I welcome all ideas.
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Throwaway comments made by people who are confused about this sort of thing, gave me a clue to one of the problems. It’s about authority. Their understanding of mathematics and statistics may be limited to being able to use a handbook called something like “Mathematical Methods for Scientists and Engineers”. If you question just one of the techniques in a textbook like that, they will wonder what else is wrong, which opens up an appalling vista.
As always, William, good stuff.
Say that I have a pair of dice. I suspect that they are loaded to make snake-eyes (1 & 1) come up more frequently so the player loses. I can make millions of throws of the dice and log the results.
What statistic would be best to use to analyze the results to determine if the dice are indeed loaded, and to estimate the solidity of that conclusion?
Best to you and yours,
w.
Willis,
The same one you used in setting up the problem. After “millions of throws” (where the manner of the throws, i.e. the conditions which bring about the effects due to the causes of the throws is left vague or tacit), you’d predict the future would look like the past, unless you had good reason to suppose the causes or conditions had changed.
You could make it all formal with math, but after millions of throws, why bother?
See also Class 30 and 31, which are highly relevant (and both badly named; maybe I’ll change).