Pardon my interference, but I think there's some confusion regarding the
events here.
When I toss the first round of coins, I get about 1/2 of them heads. No
problema.
Then, when I toss the second time, 1/2 of *those ones that fell heads* (1/4
of the total, .5*.5)
have a chance to be heads again.
and also, about .5 of those that fell tails before have a chance to fall
heads too (1/4 of the total more).
so, we now have the union of two intersections, 1/4 +1/4....
Am I on the right track here?
----- Original Message -----
From: Bill Jefferys <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Sunday, October 22, 2000 12:19 PM
Subject: Re: .05 level of significance
> In article <[EMAIL PROTECTED]>,
> [EMAIL PROTECTED] (Donald Burrill) wrote:
>
> #On Sat, 21 Oct 2000, Bill Jefferys wrote:
>
> #> However, the combined experiment is 400 heads on 800 trials,
> #
> #This however is not the _intersection_ of the two specified events.
>
> Sure it is. It's the event I get by first getting 220 heads on 400
> trials AND THEN tossing 180 heads on 400 trials. If I toss one head
> (p=1/2) and then toss 1 tail (p=1/2) then the probability that I toss
> one head and then toss 1 tail is (1/2*1/2=1/4). That is a correct use of
> probability, and the intersection of the event of first tossing one head
> and the event of second tossing 1 tail is indeed the event of tossing
> one head followed by one tail.
>
> Similarly, the probability of first tossing 220 heads on 400 trials is
> given by the binomial distribution 0.5^400*C^400_220. And the
> probability of next tossing 180 heads on 400 trials is also given by the
> binomial distribution 0.5^400C^400_180. The probability that I
> accomplish both events in that order is the product of these two, is it
> not? So how can you say that these are not independent events, and how
> can you say that the intersection of the two is not as I say?
>
> It's true that the probability of tossing 400 heads on 800 trials in any
> order is not this product, but that is irrelevant.
>
> Do you claim that there is any situation where it is correct to multiply
> p-values?
>
> #> for which the two-tailed p-value is 1.0, not 0.05^2.
> #
> #> Contrary to popular belief, observed p-values are not probabilities.
> #> They cannot be probabilities because they do not obey the rules of the
> #> probability calculus, as the example shows. They are, well, p-values.
> #
> #Sorry; the example does not show that. It shows only that if one uses
> #"combined" (in the phrase "combined event", or equivalent) to mean
> #something other than "intersection", the rules governing the behavior of
> #intersections may not apply to the behavior of combined events.
>
> Show me that it is in general correct to combine p-values by
> multiplication and I might agree with you.
>
> Best wishes, Bill
>
> --
> Bill Jefferys/Department of Astronomy/University of Texas/Austin, TX 78712
> Email: replace 'warthog' with 'clyde' | Homepage: quasar.as.utexas.edu
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