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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