On Sat, 21 Oct 2000, Bill Jefferys wrote:
> At 12:56 PM -0500 10/20/00, dennis roberts wrote:
> >randomly independent events have the p value being the multiplication of
> >each event's p value ... so ... p for getting a head in a good coin ....
> >is .5 ... 2 in a row = .25 ... etc.
>
> This is wrong. In general you cannot multiply the p-values from
> independent events to obtain the p-value of the combined event.
Surely this depends on how you define "the combined event". If "the
combined event" is the intersection of two independent events, the
probabilities do in general multiply, as Dennis asserts. If some other
definition is used (as in Bill's example below), then of course one
cannot expect the multiplication rule to hold.
> Example: You toss 220 heads on 400 trials of a fair coin. The
> two-tailed p-value for this event is almost exactly 0.05 [J.O. Berger
> and M. Delampady, Statistical Science 2, 317-352 (1987)].
I.e., the probability of observing 200 heads or more, or 180 heads or
fewer, in 400 trials is 0.05.
> Suppose you then independently toss 180 heads on an additional 400
> trials. Again, the two-tailed p-value is 0.05.
Again, the probability of observing 180 heads or fewer, or 220 heads or
more, in 400 trials is 0.05. OK so far...
> However, the combined experiment is 400 heads on 800 trials,
This however is not the _intersection_ of the two specified events.
> 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.
The antecedent proposition therefore does not follow.
-- DFB.
----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 (603) 535-2597
Department of Mathematics, Boston University [EMAIL PROTECTED]
111 Cummington Street, room 261, Boston, MA 02215 (617) 353-5288
184 Nashua Road, Bedford, NH 03110 (603) 471-7128
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
