Yes, it's worth reading too, because Guil provides a wonderful description of
independence between coin flips (I just happen to have a copy of the play next
amongst my stats book). Here is Guil, after getting 89 heads in a row (losing
every one to Ros, who is betting on heads each time), searching for
explanations for the 89 heads in a row (from Act I):
GUIL: <snip> List of possible explanations. One: I am willing it. Inside where
nothing shows, I am the essence of a man spinning double-headed coins, and
betting against himself in private atonement for an unremembered past (He spins
a coin at Ros)
ROS: Heads.
GUIL: Two: time has stopped dead, and the single experience of one coin being
spun once has been repeated 90 times .. (flips another coin, looks at it,
tosses it to Ros). On the whole, doubtful. Three: divine intervention, that is
to say, a good turn from above concerning him, cf. Lot's wife. Four: a
spectacular vindication of the principle that each individual coin spun
individually (he spins one) is as likely to come down heads as tails and
therefore should cause no surprise each individual time it does (It does. He
tosses it to Ros).
Paul Bernhardt wrote:
> tangentially related, for those of us teaching stats, last evening I
> enjoyed Rosencrantz and Guildenstern Are Dead (live stage presentation at
> U of Utah). It starts with the main characters flipping coins and
> noticing they come up heads time after time after time... about the 5th
> head in a row, the audience begins to titter acknowleging it is out of
> line with expectation. I think the movie version starts similarly and may
> serve as a nice introduction to hypothesis testing.
>
> Paul
>
> Bob Parks wrote on 3/30/00 7:44 AM:
>
> >Consider the following problem (which has a real world
> >problem behind it)
> >
> >You have 100 coins, each of which has a different
> >probability of heads (assume that you know that
> >probability or worse can estimate it).
> >
> >Each coin is labeled. You ask one person (or machine
> >if you will) to flip each coin a different number of times,
> >and you record the number of heads.
> >
> >Assume that the (known/estimated) probability of heads
> >is between .01 and .20, and the number of flips for
> >each coin is between 4 and 40.
> >
> >The question is how to test that the person/machine
> >doing the flipping is flipping 'randomly/fairly'. That is,
> >the person/machine might not flip 'randomly/fairly/...'
> >and you want to test that hypothesis.
> >
> >One can easily state the null hypothesis as
> >
> > p_hat_i = p_know_i for i=1 to 100
> >
> >where p_hat_i is the observed # heads / # flips for each i.
> >
> >Since each coin has a different probability of heads,
> >you can not directly aggregate.
> >
> >Since the expected number of heads is low, asymptotics for
> >chi-squares will not apply (each coin has substantial
> >probability of obtaining 0 heads so empirically you obtain
> >lots of cells with 0,1,2 etc.).
> >
> >Given that, I have failed to come up with a statistic to test it.
> >
> >TIA for any pointers to help.
>
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--
---------------------------------------------------------------
John W. Kulig [EMAIL PROTECTED]
Department of Psychology http://oz.plymouth.edu
Plymouth State College tel: (603) 535-2468
Plymouth NH USA 03264 fax: (603) 535-2412
---------------------------------------------------------------
"The only rational way of educating is to be an example - if
one can't help it, a warning example." A. Einstein, 1934.
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THE POSTMASTER about these messages because the postmaster has no
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problem of inappropriate messages and information about how to
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