In article <[EMAIL PROTECTED]>,
Robert J. MacG. Dawson <[EMAIL PROTECTED]> wrote:
>Bruce Weaver wrote:
>> Suppose you were conducting a test with someone who claimed to have ESP,
>> such that they were able to predict accurately which card would be turned
>> up next from a well-shuffled deck of cards. The null hypothesis, I think,
>> would be that the person does not have ESP. Is this null false?
> Technically, the null hypothesis is that
> P(card is predicted correctly) = 1/52
> - it is a statement about parameter values. Thus, any bias, no matter
>how slight, affecting this, would make Ho false - whether the subject
>had ESP or no.
> For instance, if the shuffling method tended to make a card slightly
>less likely to come up twice in a row than one would expect, *even by a
>few parts in a million*, and if the subject avoided such guesses, then
>Ho would indeed be false.
> -Robert Dawson
This indicates a problem almost completely ignored by those
using statistics; the hypothesis tested is almost never the
hypothesis claimed to be tested. One cannot actually produce
a random sample with a given probability distribution; at
best, one can come close.
How much does this matter? The indications from my paper
in the First Purdue Symposium are that if the effects are
small compared to the standard deviation of the usual
estimators, it does not make much difference; I believe
that this is true in more generality than the question
studied there. In the ESP problem above, detecting even
a few parts in a thousand would require on the order of
a million observations, so one can "get away" with it.
But this is not the case with fixing a p value. Most
testing problems have the property that the appropriate
procedure to be used corresponds to a p value for that
problem AND THAT SAMPLE SIZE, but the p value to be used
depends quite substantially on the sample size.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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