In article <p04330120b69d3c8cd6ea@[139.80.121.126]>,
Will Hopkins <[EMAIL PROTECTED]> wrote:
>At 4:17 PM -0600 30/1/01, Jay Warner wrote:
>>A technically correct conclusion is: The sample of 100 has a mu
>>different than 100. there is a 0.08 prob ability (or 0.02, or
>>0.008) that this statement is false.
>>Have I not said the same thing? As p gets small, we are more
>>confident that the null hypothesis is not valid.
>I haven't followed this thread closely, but I would like to state the
>only valid and useful interpretation of the p value that I know. If
>you observe a positive effect, then p/2 is the probability that the
>true value of the effect is negative. Equivalently, 1-p/2 is the
>probability that the true value is positive.
This is true in the translation parameter case if one has a
uniform prior. This is not always justifiable; one might
think that there is a reasonable possibility that the null
hypothesis is close to being correct. In that case, the
statement is wrong.
>The probability that the null hypothesis is true is exactly 0. The
>probability that it is false is exactly 1.
I know of no "real" situation in which the null hypothesis, as
stated in connection with the distribution of observations,
could be correct.
>Estimation is the name of the game. Hypothesis testing belongs in
>another century--the 20th. Unless, that is, you base hypotheses not
>on the null effect but on trivial effects...
This is an important problem, and can only be handled by
decision-theoretic methods. Are there any papers on this
in addition to mine in the First Purdue Symposium (1971)?
There is a general result here, but it is not what one
usually expects. If the region where one should accept
the null is small compared to the precision of the
usual estimator, one can treat this as a point null,
but should not fix a p value, but rather let the p value
be determined by the loss and LOCAL prior. See my paper
with Sethuraman in 1965 for the large sample treatment
of this.
If the region is much larger than the usual confidence
interval, just see if the usual estimate is in the region.
In between, detailed consideration of the prior assumptions
make a difference.
>Will
--
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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