Dear R-Users,
This list is observed by many great statisticians and non-statisticians.

I just want to add this valuable link to this great discussion.

http://www.stat.duke.edu/~berger/p-values.html

<http://www.stat.duke.edu/~berger/p-values.html>Thanks and Best Regards,
S.

On Sat, May 8, 2010 at 11:11 PM, David Winsemius <dwinsemius@comcast.net>wrote:

>
> On May 8, 2010, at 9:38 PM, Duncan Murdoch wrote:
>
>  On 08/05/2010 9:14 PM, Joris Meys wrote:
>>
>>> On Sat, May 8, 2010 at 7:02 PM, Bak Kuss <bakkuss@gmail.com> wrote:
>>>
>>>
>>>  Just wondering.
>>>>
>>>> The smallest the p-value, the closer  to 'reality'  (the more accurate)
>>>> the model is supposed to (not) be (?).
>>>>
>>>> How realistic is it to be that (un-) real?
>>>>
>>>>
>>>>
>>> That's a common misconception. A p-value expresses no more than the
>>> chance
>>> of obtaining the dataset you observe, given that your null hypothesis
>>> _and
>>> your assumptions_ are true.
>>>
>>
>>
>> I'd say it expresses even less than that.  A p-value is simply a
>> transformation of the test statistic to a standard scale.  In the nicer
>> situations, if the null hypothesis is true, it'll have a uniform
>> distribution on [0,1].  If H0 is false but the truth lies in the direction
>> of the alternative hypothesis, the p-value should have a distribution that
>> usually gives smaller values.  So an unusually small value is a sign that H0
>> is false:  you don't see values like 1e-6 from a U(0,1) distribution very
>> often, but that could be a common outcome under the alternative hypothesis.
>>   (The not so nice situations make things a bit more complicated, because
>> the p-value might have a discrete distribution, or a distribution that tends
>> towards large values, or the U(0,1) null distribution might be a limiting
>> approximation.)
>> So to answer Bak, the answer is that yes, a well-designed statistic will
>> give p-values that tend to be smaller the further the true model gets from
>> the hypothesized one, i.e. smaller p-values are probably associated with
>> larger departures from the null.  But the p-value is not a good way to
>> estimate that distance.  Use a parameter estimate instead.
>>
>
> And. Thank you for this paper. As a non-statistician I found it most
> instructive:
>
> http://pubs.amstat.org/doi/pdfplus/10.1198/000313008X332421
>
> --
> David.
>
>
>> Duncan Murdoch
>>
>>
>>  Essentially, a p-value is as "real" as your
>>> assumptions. In that way I can understand what Robert wants to say. But
>>> with
>>> lare enough datasets, bootstrapping or permutation tests gives often
>>> about
>>> the same p-value as the asymptotic approximation. At that moment, the
>>> central limit theorem comes into play, which says that when the sample
>>> size
>>> is big enough, the mean is -close to- normally distributed. In those
>>> cases,
>>> the test statistic also follows the proposed distribution and your
>>> p-value
>>> is closer to "reality". Mind you, the "sample size" for a specific
>>> statistic
>>> is not always merely the number of observations, especially in more
>>> advanced
>>> methods. Plus, violations of other assumptions, like independence of the
>>> observations, changes the picture again.
>>>
>>> The point is : what is reality? As Duncan said, a small p-value indicates
>>> that your null hypothesis is not true. That's exactly what you look for,
>>> because that is the proof the relation in your dataset you're looking at,
>>> did not emerge merely by chance. You're not out to calculate the exact
>>> chance. Robert is right, reporting an exact p-value of 1.23 e-7 doesn't
>>> make
>>> sense at all. But the rejection of your null-hypothesis is as real as
>>> life.
>>>
>>> The trick is to test the correct null hypothesis, and that's were it most
>>> often goes wrong...
>>>
>>> Cheers
>>> Joris
>>>
>>>
>>>  bak
>>>>
>>>> p.s. I am no statistician
>>>>
>>>>      [[alternative HTML version deleted]]
>>>>
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>>>>
>>>>
>>>>
>>>
>>>
>>>
>>>
>> ______________________________________________
>> R-help@r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> David Winsemius, MD
> West Hartford, CT
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

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