dennis roberts wrote:
>
> At 12:14 PM 1/31/01 +1100, Alan McLean wrote:
>
> >For hypothesis testing there does have to be a null model - that is the
> >first feature that identifies hypothesis testing from other forms of
> >model selection.
>
> check
>
> >
> >A hypothesis test is only carried out if the sample data disagrees with
> >the null. If it is a point null (eg mu = 20) this is almost guaranteed.
> >The p value is essentially a measure of the level of disagreement
> >between the sample data and the null. If p is low, there is strong
> >agreement, if p is high there is weak disagreement.
> >
> >So I agree that your interpretation is reasonably correct.
>
> phew ... thanks (at least so far)
>
> >
> >BUT - the p value still does not say anything about the actual value -
> >only about the level of disagreement between what the null says it
> >should be and the sample says it should be.
>
> well, since there are a zillion different possible nulls ... then sure
>
> but, in a given context there are not a zillion nulls ... only 1 (i assume)
> ... like, mu = 90 ... or, rho = .7 ... or sigma squared = 256
>
> and since the null in a context is a constant ... but, the sample could be
> telling you varying things ... what we have is a difference value ...
> between a variable and a constant ... and while your argument seems to
> focus on the actual "difference" value ... it is not a floating difference
> at both ends ... only ONE end ... the sample end ... so, in fact, the
> difference value will lead you to that constant ... even if the variable
> (sample value) is moving ... which leads you right back to THAT null value
>
> so, if that is the case ... and while you might say that if the null had
> been mu = 90 and ... a given p is attached to that test ... that the p says
> nothing about THAT particular null ... would i be correct in saying that
> the p says something therefore about 91 ... or 87 ... or NO value?
>
> you might be technically correct ... and, if you want, i will concede that
> you are ... but, the practical distinction you are making escapes me ...
>
> if the p doesn't say something about the null you have posited ... i am
> wondering what the use of positing that null was in the first place and,
> then ... what help p is really bestowing upon you (whether it be p=.09 or
> .03 or .008?) with respect to that posited null
>
> i can't wait to try to make this distinction to my students ...
>
In any given test, there is only one null. Importantly, this is
determined by the research question. Further, for a given sample there
is only one sample statistic - not 'varying things'. Certainly the
particular sample result depends on which particular sample was taken,
but here we are talking about using the result of one particular sample
to test one particular null model.
Suppose the null is that mu = 90, the alternative is then that mu =/ 90.
You decide to take a sample and test this using the sample mean - to do
a t test. (You could choose a different test - but we are talking about
one test.) Suppose the sample mean is 85. Here is evidence that mu = 90
is not the best choice; on the basis of the sample, mu should be equal
to (about) 85.
Now - if we had taken the sample without this idea that mu should be 90,
we would simply estimate mu, on the basis of the sample result, as 85.
But since we do have the idea that mu should be 90, we have to decide
whether to go ahead on the idea that mu = 90 or mu = 85. Note that in
both cases this is a *model* - we do not particularly believe that mu is
exactly equal to either. (The comment that the null is always false is
meaningless. The null does not say what *is*, but what we will take 'it'
to be.) The difference here is that if we cannot pick between the two
choices, we will plump for the null - in this case, mu = 90. This is for
nonstatistical reasons - simplicity, fairness, innate conservatism,
.....
So the 'value' that you originally referred to was (as I understood it)
the value of mu - either 90 or 85. The test, incidentally, does not say
anything about any other choices. My statement was that the p value does
not say anything about what this value is, in the sense of what the
choices are. What it does do is to help us, given the two choices, to
decide between the two choices: if p is low we will select 85; if p is
high we will select 85.
If you want to interpret this final sentence as saying something about
the value - and in a sense it does - then we agree.
Alan
--
Alan McLean ([EMAIL PROTECTED])
Department of Econometrics and Business Statistics
Monash University, Caulfield Campus, Melbourne
Tel: +61 03 9903 2102 Fax: +61 03 9903 2007
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