Hi Mike,
An hypothesis test is only done when the sample evidence disagrees with
the null hypothesis - for example, the sample mean is different from the
mean postulated by the null. So to all intents and purposes, there is
always evidence against the null. (Another way to express this - if we
were only working from the sample, so we do not have this idea that the
null 'should' be true', we would accept the evidence of the sample, in
that we would estimate the mean based on the sample mean.)
What a p value does is provide a measure of the strength of the (sample)
evidence against the null - it is not itself that evidence!
The interpretation of numerical values of p is largely a matter of
common agreement. A p-value between say .2 and .999999999 is commonly
thought to indicate that the evidence is so weak that there is no
question of rejecting the null. (Note that to say that it indicates
there is NO evidence, as some authors do, is simply wrong.) Between .1
and .2, the evidence is pretty weak, and mostly people would not reject
the null. And so on.
The real rider in all of this is that this all depends on the overall
model (in effect, the test) used is reasonably appropriate! This is
decided on evidence - from common experience, including research, from
analysing the sample data; and to a varying degree, from hope and
wishful thinking!
Regards,
Alan
Mike Granaas wrote:
>
> On Mon, 29 Jan 2001, dennis roberts wrote:
>
> >
> > one of the summary points made is the following:
> >
> > "P values, or significance levels, measure the strength of the evidence
> > against the null hypothesis; the smaller the P value, the stronger the
> > evidence against the null hypothesis"
>
> I would add that the authors also discuss p-values between .1 and .9 as
> providing weak evidence against the null. And at this level I am not at
> all comfortable with the notion of a p-value as evidence against the null.
> If anything large p-values should indicate that the data is quite likely
> if the null is true.
>
> It is only when the p-values become small that we are confronted with the
> possibility of a) bad data or b) bad null. Even then we have to hedge our
> bets since high power can give us small p-values with small effect sizes.
>
> Michael
> >
> > my main questions of this are:
> >
> > 1. does the general statistical community accept this as being correct?
> >
> > 2. if the answer to #1 is yes ...
> >
> > then what does this tell us (only this p value) about what the real
> > parameter value is? (are)
> >
> >
> > _________________________________________________________
> > dennis roberts, educational psychology, penn state university
> > 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
> > http://roberts.ed.psu.edu/users/droberts/drober~1.htm
> >
> >
> >
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> >
>
> *******************************************************************
> Michael M. Granaas
> Associate Professor [EMAIL PROTECTED]
> Department of Psychology
> University of South Dakota Phone: (605) 677-5295
> Vermillion, SD 57069 FAX: (605) 677-6604
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> All views expressed are those of the author and do not necessarily
> reflect those of the University of South Dakota, or the South
> Dakota Board of Regents.
>
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--
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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