dennis roberts wrote:
>
> this was not about a difference in rhos .. just the rho singly from that
> population ...
>
It can be framed similarly replace mu1-mu2 with rho
If the null hypothesis is H0:rho=0
and the alternative is H1:rho>0
What does the test say about rho if we reject H0 at level
alpha(say at the magical 0.05)? Not much on its own. However, what
if we plan a statistical experiment as follows:
^^^^
Given a desired power of 0.90 we would need a sample
of size 33 to detect a rho=.5 different from 0
at level alpha=0.05.
We run the experiment with a sample of size 33 and
we reject H0. Now what can we infer about
rho in terms of probabilities? Quite
a bit more than just running an experiment without
considering power.
If we do not reject H0 given this design
what does it say about rho? Not that rho=0,
but rho=0 is a more likely scenario than
rho=.5(or >.5)
> consider this to be two separate ONE sample studies ... with r values in
> each as given
>
> At 11:06 AM 4/11/00 -0400, you wrote:
> >If the null hypothesis is H0: mu1-mu2=0
> >and the alternative is H1: mu1-mu2>0
> >
> >What does the test say about mu1-mu2 if we reject H0 at level
> >alpha(say at the magical 0.05)? Not much on its own. However, what
> >if we plan a statistical experiment as follows:
> > ^^^^
> >Given a desired power of 0.90 we would need a sample
> >of size 10 to detect a difference between mu1 and mu2
> >of 1 unit or larger(different from 0) at level alpha=0.05.
> >
> >We run the experiment with a sample of size 10 and
> >we reject H0. Now what can we infer about the difference
> >between mu1 and mu2 in terms of probabilities? Quite
> >a bit more than just running an experiment without
> >considering power.
> >
> >If we do not reject H0 given this design
> >what does it say about mu1-mu2? Not that mu1-mu2=0,
> >but mu1-mu2=0 is a more likely scenario than
> >mu1-mu2=10(or >10)
> >
> >dennis roberts wrote:
> > >
> > > here are two sample r values ... done in minitab ... and the associated
> > output
> > >
> > > Correlations: C52, C53
> > >
> > > Pearson correlation of C52 and C53 = 0.599
> > > P-Value = 0.000
> > >
> > > MTB > corr c54 c55
> > >
> > > Correlations: C54, C55
> > >
> > > Pearson correlation of C54 and C55 = 0.586
> > > P-Value = 0.075
> > >
> > > now, minitab prints out a p value for the null hypothesis test of rho =0
> > > ... which for better or worse is fairly standard practice ...
> > >
> > > from the results of the 'significance' test (and nothing else) ... tell me
> > > what this says in terms of what the TRUE rho value might be?
> > >
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