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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