Ron,
Of course they are very much related to each other. However, they answer
slightly different questions. The readers who know some statistics are
aware that the p value for no treatment effect is less than alpha iff
the confidence interval for the log of the odds ratio based on 1-alpha/2
cutoffs (for 2 -sided analysis) excludes zero. However, while the
100*(1-alpha) % confidence interval will tell the reader at a glance
whether or not the treatment is effective at p=alpha, it is not obvious
at a glance from the CI what the smallest p is at which the effect is
significant.
My guess is that the more statistically oriented reader is more often
interested in the smallest p (the significance level) and the applied
reader may be more interested in a CI at a pre-assigned confidence level
as a sort of worst case scenario but that is just a guess.
Regards,
Ellen Hertz
Ron Bloom wrote:
> I frequently see in the outputs quoted from biomedical,
> epidemiological statistical software, in analysis
> of the usual 2x2 tables e.g.
>
> Disease Well
> Risk Factor a b
> No Risk c d
>
> frequently *both* chi-squared test and test on log(odds)
> are quoted.
>
> Now both of these tests rest upon the same asymptotic
> substitutions of certain continuous distributions
> for the exact (discrete) sampling distributino of
> 2x2 table under such and such hypotheses.
>
> Moreoever, it would appear that the same table that
> gives a "significantly large" chi-square would
> give a significantly large log(odds). Of course
> one checks the tail-probability of the former in
> the "chi-squared 1-df" distribution, and of the
> latter in a gaussian with approximate variance
> 1/a+1/b+1/c+|1/d. But don't the results of
> the two tests more or less support the same
> decision? Why do canned software packages
> quote so many different statistics whose
> intrinsic tendencies towards "significance"
> or non-significance are obviously correlated
> with each other. Is it because folklore
> somehow plays a large part in what the
> "right test is" ?
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