Hi: Bonferroni can be used for any hypothesis test or confidence interval
where a statistic
is calculated. The idea behind it is that, if a statistic is being
calculated many times ( as in the case of say anova where multiple
differences between groups can be calculated ), then the critical value
used to do the hypothesis test or the confidence interval needs to be
adjusted because the percent of the time you'll reject when true increases
because you're looking at more than one statistic

For example, suppose you have 3 groups in an anova and you want to
construct CI's for
the differences of the means of the three groups. Then you can't use alpha
= 0.05 if you want to the interval to be 95 percent because the true mean
will lie outside that
interval more than 5% of the time when the null is true because you're
calculating three CI's.. So, Bonferroni doesn't change the p_value of the
test. It changes the critical value used to construct the CI or the
hypothesis  test so that the effective type I error is whatever you want it
to be. I hope that makes sense.












Mark




On Thu, Aug 30, 2012 at 1:16 AM, Joshua Wiley <jwiley.psych@gmail.com>wrote:

> On Wed, Aug 29, 2012 at 6:48 PM, R. Michael Weylandt
> <michael.weylandt@gmail.com> wrote:
> > On Wed, Aug 29, 2012 at 6:23 PM, Louise Cowpertwait
> > <louisecowpertwait@gmail.com> wrote:
> >> Please can someone advise me how I can adjust correlations using
> bonferroni's correction? I am doing manny correlation tests as part of an
> investigation of the validity/reliability of a psychometric measure.
> >> Help would be so appreciated!
> >> Cheers,
> >> Louise
> >>
> >
> > The observed correlation is an immutable property of the observed data
> > and the Bonferroni correction does not change it. Rather, it should be
> > applied to the p-values of the observed correlations, much as it would
> > be for any test. Those more statistically savy than I might jump in,
> > but I don't see why the p-values of, e.g., cor.test() would be
> > adjusted in a different way than those of t.test().
>
> I am happy to be corrected, but under specific situations, I can see
> an alternative correction method being appropriate.  For p variables,
> the p x p correlation matrix has p * (p - 1) / 2 unique correlations,
> however, once you know about some of the correlations, you actually
> have some information about the other correlations.
>
> Imagine the situation where p = 3 and cor(p1, p2) = .9, cor(p2, p3) =
> 0.  Is cor(p1, p3) free to be any possible correlation?  The answer of
> course is no.  I am not sure what the exact rule would be, but this
> would hold and increase for larger matrices.
>
> > Consider a similar case for a set of t-tests: you see some data and do
> > the tests based on the sample means. It doesn't make any sense to
> > "adjust the mean" of your data, rather you might wish to adjust your
> > _interpretation_ of calculated p-values to account for multiple
> > comparisons.
> >
> > Cheers,
> > Michael
> >
> >> ______________________________________________
> >> R-help@r-project.org mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-help
> >> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> >> and provide commented, minimal, self-contained, reproducible code.
> >
> > ______________________________________________
> > R-help@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
>
>
> --
> Joshua Wiley
> Ph.D. Student, Health Psychology
> Programmer Analyst II, Statistical Consulting Group
> University of California, Los Angeles
> https://joshuawiley.com/
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

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