[R] Bonferroni correction for multiple correlation tests

[Joshua Wiley]

On Wed, Aug 29, 2012 at 6:48 PM, R. Michael Weylandt
<michael.weylandt at gmail.com> wrote:
> On Wed, Aug 29, 2012 at 6:23 PM, Louise Cowpertwait
> <louisecowpertwait at 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 at 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 at 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/