Bonferroni correction for multiple correlation tests
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
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______________________________________________ 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/