[R] Correlation adjusted Bonferroni? (was: Multiple tests on repeated measurements)

[JRG]

On 2 Aug 2006 at 13:48, R Heberto Ghezzo, Dr wrote:

> HI, just my 2 cents. Bonferroni et al, assume independent tests, thus
> p ~ p*k with k the number of tests, in repeated measures, each measure
> is correlated with the previous, so k is not 2 but 2-q. I do not know
> q but it should be a function of the correlation between measures, ie
> the Sigma in gee. A long time ago, in my days as a student i remember,
> vagely, I saw a paper in Biometics on a correction to apply to Fisher
> method for pooling several tests to take into account the correlation
> between the variables. Heberto Ghezzo McGill University Montreal - Canada 
> 
> 

Most assuredly, the (usual) Bonferroni correction does not assume independent test statistics, as 
it is based on Bonferroni's Inequality which holds for absolutely any collection of valid tests.  
If the test statistics were independent 1-(1-p)^k would replace p*k.  But strong correlation among 
test statistics can certainly reduce the limit well below 1-(1-p)^k .

---JRG


John R. Gleason

Syracuse University
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