# [R] Comparison of correlation coefficients

Date: Tue 13 Jul 2004 - 22:06:25 EST

Dear expeRts

Is it possible to compare correlation coefficients or to normalize different correlation coefficients?

Concretely, we have the following situation: We have gene expression profiles for different tissues, where the number of samples per tissue are different, ranging from 10 to 250. We are able to determine the correlation between two genes A and B for each tissue separately, using "cor.test". However, the question arises if the correlation coefficients between different tissues can be compared or if they must somehow be "normalized", since the number of samples per tissue varyies.

Searching the web I found the function "compcorr", see: http://www.fon.hum.uva.nl/Service/Statistics/Two_Correlations.html http://ftp.sas.com/techsup/download/stat/compcorr.html and implemented it in R:

compcorr <- function(n1, r1, n2, r2){
# compare two correlation coefficients
# return difference and p-value as list(diff, pval)

# Fisher Z-transform

```	zf1 <- 0.5*log((1 + r1)/(1 - r1))
zf2 <- 0.5*log((1 + r2)/(1 - r2))

#	difference

dz <- (zf1 - zf2)/sqrt(1/(n1 - 3) + (1/(n2 - 3)))

#	p-value

pv <- 2*(1 - pnorm(abs(dz)))

return(list(diff=dz, pval=pv))
```

}

Would it make sense to use the resultant p-value to "normalize" the correlation coefficients, using: corr <- corr * compcorr()\$pval

Is there a better way or an alternative to "normalize" the correlation coefficients obtained for different tissues?

Since in the company I am not subscribed to r-help, could you please reply to me (in addition to r-help)

Best regards
Christian Stratowa

Christian Stratowa, PhD
Boehringer Ingelheim Austria
Dept NCE Lead Discovery - Bioinformatics Dr. Boehringergasse 5-11
A-1121 Vienna, Austria
Tel.: ++43-1-80105-2470
Fax: ++43-1-80105-2782
email: christian.stratowa@vie.boehringer-ingelheim.com

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