[R] RE: Comparison of correlation coefficients - Details

idimakos@upatras.gr idimakos at upatras.gr
Wed Jul 21 18:07:12 CEST 2004

That sounds very close to a meta-analytic comparison of two statistics. 
As a matter of fact, the Rosenthal & Rubin approach transforms all primary
statistics into Pearson r and then to Fisher's z and then follows with
comparisons.  More, comparisons can take into account sample sizes, or the
value of some other predictor variable.

I believe there is a Rosenthal book on meta-analysis published by Sage
publications, as well as a Brian Mullen book published by Lawrence
Brian Mullen's book comes (or used to come) with a meta.exe program to
perform meta-analyses.

Hope this helps,


> Dear all
> I apologize for cross-posting, but first it is accepted custom to
> thank the repliers and give a summary, and second I have still
> the feeling that this problem might be a general statistical problem
> and not necessarily related to microarrays only, but I might be wrong.
> First, I want to thank Robert Gentleman, Mark Kimpel and Mark Reiners
> for their kind replies. Robert Gentleman kindly pointed me to the
> Bioconductor package "MeasurementError.cor" as alternative to "cor.test".
> Mark Kimpel suggested that 2-way factorial Anova or the Bioconductor
> package "limma", respectively, may be helpful. Mark Reiners suggested
> to use the p-value of "cor.test" to test the significance.
> Maybe, I miss the point, but being not a statistician I am still unsure
> if it is possible to compare correlation coefficients from different
> sample sets. Both, the p-values from "cor.test" and from "compcorr",
> could be used as measure of the significance.
> However, is it possible to "normalize" correlation coefficients from
> different sample sets? Could an expression such as "corr * (1 - pval)"
> be used for normalization? Maybe, it is not possible to normalize
> correlation coefficients?
> Would a barplot comparing the correlation coefficients between two
> genes for different tissues be meaningful? (Alternatively, I have
> tried to use (1-pval) to calculate the gray-level of the bars.)
> Any further suggestions would be appreciated very much.
> Best regards
> Christian Stratowa
> -----Original Message-----
> From: Stratowa,Dr.,Christian FEX BIG-AT-V
> Sent: Monday, July 19, 2004 15:00
> To: 'bioconductor at stat.math.ethz.ch'
> Subject: Comparison of correlation coefficients - Details
> Dear all
> Maybe, my last mail did not explain my problem correctly:
> Since we are interested, which genes have similar expression profiles in a
> certain tissue or in different tissues, we have calculated the
> correlation coefficients between all 46,000 x 46,000 genes of the
> HG_U133A/B chipset for about 70 tissues, where the number of samples
> per tissue ranges from 10 to more than 200.
> While writing an R-function to display the correlation coefficients
> between
> gene A and B in the different tissues as bar-graph, I realized that it may
> not be correct to compare the different correlation coefficients directly,
> since the number of samples per tissue varyies between 10 and 200.
> Thus, the question is: Is there a way to compare different correlation
> coefficients and/or apply some kind of normalization?
> Assuming that this might be a well known statistical problem I was
> browsing
> statistics books and the web for more information, but could only find the
> function "compcorr" which gives a p-value how well you can trust the
> comparison of two correlation coefficients from different samples.
> Even though this might currently not be a direct Bioconductor question, it
> is certainly a microarray analysis related question. Any suggestions how
> to
> solve this problem would be greatly appreciated.
> Best regards
> Christian Stratowa
> -----Original Message-----
> From: Stratowa,Dr.,Christian FEX BIG-AT-V
> Sent: Tuesday, July 13, 2004 14:40
> To: 'bioconductor at stat.math.ethz.ch'
> Subject: Comparison of correlation coefficients
> Dear Bioconductor 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?
> Thank you in advance for your help.
> Since in the company I am not subscribed to bioconductor-help, could you
> please reply to me (in addition to bioconductor-help)
> P.S.: I have posted this first at r-help and it was suggested to me to
> post it here, too.
> 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 at vie.boehringer-ingelheim.com
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