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 Erlbaum. Brian Mullen's book comes (or used to come) with a meta.exe program to perform meta-analyses. Hope this helps, Ioannis > 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: '[EMAIL PROTECTED]' > 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: '[EMAIL PROTECTED]' > 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: [EMAIL PROTECTED] > > ______________________________________________ > [EMAIL PROTECTED] mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html