Is there a way to adjust correlation based on sample size

Question

[beiki.h.m]

Hello, I'm trying to find consensus modules between 2 gene co-expression networks. But the sample size used to construct networks are different. Is there a way to adjust correlation based on sample size? Thanks in advance.

Hamid

Answer 1

[Michael]

If you use a correlation test to generate your co-expression network, the test statistics and thereby a p-value will depend on the degrees of freedom, and thereby be corrected for sample size, such that the same correlation of two larger vectors is more significant than that of a shorter one (resembling your intuition). You might then -in addition- want to correct the p-values for multiple testing.

See for example cor.test in R:

https://stat.ethz.ch/R-manual/R-devel/library/stats/html/cor.test.html

Example:

> x = c(1,1.1,1) ; y = c(1,1.5,1.2)
> cor.test (c(x),c(y))

    Pearson's product-moment correlation

data:  c(x) and c(y)
t = 2.3094, df = 1, p-value = 0.2601
alternative hypothesis: true correlation is not equal to 0
sample estimates:
      cor
0.9176629

> cor.test (c(x,x),c(y,y))

    Pearson's product-moment correlation

data:  c(x, x) and c(y, y)
t = 4.6188, df = 4, p-value = 0.00989
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.4156606 0.9911073
sample estimates:
      cor
0.9176629

[beiki.h.m]

Dear Michael

Thanks to your response. Actually I don't want to apply a threshold for correlations. I want to use WGCNA procedure to construct my networks. In short, it reach each correlation to a power of "k" to make them smaller and then apply clustering method to construct the network. So, because I have different networks and I want to compare them, I should adjust correlations in each network based on the sample size that used for its construction.

Thanks

[limo_Rachel]

have you solved the problem yet? I've been troubled by the same problem and looking forward to a solution.

[Thind amarinder]

@Michael Dondrup what if I have two correlational networks (from two experimental conditions) one of size 8 samples and one is of size 32 samples. How I can make these two compare with each other or how to readjust correlation or calculate p-adjust with respect to the different number of samples. I used psych tool to calculate Padjusted value, but it uses the t-test, is n't it biased for the small number of samples?