The best single metric for a correlation matrix

Question

[ChIP-seeker]

Hi, I am working on human microbiome and host gene expression data from two disease conditions and I want to investigate the correlation between bacterial abundance and its host (human) gene expression.

For example, I have a correlation table similar to Fig.3A in this paper (below).

https://genomemedicine.biomedcentral.com/articles/10.1186/s13073-020-0710-2

Each cell of this heatmap represents a correlation between host gene expression and matched taxa abundance across samples (Spearman's/Pearson's rho).

I have two questions:

(1) What is the best metric (or score) summarizing all correlations in this matrix?

(2) How can I statistically compare two matrices (from different disease conditions) using this metric (score)?

Any suggestion? Thanks in advance!

Answer 1

[n,n]

I don't know if I am understanding correctly but it doesn't seem like you need to summarize the matrices. If you just want to see if two matrices are different in terms of the correlations in their cells between two groups, you can just treat the them as two different samples of observations and run a routine statistical test such as Wilcoxon test. Something like this in R:

wilcox.test(as.vector(matrix1), as.vector(matrix2))

[ChIP-seeker]

Thanks for your suggestion! One of my concern is that two data sets (disease conditions) have different patient sample numbers (say, n=100, n=300). Is it ok to compare two Spearman's Rho values from this setting?