I'm trying to compare two groups of ranked lists (of genes) by test of proportion. As shown in the mosaic plot and the data, there is a gene of interest which divides each list into genes ranked above it and below it. I wish to see if there is significant difference in ranking of our gene of interest among the groups (S,N,L and K) which are comprised of two replicates, S1&S2, N1&N2 etc.

enter image description here

Sample  Above   Below
S2  34  809
S1  141 856

N2  62  715
N1  28  864

L2  30  543
L1  33  605

K2  1   542
K1  1   618

For comparison of two single lists I can do a Chi-square test as follows,and get the p-value:

L2_L1.mat <- matrix(c(30,543,33,605),nrow=2,byrow=2)

Pearson's Chi-squared test

data:  L2_L1.mat
X-squared = 0.0024441, df = 1, p-value = 0.9606

N2_L1.mat <- matrix(c(62,715,33,605),nrow=2,byrow=2)

Pearson's Chi-squared test

data:  N2_L1.mat
X-squared = 4.4074, df = 1, p-value = 0.03578

But How to compare two groups like L(L1,L2) and N(N1,N2)


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