I have 2 binary matrices, in which 1's represent "critical exons" and 0's represent "non-critical exons". Now I want to know how significant is the proportion of critical exons in first matrix than the second one.

The reason why I am confused is, I have many such pairwise comparisons to do, and they all are significant, if I simply plug in values. I have attached a graph of proportions of critical exons. On x axis, there are different clusters (each bar in a cluster represent different stages of development) and y represents the proportion of critical exons. I am using the proportion test to compare PN stage vs AD stage & EC stage vs AD stage.

I choose clusters 10 and 13 to show that everything is turning out to be

significant.

Here is the proportion test in R of critical exons in PN and AD matrix of cluster 13:

prop.test(x=c(613511,497881), n=c(162032852,162032852),conf.level=0.95, alternative = 'greater')

Here is the proportion test in R of critical exons in PN and AD matrix of cluster 10:

prop.test(x=c(2892315,1750840), n=c(162032852,162032852), conf.level=0.95, alternative = 'greater')

The p-val is < 2.2e-16 for both the cases. Since the numbers are large, do these p-values have any meaning? I tried fetching the exact p-value but it just returns a 0, maybe the p-val is too small to be calculated by the machine?

Hence, I divided all the numbers by 1000 to see if the p-values make any sense this way:

prop.test(x=c(613.511,497.881), n=c(162032.852,162032.852),conf.level=0.95, alternative = 'greater')

The p-val is 0.0002862 in this case.

prop.test(x=c(2892.315,1750.840), n=c(162032.852,162032.852), conf.level=0.95, alternative = 'greater')

The p-val is 4.561238e-64 in this case.

I was wondering if dividing these numbers is a valid thing to do in order to reduce the dimensionality of the dataset? Or should I somehow reduce the initial matrix itself before calculating the 1s and 0s? Is there a better way to test the proportions of large matrices?