how to build the contingency table

[frymor]

Hi all,

I have two lists of genes as follows:

• DEList has 282 gene names
• AllList has 32805 gene names
• DEList is a subset of AllList.

In both lists I've looked for genes which have a specific parameter (e.g. binding site for pol3 and binding site for pol2). The results of this search is in the table below.

• pol3DE 4
• pol2DE 190
• pol3all 85
• pol2all 12365

pol3DE and pol2DE are both subsets of the list DEList with the specific parameter binding site for pol3 and binding site for pol2 respectively. pol3all and pol2all are both subsets of the list AllList with the same specific parameters as above.

I would like to calculate the p-value to see if a higher proportion of pol2-specific genes are in the DEList than the AllList, and likewise for the pol3-specific genes in DEList relative to AllList.

If I understand it correctly I have six different parameters:

• AllList - 32805
• DEList - 282
• pol3DE - 4
• pol2DE - 190
• pol3all - 85
• pol2all - 12365

How do I create the contingency table for the Fisher's exact test in this case?
I have tried and created this one (s. attachment)?

Can I even use the Fisher's exact test for that, or do I need to use a different one (Xi square, equality of proportion)?

It doesn't look like it, as I don't have the sum of DEList in nowhere in the table. But does it has to be?

What I would like to know is not the significance of each group on its own, but whether or not the proportion of of pol2 in the comparison DEList relative to AllList is higher than the proportion of pol3 for the same comparison.
So Just making two McNemar tests wouldn't really solve the problem, unless I can compare the two p-values.
I have run the two tests and both p-values are very low, i.e. supposedly significant, but what about against each other. Is there a way to compare this?

pol3 = as.table(rbind(c(32720, 0), 
                     c( 81, 4) ))
colnames(pol3) <- rownames(pol3) <- c("No", "Yes")
names(dimnames(pol3)) = c("all", "DE")
pol3
mcnemar.test(pol3, correct=FALSE)

	McNemar's Chi-squared test

data:  pol3
McNemar's chi-squared = 81, df = 1, p-value < 2.2e-16

pol2 = as.table(rbind(c(32720, 0), 
                     c( 81, 4) ))
colnames(pol2) <- rownames(pol2) <- c("No", "Yes")
names(dimnames(pol2)) = c("all", "DE")
pol2
mcnemar.test(pol2, correct=FALSE)

	McNemar's Chi-squared test

data:  pol2
McNemar's chi-squared = 81, df = 1, p-value < 2.2e-16

Thanks

Assa

PS.
I have asked this question also in a different forum, but I still have difficulties to understand this topic.

[sphil]

Hi,

AFAIK fishers exact test tries to answer for independence between the two variables. First, I don't think this is what you want to test for (am I right?). Second, i think your groups are not independent from each other, are they? As shown here you can also think of using Mann-Whitney or KS test as they (Broad Institute) do in their GSEA analysis tool.

HTH

[dpryan]

I like the suggestion of McNemar's test in your post on cross-validated. That nicely captures how I would personally think about this (assuming you don't want a rank-based approach as pointed out by sphil).

[frymor]

I like the suggestion of McNemar's test in your post on cross-validated. That nicely captures how I would personally think about this (assuming you don't want a rank-based approach as pointed out by sphil).

No I don't need the ranking, as I have only two groups and I would like to show that there is (sort of) a shift in the transcription from the pol3- transcribed genes to the pol2-transcription.
But What I do need, and I can't seem to figure out how to get with the McNemar's test is the comparison between the two results.

As mentioned, I have done the test for pol3 and pol2 and both are significant by themselves.
Is there a way to say if the proportion of pol2 in the comparison is higher than the proportion of pol3 in its own comparison?
(I was thinking about something like a testing for equality of proportion for the results from the McNemar's test - But does something like that even exists?)