You can use a Fisher's test (fisher.test() in R) for the statistics.
Regarding "overlapping" data, it depends on what you mean. I would personally make a combined heatmap of the ChIP and RNAseq data (at least for the DE genes). You can use deepTools for this, though it'd be easiest if you used the develop branch from github, since the computeMatrixOperations command won't otherwise be available until the next release (ETA November 1). The general steps would be:
- Use bamCoverage to generate bigWig files (possibly input-normalized in the case of ChIPseq)
- Use computeMatrix on the ChIPseq bigWig files, likely with
reference-point and a reasonable setting for -b
- Use computeMatrix scale-regions on the RNAseq bigWig files, likely using the
--metagene option.
- Use
computeMatrixOperations cbind with the output of 2 and 3
- Make a heatmap with plotHeatmap.
This allows you to see the differences even in cases where there happened to not be a peak called.