I have 2 lists of genes that I wish to compare in terms of
1) overlap between the genes themselves
2) overlap between the their respective pathways after ORA using innateDB
Gene list A consists of approximately 500 differentially expressed genes (DEGs) from a microarray analysis with over 17000 probes and Gene list B is a list of 200 susceptibility genes drawn from various GWAS. I have converted all genes in both lists to their Ensembl ID so that I can compare like-with-like.
Firstly, to find the overlap between the genes themselves, I have then used Venny to identify that 75% of the GWAS genes are represented in the microarray platform. Venny has also showed me that 15 genes overlap between the DEG and GWAS gene lists but I understand that I also need to perform a statistical test to ensure that this overlap is not just due to chance. However, I am unsure of what test I should perform and what program I should use.
Unfortunately, I only have slight experience with MINITAB and SPSS and no experience with R.
Secondly, I have done a pathway over-expression analysis using innateDB on both DEG and GWAS genes lists. The DEG list gave ~150 over-expressed pathways while the GWAS list gave ~100. Using the unique pathway identifier, I again compared the 2 pathway lists (1 from each gene list) and found that ~50 overlapped. Again a statistical test should be done but would this be the same test as the first instance?
Thank you for all your help!
Tl;dr: I have overlapped 2 gene lists and found that they overlap in terms of genes and pathways but do not know what statistical test should be used to give evidence that these results are not due to chance.