I have two (or more) micro array data of genes of SARS (http://www.ncbi.nlm.nih.gov/geo/geo2r/?acc=GSE1739) and Parkinson disease (http://www.ncbi.nlm.nih.gov/geo/geo2r/?acc=GSE7621). I found the dysregulated genes in these sets by applying criteria log fold change is greater than 1.5 and p-vlaue < 0.01. My question is how to find the common dysregulated genes in these two sets? Which statistical tests should be applied? Which packages are available in R for this kind analysis? I am new to bioinformatics. Kindly bear with me if question is very basic. Thanks in advance.
You could make a contingency table and use a Fisher Exact test, or you could use the hypergeometric distribution (see ?phyper in R). Given a universe of genes in two experiments, if you identify a set of genes in experiment 1, and another set of genes in experiment 2, these can help you evaluate the likelihood of a given degree of overlap. As b.nota mentioned, I usually make a Venn diagram and then evaluate it with either of those tests. There's a package in R which does this for you, called GeneOverlap.
For each gene, you can use the maximum of the two p-values from the SARS and Parkinson datasets to test whether the gene is dysregulated in both diseases.
In other words, a gene is a common significant gene if it is significant in both diseases. It is as simple as that.
However, the method you have used to assess significance in each individual dataset does not seem the best. It would be better to apply an analysis method that controls the false discovery rate across the whole genome.