P and q values in RNA Seq

The q-value is an adjusted p-value, taking in to account the false discovery rate (FDR). Applying a FDR becomes necessary when we're measuring thousands of variables (e.g. gene expression levels) from a small sample set (e.g. a couple of individuals). A p-value of 0.05 implies that we are willing to accept that 5% of all tests will be false positives. An FDR-adjusted p-value (aka a q-value) of 0.05 implies that we are willing to accept that 5% of the tests found to be statistically significant (e.g. by p-value) will be false positives. Such an adjustment is necessary when we're making multiple tests on the same sample. See, for example, http://www.totallab.com/products/samespots/support/faq/pq-values.aspx. -HomeBrew

What are p-values? The object of differential 2D expression analysis is to find those spots which show expression difference between groups, thereby signifying that they may be involved in some biological process of interest to the researcher. Due to chance, there will always be some difference in expression between groups. However, it is the size of this difference in comparison to the variance (i.e. the range over which expression values fall) that will tell us if this expression difference is significant or not. Thus, if the difference is large but the variance is also large, then the difference may not be significant. On the other hand, a small difference coupled with a very small variance could be significant. We use the one way Anova test (equivalent t-test for two groups) to formalise this calculation. The tests return a p-value that takes into account the mean difference and the variance and also the sample size. The p-value is a measure of how likely you are to get this spot data if no real difference existed. Therefore, a small p-value indicates that there is a small chance of getting this data if no real difference existed and therefore you decide that the difference in group expression data is significant. By small we usually mean 0.05.

Reference:

http://www.science.smith.edu/cmbs/wp-content/uploads/sites/36/2015/09/P-and-q-values-in-RNA-Seq.pdf