I am performing differential analysis for two conditions (two replicates each), and found that my results is not significant at all (FDR) while some of the p values are very small. However, with other omics data, I confirmed that there should be some significant differentiation. I am trying the find the degree of freedom of edgeR limma so that I can understand why I have this kind of not significant results, and to see if I need to customize it, but cannot find a clear explanation. May I have your suggestions? Thank you very much.
The degrees of freedom are not an option that you can choose as will. It is determined by your sample size and the number of covariates in your design, so it's not an option you can toggle to magically gain power in your analysis.
That having said, n=2 per condition so a total of four samples is not a powerful analysis. Depending on the magnitude of the effect and the levels of noise it is quite plausible that you obtain no DEGs. The typical diagnosis is a PCA or MDS plot to see whether there is maybe some unwanted variation (e.g. batch effects) that keep you from observing significant DEGs. Keep in mind that absence of DEGs does not mean no effect, it only means no statistically significant effect, which can be due to mentioned low sample size and/or lots of noise.
