I am somewhat surprised by my GO enrichment analysis resuts. Is it possible that using gene sets with lower p-value threshold for differential gene expression, gives me more GO terms than using higher p-value threshold? I would expect that as I make the criterion for differential gene expression more stringent, the number of enriched/underepresented terms would go down and certainly no new terms pop up.
If I understand it correctly, you obtain more enriched GO terms with a smaller (more conservative) set of differentially expressed genes. You were expecting to obtain less enriched GO terms therefrom, right?
In my opinion, what you are seeing is perfectly possible. GO has a DAG structure, and most GO enrichment analysis tools take this DAG into account. You might well be obtaining more specific terms now, for instance. Have a look at the depth of your enriched terms.
If, at the end, what you want to achieve is a reduction of the number of terms, why don't you just go more conservative in the GO enrichment analysis?
It is a bit unclear what you mean above. If you're asking wether a different geneset with lower p-value could produce more GO terms, then that is just fine. If you mean that the same geneset produces more GO terms at a lower p-value cutoff then it is most likely that the cutoff parameter is doing something else than just applying the cutoff.