I think the issue is whether P(detected|positive) and P(detected|negative) are the same, right? It's whether they have equal coverage of all possible phrases.

I think the issue is whether P(detected|positive) and P(detected|negative) are the same, right? It's whether they have equal coverage of all possible phrases. Having more positive or negative words, as you say, doesn't inherently bias things. Is your hypothesis that your corpus doesn't skew negative, which seems to be the basis of this question, correct? Can you do some manual sampling to get a good bound on it?