Suppose you have a large but finite collection of tweets. You want to know whether talking about football tends to correlate with talking about basketball. You can generate a table for a few hundred users with x's of "NFL" mentions, and y's of "NBA" mentions for each user. Now consider the case where over half of them are (0,0). I actually have such tables for many word pairs: some graphs look like a messy y=mx, some look as if bounded by y=1/mx, some are one quadrant of a shotgun blast.
Q: is there any mathematically sound way of describing the statistics, the correlations, when so many values are (0,0)?
Intuitively speaking, I've run into two problems:
1) Using a simple linear correlation function in a spreadsheet, I seem to get similar correlation (r^2) values whether "I can tell" it's a shotgun or it's a y=1/x bounded system (i.e., exclusivity). I.d like a measure that distinguishes between exclusivity and no relation at all.
2) Sometimes I've generated graphs which look like y=1/x, and proves a case of exclusivity (such as sheep vs. goats) which I already believe to be true. Other times for very similar concepts, however, I see the same graph shape which implies exclusivity, a discrepancy that seems illogical (such as "football" vs. "NFL"), unless I've somehow discovered distinct populations that use different words to describe a similar interest. I'm wondering if what my intuitive response to these exclusivity graphs is ignoring hundreds of points squished at the origin : (1,1)'s.
I hope for a statistical operation that would take my gut feel out of this analysis. Thanks