Statistics for correlations with many (0,0) values 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.  Say, 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/x.
Q: is there any mathematically sound way of describing the statistics, the correlations, when so many values are (0,0)?
 A: Since so many of your values are $(0,0)$, there probably isn't much harm (and maybe some benefit, since some people repeat terms more than others) in just asking for each tweet, "Did they mention NFL?" and "Did they mention NBA?". There are 4 possible combinations of yes/no for these questions. You want to know if the answers to the questions are independent or positively correlated. For that you can consider contingency tables (you can look it up online if you're unfamiliar, wikipedia is good) and then use at least 3 different methods to get a p-value of how unlikely the positive correlation of mentions is by chance: 1) Fischer's exact test 2) Chi-squared approximation 3) (My favorite for your situation) Assume the "yes/yes" count is Poisson with rate given by the product of observed rates of the individual "yes" for each question (i.e., assume independence), and then compute the Poisson p-value for the probability that the "yes/yes" is greater than or equal to the observed value, using the Poisson distribution directly. This is especially a fast and easy and very (VERY) good approximation if the probability of each mention's individual "yes" is very low.
