# What is a noise-resistant method for testing correlations of proportions

I have a friend who is trying to analyse a large Sanskrit corpus with many verbs in. Verbs can occur in the active or the passive, and they can occur in the past tense or the present tense. She wants to run a statistical test to see whether verbs which occur more often in the active (than the passive) in the present tense also occur more often in the active in the past tense. Here is (made up) data to illustrate:

       Present-Active   Present-Passive  Past-Active   Past-Passive
run    102              50               130           79
seize  40               84               59            120
rebel  1                2                3             1


One method would be to compute %active stats for a) present tense and b) past tense and then look at the correlations between these two.

          Present %Active  Past %Active
run       67%              62%
seize     32%              33%
rebel     33%              75%


[Here for 'run' 102/(102+50) = 67%, and so on.]

This method is not ideal because some verbs are very rarely attested, like rebel above, and those will introduce a lot of noise into the system. Could anyone point us at a better method? I feel like we need some hybrid of correlation and a chi-squared test...

• Indeed, rebels are known for using verbs noisily. (Sorry, couldn't resist...)
– whuber
May 25 at 22:38