is there a Fisher's exact test (or similar) for continuous data?

#1
I have a simple statistical problem, but am having a hard time identifying a good solution.

I am interested in testing to see if an independent factor (length of time interval between 2 different 1 choice tests) influences the association time (a continuous variable) between two options (fast and slow males).

Experiment 1: I tested females for the duration of time they associated with a fast male and then re-tested the same females 20 min later for their association time with a slow male. Here I can simply do a paired t-test -- I show that females associate more with the fast male type.

Experiment 2: I repeated experiment 1 with a different set of females but changed the interval from 20 min to 24 hours. Again, I can examine the difference in association time between the fast and slow stimuli tests (now separated by 24 hrs) with a simple paired t-test -- here I show that females do not differ in their association between the two male types.

What I would really like to do is test for the following: the ratio of association time in fast:slow in experiment 1 VERSUS the ratio of association time in fast:slow in experiment 2.

If these data were count data instead of continuous data then a Fisher's exact test would do the trick. Since they are continuous data, I'm not sure which test can be used and can't find an answer elsewhere.

The continuous data could be discretized and thus transformed into count data, but I feel like there must be a better way? I might just be missing something very simple here.

Thanks in advance
 
#2
If these data were count data instead of continuous data then a Fisher's exact test would do the trick. Since they are continuous data, I'm not sure which test can be used and can't find an answer elsewhere.
I think you can use correlation tests. And yes, as you pointed out, we can also dichotomize those variables to use a Fisher test. Nevertheless, the correlation would be much better since dichotomizing would discard a great deal of your data. So try Pearson's or Spearman's correlation coefficients, depending on your data type.
 
#3
I don't think a correlation analysis will work. The independent factor Time Interval is dichotomous (20 min versus 24 hours), not continuous.