How to test relationship between categorical and numerical variables I have a list of sites and a list of survival probabilities associated with those sites. The data looks like this:
Site     Probability
A        0.8
B        0.4
C        0.2
...
(14 sites in total)

Is there any way to test if survival probability varies significantly between sites? What I'm finding difficult is that the factor (sites) has so many categories.
 A: i can think of two different answers from what you've described..
answer #1 assumes you know something about the population not the sample
you can say that survival probability varies between sites without performing any sort of statistical test.  if your method of data collection allows you to be 100% confident that site A's survival probability is 0.8 and site B's survival probability is 0.4, then you're done.  site A statistically significantly differs from site B.
if you are not 100% certain that site A's survival probability is 0.8, that's when you need to figure out what the confidence interval around site A's survival probability of 0.8 before you try to compare it to other sites.
think of this like comparing your height to your friend's height - you know who is taller with 100% certain because it's trivial to sample 100% of the population (you just need a tape measure and a friend)
answer #2 assumes these are just samples
for each of these 14 sites, you basically have an N of one.  so treating them as independent observations with no relationship doesn't give you nearly enough of a sample to compare any of the sites to any of the other sites.  you can calculate some descriptive statistics (like the variance) to determine how much variation there is across the 14 sampled sites, but, really, you cannot break them out into groups that small.  you probably won't detect any statistically significantly different results unless you bin them into two or three groups and perform a fisher's exact test between those two groups.  but then, is it useful for you to break the 14 sites into two groups of 7 sites and compare them?  :)
