I'm sorry that I am not at all an expert in statistics, so my question may sound vague, or very easy.
I have a group of people that I divide into two categories, $A$ and $B$, depending on some visible characteristic (say blue-eyed vs brown-eyed). There are $n_A$ individuals in $A$ and $n_B$ individuals in $B$.
I am interested in a certain eye disease, so for a fixed period (1 year) I observe them, and in the end I count how many people of each group got the disease. Say I count $m_A$ in group $A$ and $m_B$ in group $B$. Those are not samples; I have counted them on the entire group.
What I want to determine is whether eye color is relevant to the outbreak of the disease, i.e., what I would naively call the correlation between eye color and disease outbreak. Hence: how can I quantify, as a function of $m_A$, $n_A$, $m_B$ and $n_B$, whether it is likely that eye color is correlated to getting the disease, or whether the fluctuations between both groups are just caused by chance?
From my naive understanding, one possibility would be to consider two hypotheses, one that says that the disease occurs with some probability $p$, independently over individuals, no matter the group; one that says that there is a probability $p_A$ in group $A$ and a probability $p_B$ in group $B$. One should then determine which of these hypotheses is more likely... but I'm not sure how to do that.
Edit: after some more investigation I'm starting to believe that the correct way to proceed would be perhaps to construct a contingency table containing $m_A$, $m_B$, $n_A - m_A$ and $n_B - m_B$, and use Fisher's test to compute the probability of observing data which is as imbalanced or more imbalanced (in favor of one eye color being positively correlated to the disease outbreak) if the null hypothesis (that disease outbreak does not depend on eye color) is true. Would this be a sensible way to proceed?