I am thinking about this interesting question which arises in the following realistic setting. For example, in one medical experiment one drug and one placebo are applied to two randomized groups of people with eye disease for sample size n respectively. Responses are the cure rates for some eye disease. But we know that two eyes of one person are correlated with each other. So during our traditional model we are required to take into account the correlation between two eyes in some categorical data analysis. Otherwise we can not consider two eyes of one person are independent and use simple two sample t-test based on independence assumption.
So my naive thinking is that if we could transform the correlated two random variables into independent ones, so we could just use simple two sample test. But could we do it without knowing the independence structure?? just for curious exploring.
thank you everyone for any suggestions.