# Categorical Variables With Little Variation. Chi-Square Test Power

Suppose you are trying to determine whether there is an association between gender and a rare disease, I suppose using the Chi-Square test. My intuition tells me that you must observe so many men, women and at least some people have to have the disease. After all, if you don't observe anyone with the disease how can you claim there is an association between the disease and gender? But, how many? Can you express the power function of a Chi Square test in terms of these proportions? Can anyone provide a reference to the power function of a Chi Square test? Perhaps other tests such as Fisher's or the logistic regression model, may be better for this kind of situation where one variable is very rare. But, I would think that you should be able to express the power function in terms of these proportions, correct?

• In answering my own question from what I have learned since I have asked is that apparently the Chisquare test would not be such a good choice to determine such an association because some of the expected frequencies would be very low. In this case the Fisher Test might be better and indeed you can find functions that compute the power of fisher's test with samples sizes n1,n2 and two differerent probs p1, p2. Some (at least) are done by simulation but all appear to be very computationally intensive Oct 23, 2015 at 14:48
• Fisher's test doesn't have more power than the chi-squared test. See stats.stackexchange.com/questions/407553/… . You could compare the two by simulation too, to see it for yourself. If your problem is limited resources, then you could consider using a different sampling method than simple random sampling, that wouldn't require sampling millions of people. Here's an example, commonly used for studying rare diseases: ncbi.nlm.nih.gov/books/NBK448143 Jan 14 at 16:30