I want to determine if there is significant variation in the effect of a treatment amongst my replicates. The treatment effect is measured as a proportion.
Let me describe:
I study heart defects (in mice) and I found that babies from older mothers have a higher incidence of heart defects compared to babies from young mothers. Simply put, each mother is given a treatment (age), and we compare the incidence of heart defects in her babies before and after treatment. I simply compared the population-wide percent of babies with heart defects from when the mothers are young to the same mothers when they get old.
Now I want to know if there is quantifiable variation in this age effect between mothers. Simply put, I want to know if some mothers have a higher treatment (age) effect than other mothers in the population. The goal is to implicate genetic variation as the source of the variation in age effect.
I am having problems because of the proportion scale measurement. I looked at Cochran's Q Test, but it did not seem to fit my problem. I think I want a statistic that tests for homogeneity of differences between paired proportions that also accounts for unequal sample sizes (some mothers have more babies than others). I don't think that test exists, but any suggestions would be greatly appreciated.