In genomics, you have an input control (I) and a treatment (T) where then you determine the ratio T/I. You perform multiple replicates for each but the number of replicates is not always the same. Typically, you just average out each of them before finding the ratio. I want to use the information of the variation in the replicates. So, I want to determine the ratio as well as the variation.
I've found the Delta Method variance but it doesnt work as it uses covariance which requires the same number of members in each set.
Throughout the search, this has been the most relevant but I'm not fully convinced: How to report the ratio of two sets of experimental results?
Would it make sense to determine the expectation and the variance by using the pairwise ratios?
For example given two sets: {T_1, T_2} {I_1, I_2, I_3}
pairwise ratios = {T_1 / I_1, T_1 / I_2, ... T_2 / I_3}
then you find the mean(pairwise ratios) and var(pairwise ratios).
(sorry about the improper notations)
