Provided 3 datasets: x1, x2 and x3 (=x2 processed), 1D, same size and sampled from a normal distribution with equal variances, with x1 and x2 completely independent, do you think it would be possible to derive the confidence interval for the ratio:
mean(x1) - mean(x2) / mean(x1) - mean(x3) (1) ?
I know Fieller's theorem provides the confidence interval for the ratio mean(A)/mean(B).
Given that z = x - y is such that mean(z) = mean(x) - mean(y) and z is normally distributed, could I adapt the Fieller's ratio to build the IC for:
mean(Z_12)/mean(Z_13) = (1),
by simply adapting the MSEs and the degrees of freedom?
Thank in advance for any kind of help.