Consider a biochemical method which is sensitive to the concentration of reagent A.
The method produces a signal with variance var(method) when reagent A is repeatedly sampled from the same stock (no difference in concentration between experimental repeats). The method produces a total variance, var(total) = var(A)+var(method) when reagent A is sampled from difference stocks where its concentration is expected to vary due to small variations in preparation.
I have been estimating the variance caused by using different reagent A stocks by subtraction: var(A) = var(total)-var(method). I have subsequently estimated the standard deviation and coefficient of variation of the variation due to reagent A.
How can I propagate the (95%) confidence intervals of the estimates of var(total) and var(method) into conidence intervals on my estimate of var(A)? My only experience of error propagation so far has been using quadrature to propagate standard deviation when adding/multipling means but here I am wanting to propagate confidence limits when subtracting variances.
Additional info if helpful:
- var(total) and var(method) may be unequeal
- replicate measurements are in abundance
- I would like to estimate the confidence limits analytically and not use bootstrapping
