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I have a set of N samples, each of which yields the measurable variables A and B. I am interested in computing the mean and standard error of the ratio A/B within the group. The catch is that I need to do background subtraction on both A and B, and the two different background values BG_{A}and BG_{B}are themselves the mean values of ~100 replicate measurements, which means they have their own error which must be propagated.

Based on a previous thread that I made a long time ago, I gather that since the same BG values are subtracted from each of the N measurements, the error is 100% correlated and should be added in quadrature to the calculated SEM of my set of (A/B) values. However, since I have a ratio of uncertainties (BG_{A}/BG_{B}), how do I treat this?

I know that the formula for propagating the error of a ratio is Δz = aΔb + bΔa. However, the values of a and b are specific to the given sample within the set, so I no longer have a single value that I can add in quadrature. What is the correct approach to handle the error propagation?

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# I Propagating Error in both numerator and denominator of ratio

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