Timeline for 95 % CI for ratio of variables subject to measurement imprecision

8 events

when toggle format	what		by	license	comment
Mar 10, 2022 at 13:21	history	edited	EdM	CC BY-SA 4.0	added link to other approaches
Mar 10, 2022 at 5:06	vote	accept	Peder Holman
Mar 10, 2022 at 5:06	comment	added	Peder Holman		Aha, of course! Thank you for clearing that up. You have answered my question perfectly, much appreciated!
Mar 9, 2022 at 18:04	history	edited	EdM	CC BY-SA 4.0	added 119 characters in body
Mar 9, 2022 at 17:57	comment	added	EdM		@PederHolman with an assumed 0.1 CV in the original scale, you have an assumed SD in the log scale of 0.1 and thus an assumed variance of $0.1^2 = 0.01$ in the log scale. The variance of the difference between 2 uncorrelated observations each with a variance of 0.01 is 0.02.
Mar 9, 2022 at 17:50	comment	added	Peder Holman		Thank you! This is very helpful, but how do I obtain the variances of `log(x1)` and `log(x2)` if all the information I have is `cv <- .1; x1_measured <- 100; x2_measured <- 50`? I can simulate values of `x1_true` by dividing `x1_measured` by `rnorm(1e6, 1, cv)` and then simply use `var(x1_true)` to find the variance, but how do I find it without simulation? Won't the distribution of `x1_true` be a kind of reciprocal normal distribution?
Mar 9, 2022 at 17:18	history	edited	EdM	CC BY-SA 4.0	added 263 characters in body
Mar 9, 2022 at 17:13	history	answered	EdM	CC BY-SA 4.0