Using Fieller’s theorem to calculate the confidence interval of a ratio (paired measurements)

If you have two means (with their own confidence intervals) and want to represent them as a ratio, how do calculate the confidence interval for the ratio?

An answer that was given to me, mentions Fieller’s theorem, which enables you to compute a confidence interval for a ratio quite easily (see calculator here).

Unfortunately, I cannot use this tool as my measurements are paired. Is there any way around this?

I might have been clearer in the following image:
enter image description here


The problem of calculating confidence/likelihood intervals for the ratio of two means is addressed in Chapter 7 of the book Statistical Inference in Science, and in Chapter 10 of Empirical Bayes and Likelihood Inference.

Note also that (i) the ratio of the means is different to the [mean of the ratio] (, (ii) the distribution of the ratio of two normal variables [is not normal] (

Source : Link , Question Author : Marc , Answer Author : Laikon

Leave a Comment