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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

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    $\begingroup$ The fact that your measurements are paired might also play a role on how you compute this ratio. As you work with paired measurement, don't you want to compute the mean ratios (each individual has a ratio, and you mean it) instead of the ratio of the means ? $\endgroup$
    – brumar
    Commented Jun 24, 2015 at 9:39
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    $\begingroup$ The problem is that the were many zeros in the measurements thereby making ratios of paired measurements impossible $\endgroup$
    – Marc
    Commented Jun 24, 2015 at 9:50
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    $\begingroup$ @Marc Then one might question why you're computing ratios in the first place. If you find yourself in a situation where you literally can't compute something then that makes me question how you are/were planning on interpreting it in the first place. $\endgroup$
    – Dason
    Commented Mar 29, 2017 at 17:25

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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] (http://www.hindawi.com/journals/ads/2006/078375/abs/), (ii) the distribution of the ratio of two normal variables [is not normal] (http://link.springer.com/article/10.1007%2Fs00362-012-0429-2#page-1).

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    $\begingroup$ These does not really answer the question about using Fiellers' theorem ... $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jan 29, 2018 at 14:57

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