Ratios: A short guide to confidence limits and proper use

TL;DR

This paper reviews methods for calculating confidence limits for ratios of measured quantities, highlighting the appropriate techniques, potential pitfalls, and when to use specific models, with simulations illustrating their performance.

Contribution

It provides a comprehensive overview of methods for confidence limits on ratios, including Fieller, Taylor, and bootstrap, with practical guidance and simulation results.

Findings

Fieller method has a simple geometric interpretation

Common methods like index and zero-variance can be liberal

Simulations show when methods are appropriate

Abstract

Researchers often calculate ratios of measured quantities. Specifying confidence limits for ratios is difficult and the appropriate methods are often unknown. Appropriate methods are described (Fieller, Taylor, special bootstrap methods). For the Fieller method a simple geometrical interpretation is given. Monte Carlo simulations show when these methods are appropriate and that the most frequently used methods (index method and zero-variance method) can lead to large liberal deviations from the desired confidence level. It is discussed when we can use standard regression or measurement error models and when we have to resort to specific models for heteroscedastic data. Finally, an old warning is repeated that we should be aware of the problems of spurious correlations if we use ratios.