Fieller's theorem vs. The delta method for significance intervals for ratios

Fuller's Theorem and the Delta Method are both proposed as methods for obtaining a significance interval for the ratio of two parameters. The relative difference between Fieller and Delta Method lower limits and the relative difference between Fieller and Delta Method upper limits for 95% significance intervals are examined conditional on the observed sample coefficients of variation of the estimators of the unknown parameters and correlation between the estimators The behavior of relative differences are discussed in terms of maximum values of relative differences, conditions for which relative differences are greater than 100% and for which they are less than 10 %. Several rules of thumb for deciding when to approximate a Fieller interval by a Delta Method interval are discussed and evaluated.