Occasionally, one has needfor confidence intervals or tests of significance for ratios of normal variables. For instance, tests of significance on the therapeutic safetyratio are needed in pharmacology. This ratio is the doseof a compound that is lethal to 50% of subjects tested (LDso) divided by the dose that is for 50% of treated subjects (EDso) . The bigger this ratio is, the largerthe lethaldoseis compared withthe effective dose and, therefore, the safer the drug. Although it is probablysafeto assume thatestimates suchas EDso and LDso haveapproximately normal distributions, thedistribution of the ratioof twonormal variables is quite complex. This distribution has been investigated first by Geary (1930), then more extensively by Fieller (1932), and more recently by a number of researchers (see, e.g., Hinkley, 1969; Marsaglia, 1965; Paulson, 1942; Shanmugalingam, 1982). Because of extensive early work, the generaltheoryof the distribution of the ratio of two normal variables is called Fieller's Theorem by some authors (see, e.g., Davies, 1961). FieUer's Theorem. A goodapproximation to the confidence interval for a ratio of normal variables can be solvedin the following manner. For normal variables y and x, call their ratio v, where y are normally distributed, which is certainly tenable when x andyare means; the effects of nonnormality on thedistribution of a ratio has not to our knowledge been investigated. Because d in Equation 2 is normally distributed, Equation 2 divided by the square root of Equation 3 is distributed as Student's t (See Kendall & Stuart, 1979, pp. 137-138, for a derivation). Squaring both sides we can write