ABSTRACT
For two variables x and y , interest may center on the ratio of their means 77/jU, where [i = E (x ) and 77 = E(y). The mean ratio is pertinent when one wants to know the average amount of variable y per unit of variable x . An example might be the protein content of cells per unit DNA. The mean ratio is also involved when the parameter of interest is the percentage change or relative change between experimental (y ) and control (x ) conditions. Percentage change is defined by
and relative change is defined by (6.1) without the factor 100. For a sample of pairs (x?-, y*), i = 1, • • •, n, an obvious estimator
of T}/ji is y / x , where x and y are the sample means. This estima tor, which is the ratio of the sample means, will converge to rj/fi as n —» 00, but the estimator (1 /n) which is the mean of the sample ratios, will not. The latter estimator is consistent for the expectation E (y/x). The two quantities E (y /x ) and E (y) /E (x ) are rarely equal. They can be nearly equal or quite far apart, as de termined by the joint distribution of x and y. The investigator and statistician should have clearly in mind which quantity they want to estimate. In most cases it is the ratio of the population means 77/jU.
