Let us assume that in an experiment to study the ameliorative effect of a new treatment, a control (or standard) group of n, subjects receive a standard treatment, and an experimental (or test) group of n, subjects receive the new treatment, both groups being chosen at random from the population available, and that over a fixed period of experimentation the values of some measure of deterioration on the control subjects are x,, , XC2 * xCn , with mean xc ; and those on the experimental subjects are xei, Xe2, ., Xen ,, with mean ; . The random variables Xc and X, are taken to have means g, and g. and standard deviations as, and o-e (crc i cre), and cannot usually be taken to be normal. We assume that pu # 0, and that it is large enough