A contribution to the problem of two samples

(a) The use of a single comprehensive test of the hypothesis H of a common origin for the two samples is discussed. It is shown that a single best test of the hypothesis H does not exist. A comparison between L and two alternative two sample tests is made, which illustrates how the use of one test may be more efficient than the other with regard to a given alternative. (b) The sampling distribution of L is obtained. It is found that the distribution involves an elliptic function of the first order when the samples are of equal size. (c) Tables of the 5% and 1% levels of probability for L have been provided. (d) Finally the question whether the test is suitable for application to non-normally distributed material is discussed. It is found that unless the distribution is extremely non-normal the test may be applied in practice