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hypothesis underlying this test, however, is that the variances are equal. Although in many cases this may seem a reasonable assumption to adopt concurrently with that of equal means, it is undoubtedly not a necessary one, and it is, therefore, desirable that the test should be adapted to meet this difficulty. The first advance on the problem was made by W. V. Behrens3 who suggested that the distribution of the difference of the means could be expressed in terms of the observatiops in the samples from the two populations, the argument being entirely independent of the variances. R. A. Fisher4 obtained substantially the same result, but expressed the argument in termns of fiducial probability. M. S. Bartlett5 was of the opinion that Behrens' reasoning was incorrect, as he obtained some restults which were apparently inconsistent with those tabulated in Behrens' paper, but R. A. Fisher6 showed that Bartlett's argument was open to criticism. In the latter work, he actually obtained distributions for the case of two samples of two observations, and in the following we shall indicate some extensions of this more detailed work of Fisher, firstly, to the case
Daisy M. Starkey (Thu,) studied this question.