Showing papers in "Annals of Mathematical Statistics in 1938"

Distributions of Sums of Squares of Rank Differences for Small Numbers of Individuals

Abstract: In a recent article,2 reporting the results of research under a grant-in-aid from the Carnegie Corporation of New York, Hotelling and Pabst have given a comprehensive treatment of the theory and application of rank correlation and have contributed significantly to existing knowledge on the subject. It is not the purpose of this note to evaluate their contribution but to attempt the solution of a problem they suggest. In ?33 they have given the well-known formula for rank correlation, r' = 1 -

A Test of the Significance of the Difference Between Means of Samples from Two Normal Populations Without Assuming Equal Variances

Abstract: 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

On Combined Expansions of Products of Symmetric Power Sums and of Sums of Symmetric Power Products with Applications to Sampling (Continued)

Abstract: the (N) variances in terms of the moments of the moments of the universe. n Numerous attempts have been made to solve this problem, but each has been restricted in some way. It is the aim of Part II to indicate an approach which is broad enough to include many of the fundamental variations. The first chapter is devoted to a listing of criteria which should be satisfied by a theoretical development which is to be considered sufficiently general. These criteria might be applied to other statistics but the theory developed here is limited to those statistics which are moments (or functions of moments) of moments. The first chapter continues with an account of the more significant papers which have contributed to a general solution of the problem. No attempt is made to indicate a complete history, but rather there is presented a brief summary of a number of the most significant contributions. The second chapter is devoted to definitions and notation. An attempt has been made to use conventional notation whenever it is suitable. The third chapter deals with some of the fundamental principles which are used in the general approach. It presents a crucial part of the argument as it shows how various types of sampling problems can be reduced to Carver functions. The last three chapters deal with specific applications to some of the simpler problems. Chapter IV discusses the case of moments of the mean of the sample.