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Showing papers in "Journal of the royal statistical society series b-methodological in 1951"


Book ChapterDOI
TL;DR: The work described in this article is the result of a study extending over the past few years by a chemist and a statistician, which has come about mainly in answer to problems of determining optimum conditions in chemical investigations, but they believe that the methods will be of value in other fields where experimentation is sequential and the error fairly small.
Abstract: The work described is the result of a study extending over the past few years by a chemist and a statistician. Development has come about mainly in answer to problems of determining optimum conditions in chemical investigations, but we believe that the methods will be of value in other fields where experimentation is sequential and the error fairly small.

4,359 citations







Journal ArticleDOI
TL;DR: In this paper, the distribution of the sum of the squares of the intervals into which the line is divided is further considered, and the lower 5 per cent and 1 per cent points of the distribution can be found exactly up to n = 8 and n = 9 respectively.
Abstract: SUMMARY THE present paper is a sequel to two previous papers on this subject (Moran (1947), (1951)), and was suggested by reading Dr. A. Gardner's recent note (1952). The distribution of the sum of the squares of the intervals into which the line is divided is further considered. The lower 5 per cent. and 1 per cent. points of the distribution can be found exactly up to n= 8 and n = 9 respectively (nine and ten intervals). Beyond about n = 20 an approximation based on the variance ratio distribution is probably adequate. In between n = 9 and n = 20 no workable formula has been reached.

75 citations


Journal ArticleDOI
TL;DR: In this paper, a relation between Spearman's coefficient of rank correlation rs and the inversions in the two rankings is developed, which leads to an expression for the mean value of rs in samples from a finite population, and to the improvement of Daniels' inequality relating rs and Kendall's coefficient t.
Abstract: A relation is developed between Spearman's coefficient of rank correlation rs and the inversions in the two rankings. This leads to an expression for the mean value of rs in samples from a finite population, and to the improvement of Daniels' inequality relating rs and Kendall's coefficient t.

71 citations










Journal ArticleDOI
TL;DR: This paper, like the earlier one (Fox, 1950), has been written for the computer, and the methods given in the two papers provide him with methods for the solution of equations and the inversion of matrices which are among the fastest and most convenient available, for use with ordinary desk calculating machines.
Abstract: SUMMARY Two methods are illustrated for the inversion of matrices, with special attention to the arrangement of the work on the computing sheet, and the application of frequent and powerful checks. The necessity for checking cannot be overemphasized, and if the checks are too widely spaced an early mistake may cause a lot of unnecessary work. This paper, like the earlier one (Fox, 1950) has been written for the computer, and the methods given in the two papers provide him with methods for the solution of equations and the inversion of matrices which are among the fastest and most convenient available, for use with ordinary desk calculating machines.