An Introduction to the theory of statistics

Bibliographic data

Monograph

Identifikator:: 1751730271

URN:: urn:nbn:de:zbw-retromon-127610

Document type:: Monograph

Author:: Yule, George Udny http://d-nb.info/gnd/12910504X

Title:: An Introduction to the theory of statistics

Edition:: 8. ed. rev

Place of publication:: London

Publisher:: Griffin

Year of publication:: 1927

Scope:: XV, 422 S; Ill., Diagr

Digitisation:: 2021

Collection:: Economics Books

Usage license:: Get license information via the feedback formular.

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part I. The theory of atributes

Collection:: Economics Books

THEORY OF STATISTICS. is therefore given in full in the following section. The advanced student should refer to the original memoir (ref. 1) for a completer treatment of the theory of the coefficient, and of its relation to the theory of variables. 6. Generalising slightly the notation of the preceding chapters, let the frequency of 4,’s be denoted by (4,), the frequency of Bs by (B,), and the frequency of objects or individuals possessing both characters by (4,B,). Then, if the A’s and B’s be com- pletely independent in the universe at large, we must have for all values of m and n— An Bn (4,.B,) = ad =(4dnBn)y - : +35{1) If, however, 4 and B are not completely independent, (4,.B,) and (A,.B,), will not be identical for all values of m and n. Let the difference be given by On = (4B) TF (4B) - (2) A coefficient such as we are seeking may evidently be based in some way on these values of 8. It will not do, however, simply to add them together, for the sum of all the values of d, some of which are negative and others positive, must be zero in any case, the sum of both the (4B)’s and the (4B),’s being equal to the whole number of observations XV. It is necessary, therefore, to get rid of the signs, and this may be done in two simple ways: (1) by neglecting them and forming the arithmetical instead of the algebraical sum of the differences 3, or (2) by squaring the differ- ences and then summing the squares. The first process is the shorter, but the second the better, as it leads to a coefficient easily treated by algebraical methods, which the first process does mot: as the student will see later, squaring is very usefully and very frequently employed for the purpose of elimin- ating algebraical signs. Suppose, then, that every 0 is calculated, and also the ratio of its square to the corresponding value of (4B), and that the sum of all such ratios is, say, x2; or, in symbols, using 2 to denote “the sum of all quantities like ” :— Pel 3 elie a 49 Being the sum of a series of squares, x2 is necessarily positive, and if 4 and B be independent it is zero, because every 6 is zero. If, then, we form a coefficient C' given by the relation = x “A # VF + x2 ) 64 or

Access restriction

Copyright

fullscreen: An Introduction to the theory of statistics

Monograph

Chapter

Table of contents

Download

Monograph

Chapter

This page

Image fragment

Citation links

Citation recommendation