An Introduction to the theory of statistics

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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

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Document type:: Monograph

Structure type:: Chapter

Title:: Part I. The theory of atributes

Collection:: Economics Books

THEORY OF STATISTICS. than, less than, or equal to the ratio (8, (Anyi Dae). The whole of the contingency table can be analysed into a series of elementary groups of four frequencies like the above, each one overlapping its neighbours so that an rsfold table contains (r—1) (s—1) such “tetrads,” and the associations in them all can be very quickly determined by simply tabulating the ratios like (428,) (Ani 8.) (4,801) (4dnsi Bor), ete., or perhaps better, the proportions (4.,.8,)/{ (AnB,) + (4118), ete., for every pair of columns or of rows, as may be most convenient. Taking the figures of Table II. as an illustration, and working from the rows, the proportions run as follows :— For rows 1 and 2. For rows 2 and 3. 1768/2714 0-651 946/1061 0-892 807/2194 0-368 1387/1825 0-760 189/935 0-202 746/1034 0-721 47/100 0-470 53/69 0-768 In both cases the first three ratios form descending series, but the fourth ratio is greater than the second. The signs of the associations in the six tetrads are accordingly— The negative sign in the two tetrads on the right is striking, the more so as other tables for hair- and eye-colour, arranged in the same way, exhibit just the same characteristic. But the peculiarity will be removed at once if the fourth column be placed immediately after the first : if this be done, 7.e. if “red ” be placed between “fair” and “brown ” instead of at the end of the colour- series, the sign of the association in all the elementary tetrads will be the same. The colours will then run fair, red, brown, black, and this would seem to be the more natural order, consider- ing the depth of the pigmentation. 11. A distribution of frequency of such a kind that the association in every elementary tetrad is of the same sign possesses several useful and interesting properties, as shown in the following theorems. It will be termed an isotropic dis- tribution. (1) In an isotropic distribution the sign of the association is the same not only for every elementary tetrad of adjacent Jrequen- cies, but for every set of four frequencies in the compartments common to two rows and two columns, e.g. (4,B,), (dn.,B,) (4dnBrio) (drei pBrig): 68

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