Das Land der unbegrenzten Möglichkeiten

Répertoire des administrateurs & commissaires de société, des banques, banquiers et agents de change de France et de Belgique

Bibliographic data

Monograph

Identifikator:: 881661368

URN:: urn:nbn:de:zbw-retromon-3236

Document type:: Monograph

Author:: Goldberger, Ludwig Max http://d-nb.info/gnd/117548804

Title:: Das Land der unbegrenzten Möglichkeiten

Edition:: Achte Auflage

Place of publication:: Berlin

Publisher:: F. Fontane & Co.

Year of publication:: 1911

Scope:: 1 Online-Ressource (299 Seiten)

Digitisation:: 2017

Collection:: Economics Books

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

2: THEORY OF STATISTICS. one family with statures 5 ft. 9, 5 ft. 10, and 5 ft. 11, these are regarded as giving the six pairs 5 ft. 9 with 5 ft. 10 5 ft. 10 with 5 ft. 9 o sy, ite 1] Bub Ll : 3 16.10, n ™ » oD 16.10 which may be entered into the table. The entire table will be formed from the aggregate of such subsidiary tables, each due to one family. Let it be required to find the correlation-coefficient, however, for a single subsidiary table, due to a family with & members, the numbers of pairs being therefore NV (V —1). As each observed value of the variable occurs &/ —1 times, t.e. once in combination with every other value, the means and standard-deviations of the totals of the correlation-table are the same as for the original IV observations, say # and o. If 2; 2, Zz. .. .be the observed deviations, the product sum may be written TZo + XX +2124 F oo a + Xo%; + Xg +22, + + Xg%y + XT + Xgl + 0. + =2,{3(2) — @} +2 {3(@) = 2} +2 {3(w) ag} +. LLL = a l-pl-mlo lL = Vg, whence, there being N(& — 1) pairs, No? 1 pita ag rn dns nl 2 For ¥=2, 3,4... . this gives the successive values of r= -1, -1, —1.... Itis clear that the first value is right, for two values x, x, only determine the two points (#;, x,) and (x, ,), and the slope of the line joining them is negative. The student should notice that a corresponding negative association will arise between the first and second member of the pair if all possible pairs are formed in a mixture of 4’s and a’s. Looking at the association, in fact, from the standpoint of § 10, the equation (13) still holds, even if the variables can only assume two values, e.g. 0 and 1. This result is utilised in § 14 of Chapter X1Y. 12. Correlation due to Heterogeneity of Material.—The following theorem offers some analogy with the theorem of Chap. IV. § 6 for attributes.—If X and Y are uncorrelated vn each of two records, they will nevertheless exhibit some correlation when the 18

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