Die Kaufkraft des Geldes

An Introduction to the theory of statistics

Bibliographic data

Monograph

Identifikator:: 1028803699

URN:: urn:nbn:de:zbw-retromon-43559

Document type:: Monograph

Author:: Fisher, Irving http://d-nb.info/gnd/118533541; Brown, Harry Gunnison http://d-nb.info/gnd/123548152

Title:: Die Kaufkraft des Geldes

Place of publication:: Berlin

Publisher:: Druck und Verlag von Georg Reimer

Year of publication:: 1916

Scope:: 1 Online-Ressource (XX, 435 Seiten)

Digitisation:: 2018

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: IV. Kapitel. Störung der Gleichung und der Kaufkraft in Perioden des Übergangs

Collection:: Economics Books

te THEORY OF STATISTICS. B were independent in the universe of (’s, and the corresponding differences for the frequencies (4B), (AC), and (BC). The four quantities in the brackets on the right represent, say, the four known associations, the bracket on the left the unknown association. Clearly, the relation is not of such a simple kind that the term on the left can be, in general, mentally evaluated. Hence in con- sidering the choice and number of associations to be actually tabulated, regard must be had to practical considerations rather than to theoretical relations. 13. The particular case in which all the 2” —n +1 given associa- tions are zero is worth some special investigation. It follows, in the first place, that all other possible associations must be zero, z.e. that a state of complete independence, as we may term it, exists. Suppose, for instance, that we are given— (4)(B) _(4)(©) (4B) = 7 (40) = v _(B)C) _(4OXBO) _ (4)(B)(C) (BC) aN (4B0C) Tw (0) Ce Then it follows at once that we have also— AB)(BC) (4B)(AC) A450) = EENBC) (ABYC, ents a t.e. 4 and C are independent in the universe of B’s, and B and C in the universe of 4’s. Again, = (AE) _ DB) _ (A)XB)C) (4By)=(4B) - (4BC) = Sa _ AB) _ 4y)(By) re (r) Therefore 4 and B are independent in the universe of fs. Similarly, it may be shown that 4 and C' are independent in the universe of 8’s, B and C in the universe of a’s. In the next place it is evident from the above that relations of the general form (to write the equation symmetrically) “BO _(1) (#) (©) = N x. aN : 2 must hold for every class-frequency. This relation is the general form of the equation of independence, (2) (d), Chap. III. (p. 26). 14. It must be noted, however, that (8) is not a criterion for the 56

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