Konzentrationstendenzen im badischen Bankgewerbe

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Monograph

Identifikator:: 1013266285

URN:: urn:nbn:de:zbw-retromon-23296

Document type:: Monograph

Author:: Lenz, Adolf http://d-nb.info/gnd/11764000X

Title:: Der Wirtschaftskampf der Völker und seine internationale Regelung

Place of publication:: Stuttgart

Publisher:: Verlag von Ferdinand Enke

Year of publication:: 1920

Scope:: 1 Online-Ressource (XVI, 315 Seiten)

Digitisation:: 2018

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Erstes Kapitel. Der Kampf des wirtschaftlichen Imperialismus

Collection:: Economics Books

IV.—PARTIAL ASSOCIATION. { complete independence of 4, B, and C in the sense that the equation (4B) _(4) (B) NTN NN is a criterion for the complete independence of 4 and B. If we are given JV, (4), and (B), and the last relation quoted holds good, we know that similar relations must hold for (48), (aB), and (a3). If &, (4), (8B), and (C) be given, however, and the equation (8) hold good, we can draw no conclusion without further information ; the data are insufficient. There are eight algebraically independent class-frequencies in the case of three attributes, while , (4), (B), (C) are only four: the equation (8) must therefore be shown to hold good for four frequencies of the third order before the conclusion can be drawn that it holds good for the remainder, 7.e. that a state of complete independence subsists. The direct verification of this result is left for the student. Quite generally, if &, (4), (B), (C), . . .. be given, the relation {4BC ..., J _ (4) (8B) (©) (9) A = 5% Fa : must be shown to hold good for 2" —n +1 of the nth order classes before it may be assumed to hold good for the remainder. It is only because 2" —n+1=1 when n= 2 that the relation 4B) (4) (B) ¥ 5A: may be treated as a criterion for the independence of 4 and B. If all the n (n>2) attributes are completely independent, the relation (9) holds good ; but it does not follow that if the relation (9) hold good they are all independent. REFERENCES. (1) Youre, G. U., “On the Association of Attributes in Statistics,” Phil. Trans. Roy. Soc., Series A, vol. cxciv., 1900, p- 257. (Deals fully with the theory of partial as well as of total association, with numerous illustrations : a notation suggested for the partial coefficients.) (2) YuLe, G. U., ‘““Notes on the Theory of Association of Attributes in Statistics,” Biometrika, vol, ii., 1903, p. 121. (Cf. especially §§ 4 and 5, on the theory of complete independence, and the fallacies due to mixing of records.) LY

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