Allgemeine Gesellschaftslehre

An Introduction to the theory of statistics

Bibliographic data

Monograph

Identifikator:: 834086425

URN:: urn:nbn:de:zbw-retromon-82719

Document type:: Monograph

Author:: Helfferich, Karl http://d-nb.info/gnd/118773828

Title:: Zur Erneuerung des deutschen Bankgesetzes

Edition:: Sonderabdruck

Place of publication:: Leipzig

Publisher:: Duncker & Humblot

Year of publication:: 1899

Scope:: 1 Online-Ressource (XI, 135 S.)

Collection:: Economics Books

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IL.—CONSISTENCE. J consistent with one another. They conform with one another, and do not in any way conflict. The conditions of consistence are some of them simple, but others are by no means of an intuitive character. Suppose, for instance, the data are given— : 1000 (4D) 42 (4) 525 (AC) 147 (5) 312 (BO) 86 (C) 470 (4BC) 25 —there is nothing obviously wrong with the figures. Yet they are certainly inconsistent. They might have been observed at different times, in different places or on different material, but they cannot have been observed in one and the same universe. They imply, in fact, a negative value for (afy)— (aBy)=1000 — 525 — 312 — 470 +42 + 147 + 86 — 25. =1009 - 1307 + 275 - 25. = — 57. Clearly no class-frequency can be negative. If the figures, consequently, are alleged to be the result of an actual inquiry in a definite universe, there must have been some miscount or misprint. 6. Generally, then, we may say that any given class-frequencies are inconsistent if they imply negative values for any of the unstated frequencies. Otherwise they are consistent. To test the consistence of any set of 2" algebraically independent frequencies, for the case of = attributes, we should accordingly calculate the values of all the unstated frequencies, and so verify the fact that they are positive. This procedure may, however, be limited by a simple consideration. If the ultimate class-frequencies are positive, all others must be so, being derived from the ultimate frequencies by simple addition. Hence we need only calculate the values of the ultimate class-frequencies in terms of those given, and verify the fact that they exceed zero. 7. As we saw in the last chapter, there arc two sets of 2° algebraically independent frequencies of practical importance, viz. (1) the ultimate, (2) the positive class-frequencies. It follows from what we have just said that there is only one condition of consistence for the ultimate frequencies, viz. that they must all exceed zero. Apart from this, any one frequency of the set may vary anywhere between 0 and co without becoming inconsistent with the others. For the positive class-frequencies, the conditions may be 1¢

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