An Introduction to the theory of statistics

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Monograph

Identifikator:: 1024536734

URN:: urn:nbn:de:zbw-retromon-42508

Document type:: Monograph

Author:: Jaeckel, Reinhold http://d-nb.info/gnd/117051152

Title:: Statistik und Verwaltung mit besonderer Berücksichtigung der preussischen Verwaltungsreform

Place of publication:: Jena

Publisher:: Verlag von Gustav Fischer

Year of publication:: 1913

Scope:: 1 Online-Ressource (62 Seiten)

Digitisation:: 2018

Collection:: Economics Books

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

THEORY OF STATISTICS. (B)= (4B), so that all A’s are B and also all B’s are 4. The three corresponding cases of complete disassociation are— (4) (7) (8) ol [tayias) Bryce cay | (aB) i . | ’ i ‘a) GES —— — a] te -— Cr — B® SI yaw It is required to devise some formula which shall give the value +1 in the first three cases, —1 in the second three, and shall also be zero where the attributes are independent. Many such formule may be devised, but perhaps the simplest possible (though not necessarily the most advantageous) is the expression— @=(4B)(aB) - (4B)(aB) (48)(af) + (4F)(eB) 151 No (@B)ah) + (BYE) —where § is the symbol used in the two last sections for the difference (4B) —~ (4B),. It is evident that @ is zero when the attributes are independent, for then 6 is zero: it takes the value +1 when there is complete association, for then the second term in both numerator and denominator of the first form of the expression is zero: similarly it is — 1 where there is complete disassociation, for then the first term in both numerator and denominator is zero. () may accordingly be termed a coefficient of association. As illustrations of the values it will take in certain cases, the association between deaf-mutizm and imbecility, on the basis of the English census figures (Example vi.) is +091 ; between light eye colour in father and in son (Ex _ ‘nla vii.) +066 ; between colour of flower and prickliness of fruit ia vatura (Example ix.) — 0°28, an association which, however, as already stated, is probably of no practical significance and due to mere fluctuations of sampling. The student should note that the value of @ for a given table is unaltered by multiplying either a row or a column by any arbitrary number, 7.c. the value is independent of the relative proportions of A’s and o’s included in the table. This property is of importance, and renders such a measure of association specially adapted to cases (e.g. experiments) in which the propor- tions are arbitrary. A form possessing the same property but certain marked advantages over @ is suggested in ref. (3). 38

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