Denkschrift über die Maschinenindustrie der Welt, bestimmt für das Komitee B des Vorbereitenden Ausschusses der Internationalen Wirtschaftskonferenz des Völkerbundes

An Introduction to the theory of statistics

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Monograph

Identifikator:: 1724926314

URN:: urn:nbn:de:zbw-retromon-103958

Document type:: Monograph

Title:: Denkschrift über die Maschinenindustrie der Welt, bestimmt für das Komitee B des Vorbereitenden Ausschusses der Internationalen Wirtschaftskonferenz des Völkerbundes

Place of publication:: Bln-Charlottenburg

Publisher:: Verein Deutscher Maschinenbau-Anstalten

Year of publication:: 1926

Scope:: V, 194 S.

Digitisation:: 2020

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Anhang. Statistischer Material

Collection:: Economics Books

V.—MANIFOLD CLASSIFICATION. ’ The eye- and hair-colour data of Table II. may be treated in a precisely similar fashion. If, e.g., we desire to trace the associa- tion between a lack of pigmentation in eyes and in hair, rows 1 and 2 may be pooled together as representing the least pigmenta- tion of the eyes, and columns 2, 3, and 4 may be pooled together as representing hair with a more or less marked degree of pigmentation. We then have— Proportion of light-eyed with ) 2714/5943 = 46 per cent. fair hair . J Proportion of brown-eyed with 115/857 =13 fair hair . : The association is therefore well-marked. For comparison we may trace the corresponding association between the most marked degree of pigmentation in eyes and hair, 7.e. brown eyes and black hair. Here we must add together rows 1 and 2 as before, and columns 1, 2, and 4—the column for red being really mis- placed, as red represents a comparatively slight degree of pigmenta- tion. The figures are— roportion rown- v p Spt of % ge ged Mth } 288/857 = 34 per cent. Proportion of light-eyed with mip pd }935/5943=16 The association is again positive and well-marked, but the difference between the two percentages is rather less than in the last case. 5. The mode of treatment adopted in the preceding section rests on first principles, and, if fully carried out, it gives the most detailed information possible with regard to the relations of the two attri- butes. At the same time a distinct need is felt in practical work for some more summary method—a method which will enable a single and definite answer to be given to such a question as—Are the 4’s on the whole distinctly dependent on the B’s; and if so, is this dependence very close, or the reverse? The subject of coefficients of association, which affords the answer to this question in the case of a dichotomous classification, was only dealt with briefly and incidentally, for it is still the subject of some controversy : further, where there are only four classes of the second order to be considered the matter is not nearly so complex as where the number is, say, twenty-five or more, and the need for any summary coefficient is not so often nor so keenly felt. The ideas on which Professor Pearson’s general measure of de- pendence, the “coefficient of contingency,” is based, are, more- over, quite simple and fundamental, and the mode of calculation 62

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