An Introduction to the theory of statistics

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Monograph

Identifikator:: 1751730271

URN:: urn:nbn:de:zbw-retromon-127610

Document type:: Monograph

Author:: Yule, George Udny http://d-nb.info/gnd/12910504X

Title:: An Introduction to the theory of statistics

Edition:: 8. ed. rev

Place of publication:: London

Publisher:: Griffin

Year of publication:: 1927

Scope:: XV, 422 S; Ill., Diagr

Digitisation:: 2021

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part I. The theory of atributes

Collection:: Economics Books

IIL.—ASSOCIATION. 1 The advantage of the forms (2) over the form (1) is that they give expressions for the second-order frequency in terms of the frequencies of the first order and the whole number of observa- tions alone ; the form (1) does not. Example i.—I1f there are 144 4’s and 384 B’s in 1024 observa- tions, how many 4B’s will there be, 4 and B being independent ? 144 x 384 ras = OL, 1024 There will therefore be 54 AB's. Example ii.—1If the A’s are 60 per cent., the B’s 35 per cent., of the whole number of observations, what must be the percentage of ABs in order that we may conclude that 4 and B are independent ? 60 x 35 rp 2 3] 100 and therefore there must be 21 per cent. (more or less closely, cf. §§ 7, 8 below) of 4B’s in the universe to justify the conclusion that 4 and B are independent. 3. It follows from § 1 that if the relation (2) holds for any one of the four second-order frequencies, e.g. (4B), similar relations must hold for the remaining three. Thus we have directly from (1)— (4B) _(AB)+(4B) _ (4) > B) @B+B ¥ giving 4)(B) Prml (4B) ="=4 and so on. This is seen at once to be true on consideration of the fourfold table on p. 26. For if (4B) takes the value (4)(B)/N, (AB) must take the value (4)(B3)/N to keep the total of the row equal to (4), and so on for the other rows and columns, The fourfold table in the case of independence must in fact have the form— Attribute. Attribute. Total. - (4XBIN ~~ (4)B)N (4) a (a)(B)/N (a)(B)/N (a) Total {rs a i 2k

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