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 II. The theory of variables

Collection:: Economics Books

- THEORY OF STATISTICS holds for all values of @;,, ®, and #; (which are, in our usual notation, deviations from their respective arithmetic means), find the correlations between @,, 2, and «3; in terms of their standard-deviations and the values of a, b and c. 10. What is the effect on a weighted mean of errors in the weights or the quantities weighted, such errors being uncorrelated with each other, with the weights, or with the variables—(1) if the arithmetic mean values of the errors are zero ; (2) if the arithmetic mean values of the errors are not zero ? 11. Cf. (Pearson, ‘‘On a Generalised Theory of Alternative Inheritance,” Phil. Trams., vol. cciii., A; 1904, p. 53). If we consider the correlation between number of recessive couplets in parent and in offspring, in a Mendelian population breeding at random (such as would ultimately result from an initial cross between a pure dominant and a pure recessive), the correlation is found to be 1/3 for a total number of couplets n. If n=1, the only possible numbers of recessive couplets are 0 and 1, and the correlation table between parent and offspring reduces to the form Parent. Offspring. . Total 3 Total Verify the correlation, and work out the association coefficient Q. 12. (Cf. the above, and also Snow, Proc. Roy. Soc., vol. Ixxxiii., B, 1910, Table III, p. 42.) For a similar population the correlation between brothers, assuming a practically infinite size of family, is 5/12. The table is First Brother. Second Brother. | Total. 0 18 2 Tl ° Total NRO! : Verify the correlation, and work out the association coefficient Q. : 18. Referring to the notation of § 10, show that we have the following expressions for the regressions in a fourfold table :— you Nb (4B) (48) op (B)B) (B) (B) yO V5 (4B) — (eB) gp (4)a) (4) (a) Verify on the tables of questions 11 and 12. 228

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