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

XI.—CORRELATION : MISCELLANEOUS THEOREMS. 219 two records are mingled, unless the mean value of X in the second record is identical with that in the first record, or the mean value of Y in the second record is identical with that in the first record, or both. This follows almost at once, for if M,, M, are the mean values of X in the two records K,, K, the mean values of ¥, N,, N, the numbers of observations, and M, KX the means when the two records are mingled, the product-sum of deviations about 27, X is Ny (My — M)(K, - K) + N(M,- M)(K,- K). Evidently the first term can only be zero if M=M or K=K,. But the first condition gives NM +N, M, is St = M. » that is, A =f, Similarly, the second condition gives K,=K, Both the first and second terms can, therefore, only vanish if A=, or K,=K, Correlation may accordingly be created by the mingling of two records in which X and ¥ vary round different means. (For a more general form of the theorem cf. ref. 20) 13. Reduction of Correlation due to mingling of uncorrelated with correlated pairs.—Suppose that n, observations of z and y give a correlation-coefficient x / oe ey) n,o,0, Now let m, pairs be added to the material, the means and standard-deviations of x and » being the same as in the first series of observations, but the correlation zero. The value of 3(xy) will then be unaltered, and we will have r= xy) (ng +ny)o,0, Whence a P_, (14) ry nt Suppose, for example, that a number of bones of the human skeleton have been disinterred during some excavations, and a correlation 7, is observed between pairs of bones presumed to come from the same skeleton, this correlation being rather lower than might have been expected, and subject to some uncertainty owing to doubts as to the allocation of certain bones. If 7, is the value that would be expected from other records, the difference might be accounted for on the hypothesis

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