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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Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

XIL—PARTIAL CORRELATION. l The student should notice that the set of three coefficients of order zero and value unity are only consistent if either one only, or all three, are positive, z.e. +1, +1, +1,0r = 1, —=1, +1; but not —1, —1, —1. On the other hand, the set of three coefficients of the first order and value unity are only consistent if one only, or all three, are negative: the only consistent sets are +1, +1, —land —1, —1, —1. The values of the two given 7’s need to be very high if even the sign of the third can be inferred ; if the two are equal, they must be at least equal to 4/05 or *707 . . . . Finally, it may be noted that no two values for the known coefficients ever permit an inference of the value zero for the third ; the fact that 1 and 2, 1 and 3 are uncorrelated, pair and pair, permits no inference of any kind as to the correlation between 2 and 3, which may lie anywhere between +1 and — 1, 19. We do not think it necessary to add to this chapter a detailed discussion of the nature of fallacies on which the theory of multiple correlation throws much light. The general nature of such fallacies is the same as for the case of attributes, and was discussed fully in Chap. IV. §§ 1-8. It suffices to point out the principal sources of fallacy which are suggested at once by the form of the partial correlation 7, =n eee ° a eT) & and from the form of the corresponding expression for r, in terms of the partial coefficients Premills b TTR, b li (1 = risa)(1 = 731) 2) From the form of the numerator of (a) it is evident (1) that even if 7, be zero, ry,, will not be zero unless either 7,5 or 7,, or both, are zero. If 7; and 7,, are of the same sign the partial correlation will be negative ; if of opposite sign, positive. = Thus the quantity of a crop might appear to be unaffected, say, by the amount of rainfall during some period preceding harvest : this might be due merely to a correlation between rain and low temperature, the partial correlation between crop and rainfall being positive and important. We may thus easily misinterpret a coefficient of correlation which is zero. (2) 7,55 may be, indeed often is, of opposite sign to 7, and this may lead to still more serious errors of interpretation, From the form of the numerator of (5), on the other hand, we see that, conversely, r,, will not be zero even though 7, , is zero, unless either r,, or ry, is zero. This corresponds to the theorem 925°

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