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

XII.—PARTIAL CORRELATION, or, transferring the origins to zero, (1) Earnings X;=+190-1-21 X,+0-23 X, (2) Pauperism X,=+955-045 X, +022 X, (3) Out-relief ratio X,= —15-7+ 085 X, +218 X, The units are throughout one shilling for the earnings Xyil per cent. for the pauperism X,, and 1 for the out-relief ratio Xj. The first and second regression-equations are those of most practical importance. The argument has been advanced that the giving of out-relief tends to lower earnings, and the total coefficient (r;= —0'13) between earnings (X;) and out-relief (X,), though very small (¢f. Chap. IX. § 17), does not seem inconsistent with such a hypothesis. The partial correlation coefficient (r3,= +044) and the regression-equation (1), how- ever, indicate that in unions with a given percentage of the population in receipt of relief (X,) the earnings are highest where the proportion of out-relief is highest; and this is, in so far, against the hypothesis of a tendency to lower wages. It remains possible, of course, that out-relief may adversely affect the possibil- ity of earning, e.g. by limiting the employment of the old. As regards pauperism, the argument might be advanced that the observed correlation (ry; = +060) between pauperism and out- relief was in part due to the negative correlation (r;3=-1013) between earnings and out-relief. Such a hypothesis would have little to support it in view of the smallness and doubtful signifi- cance of ry; and is definitely contradicted by the positive partial correlation 7,,, = + 0°69, and the second regression-equation. The third regression-equation shows that the proportion of out-relief is on the whole highest where earnings are highest and pauperism greatest. It should be noticed, however, that a negative ratio is clearly impossible, and consequently the relation cannot be strictly linear; but the third equation gives possible (positive) average ratios for all the combinations of pauperism and earnings that actually occur. Example ii.—(Four variables.) As an illustration of the form of the work in the case of four variables, we will take a portion of the data from another investigation into the causation of pauperism, viz. that described in the first illustration of Chapter X., to which the student should refer for details. The variables are the ratios of the values in 1891 to the values in 1881 (taken as 100) of— 1. The percentage of the population in receipt of relief, 2. The ratio of the numbers given outdoor relief to the numbers relieved in the workhouse, 3. The percentage of the population over 65 years of age, qr 241 10

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