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

THEORY OF STATISTICS. infantile mortality fell, the general mortality also fell. There were, in fact, only five or six exceptions to this rule during the whole period under review. The correlation between the annual values of the two mortalities would nevertheless not be very high, as the general mortality has been falling more or less steadily since 1875 or thereabouts, while the infantile mortality attained almost a record value in 1899. During a long period of time the correla- tion between annual values may, indeed, very well vanish, for the two mortalities are affected by causes which are to a large extent different in the two cases. To exhibit, therefore, the closeness of the relation between infantile and general mortality, for such causes as show marked changes between one year and the next, it will be best to proceed by correlating the annual changes, and not the annual values. The work would be arranged in the following form (only suflicient years being given to exhibit the principle of the process), and the correlation worked out between the figures of cols. 3 and 5. L. Z, 3. A OD. Infantile Increase or General Increase or Year. Mortality per Decrease from Mortality per Decrease from 1000 Births. Year before. 1000 living. Year before. 1838 150 > 29-4 - 1839 151 -8 218 -06 1840 154 +3 : 229 +11 1841 145 -9 216 -1-3 1842 152 | +7 217 +0°1 1843 150 -2 21-2 -0'5 For the period to which the diagram refers, viz. 1838-1904, the following constants were found by this method :— Infantile mortality, mean annual change — 0-21 standard deviation 9:63 General mortality, mean annual change — 0-09 standard deviation 1°14 Coefficient of correlation + 0-77. This is a much higher correlation than would arise from the mere fact that the deaths of infants form part of the general mortality, and consequently there must be a high correlation between the annual changes in the mortality of those who are over and under 1 year of age. (Cf. Exercises 7 and 8, Chap. XI.) This method, which appears to have been first used by Miss Cave and by Mr Hooker independently in the papers cited in refs. 4 and G6, has recently been generalised by “Student” and the theory fully developed by O. Anderson (cf. refs. 13, 14, 15). By taking the first differences the influence of the slower changes of the two variables with time may not be wholly eliminated, but this elimination may be mniore completely effected by pro- 198

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