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

X.—CORRELATION : ILLUSTRATIONS AND METHODS. 197 harvest are themselves very largely dependent on the weather, and consequently, on an average of many years, the limits of the critical period will not be very well defined. If, therefore, we correlate the produce of the crop (X) with the characteristics of the weather (¥) during successive tervals of the year, it will be as well not to make these intervals too short. It was accordingly decided to take successive groups of 8 weeks, over- lapping each other by 4 weeks, 7.e. weeks 1-8, 5-12, ete. Correlation coefficients were thus obtained at 4-weeks intervals, but based on 8 weeks’ weather. 13. It remains to be decided what characteristics of the weather are to be taken into account. The rainfall is clearly one factor of great importance, temperature is another, and these two will afford quite enough labour for a first investigation. The weekly rainfalls were averaged for eight stations within the area, and the average taken as the first characteristic of the weather. Temperatures were taken from the records of the same stations. The average temperatures, however, do not give quite the sort of information that is required: at temperatures below a certain limit (about 42° Fahr.) there is very little growth, and the growth increases in rapidity as the temperature rises above this point (within limits). It was therefore decided to utilise the figures for “accumulated temperatures above 42° Fahr.” i.e. the total number of day-degrees above 42° during each of the 8-weekly periods, as the second characteristic of the weather ; these “accumulated temperatures,” moreover, show much larger variations than mean temperatures. The student should refer to the original for the full dis- cussion as to data. The method of treating the correlations between three variables, based on the three possible correlations between them, is described in Chapter XII. 14. Problems of a somewhat special kind arise when dealing with the relations between simultaneous values of two variables which have been observed during a considerable period of time, for the more rapid movements will often exhibit a fairly close consilience, while the slower changes show no similarity. The two following examples will serve as illustrations of two methods which are generally applicable to such cases. Hlustration iv.—Fig. 41 exhibits the movements of (1) the infantile mortality (deaths of infants under 1 year of age per 1000 births in the same year) ; (2) the general mortality (deaths at all ages per 1000 living) in England and Wales during the period 1838-1904. A very cursory inspection of the figure shows that when the infantile mortality rose from one year to the next the general mortality also rose, as a rule; and similarly, when the

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