An Introduction to the theory of statistics

Bibliographic data

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. of Chap. IV. § 6, and indicates a source of fallacies similar to those there discussed. 20. We have seen (§ 9) that r,, is the correlation between x, , and x,,, and that we might determine the value of this partial correlation by drawing up the actual correlation table for the two residuals in question. Suppose, however, that instead of drawing up a single table we drew up a series of tables for values of x, and z,, associated with values of x, lying within successive class-intervals of its range. In general the value of r,,, would not be the same (or approximately the same) for all such tables, but would exhibit some systematic change as the value of x, increased. Hence 7, should be regarded, in general, as of the nature of an average correlation: the cases in which it measures the correlation between x,, and x,, for every value of x, (cf. Chap. XVI.) are probably exceptional. The process for deter- mining partial associations (¢f. Chap. IV.) is, it will be remembered, thorough and complete, as we always obtain the actual tables exhibiting the association between, say, 4 and B in the universe of C’s and the universe of y's: that these two associations may differ materially, is illustrated by Example i. of Chap. IV. (pp. 45-6). It might sometimes serve as a useful check on partial-correlation work to reclassify the observations by the fundamental methods of that chapter. For the general case an extension of the method of the “ correlation-ratio ” (Chap. X., § 20) might be useful, though exceedingly laborious. It is actually employed in the paper cited in ref. 7 and the theory more fully developed in ref. 8. REFERENCES. The preceding chapter is written from the standpoint of refs. 3 and 4, and with the notation and method of ref. 5. The theory of correlation for several variables was developed by Edgeworth and Pearson (refs. 1 and 2) from the standpoint of the normal ” distribution of frequency (cf. Chap. XVL.). Theory. (1) EpGEWoRTH, F. Y., “On Correlated Averages,” Phil. Mag., 5th Series, vol. xXxiv., 1892, p. 194. (2) PEARSON, KARL, ‘ Regression, Heredity, and Panmixia,” Phil. Trans. Roy. Soc., Series A, vol. clxxxvii., 1896, p. 253. (3) YULE, G. U., *“On the Significance of Bravais’ Formulae for Regression, etc., in the case of Skew Correlation,” Proc. Roy. Soc., vol. Ix., 1897, p. 477. (4) YULE, G. U., “On the Theory of Correlation,” Jour. Roy. Stat. Soc., vol. 1x., 1897, p. 812. (5) YULE, G. U., “On the Theory of Correlation for any number of Variables treated by a New System of Notation,” Proc. Roy. Soc., Series A, vol. 1xxix., 1907, p. 182. (6) HOOKER, R. H., and G. U. YULE, ‘Note on Estimating the Relative Influence of Two Variables upon a Third,” Jour. Roy. Stat. Soc., vol. Ixix., 1906, p. 197. (7) BROWN, J. W., M. GREENWOOD, and FRANCES Woob, “A Study of Index-Corre- lations,” Jour. Roy. Stat. Soc., vol. 1xxvii., 1614, pp. 317-46. (The partial or “solid ” correlation-ratio is used.) : " ; (8) ISSERLIS, L., “On the Partial Correlation-Ratio, Pt. I. Theoretical,” Biometrika, vol. x., 1914, pp. 391-411. 259

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