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 I. The theory of atributes

Collection:: Economics Books

V.—MANIFOLD CLASSIFICATION. 73 (2) Lrers, G. F., ‘““Die Bestimmung der Abhingigkeit zwischen den Merkmalen eines Gegenstandes,” Berichte der math.-phys. Klasse der kgl. Sachsischen Gesellschaft der Wissenschaften ; Leipzig, 1905. (A general discussion of the problems of association and contingency.) (3) PEARSON, KARL, “On a Coefficient of Class Heterogeneity or Divergence,” Biometrika, vol. v. p. 198, 1906. (An application of the contingency coefficient to the measurement of heterogeneity, e.g. in different districts of a country, by treating the observed frequencies of some quality A,, A, . ... A, in the different districts as rows of a con- tingency table and working out the coefficient: the same principle is also applicable to the comparison of a single district with the rest of the country.) Isotropy. (4) Youre, G. U., “On a Property which holds good for all Groupings of a Normal Distribution of Frequency for Two Variables, with applications to the Study of Contingency Tables for the Inheritance of Unmeasured Qualities,” Proc. Roy. Soc., Series A, vol. lxxvii., 1906, p. 324. (On the property of isotropy and some applications.) (6) YuLe, G. U., “On the Influence of Bias and of Personal Equation in Statistics of Ill-defined Qualities,” Jour. Anthrop. Inst., vol. Xxxvi., 1906, p. 325. (Includes an investigation as to the influence of bias and of personal equation in creating divergences from isotropy in contingency tables.) Contingency Tables of two Rows only. (6) PEARSON, KARL, “On a New Method of Determining Correlation between a Measured Character 4 and a Character B of which only the Percentage of Cases wherein B exceeds (or falls short of) a given Intensity is recorded for each Grade of 4,” Biometrika, vol. vii., 1909, p. 96. (Deals with a measure of dependence for a common type of table, e.g. a table showing the numbers of candidates who passed or failed at an examination, for each year of age. The table of such a type stands between the con- tingency tables for unmeasured characters and the correlation table (chap. 1x.) for variables. Pearson’s method is based on that adopted for the correlation table, and assumes a normal distribution of fre- quency (chap. xv.) for B.) (7) PearsoN, KARL, “On a New Method of Determining Correlation, when one Variable is given by Alternative and the other by Multiple Categories,” Biometrika, vol. vii., 1910, p. 248. (The similar problem for the case in which the variable is replaced by an un- measured quality.) EXERCISES. (1) (Data from Karl Pearson, ‘“ On the Inheritance of the Mental and Moral Characters in Man,” Jour. of the Anthrop. Inst., vol. xxxiil., and Biometrika, vol. iii.) Find the coefficient of contingency (coefficient of mean square contingency) for the two tables below, showing the resemblance between brothers for athletic capacity and between sisters for temper. Show that neither table is even remotely isotropic. {As stated in § 7, the coefficient of contingency should not as a rule be used for tables smaller than 5 x 5-fold : these small tables are given to illustrate the method, while avoiding lengthy arithmetic.) “ =

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