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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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part I. The theory of atributes

Collection:: Economics Books

XVIL.—NORMAL CORRELATION, ; this group of four frequencies is also of the same sign as r,, the ratio of the cross-products being unity, or the association zero, if 71, is zero. Ina normal distribution, the association is therefore of the same sign—the sign of rg—for every tetrad of frequencies in the compartments common to two rows and two columns ; that is to say, the distribution is isotropic. It follows that every grouping of a normal distribution is isotropic whether the class- intervals are equal or unequal, large or small, and the sign of the association for a normal distribution grouped down to 2- x 2-fold form must always be the same whatever the axes of division chosen. These theorems are of importance in the applications of the theory of normal correlation to the treatment of qualitative characters which are subjected to a manifold classification. The contingency tables for such characters are sometimes regarded as groupings of a normal distribution of frequency, and the coefficient of correlation is determined on this hypothesis by a rather lengthy procedure (ref. 14). Before applying this procedure it is well, therefore, to see whether the distribution of frequency may be regarded as approximately isotropic, or reducible to isotropic form by some alteration in the order of rows and columns (Chap. V. $3 9-10). If only reducible to isotropic form by some rearrange- ment, this rearrangement should be effected before grouping the table to 2-x 2-fold form for the calculation of the correlation coefficient by the process referred to. If the table is not reducible to isotropic form by any rearrangement, the process of calculating the coefficient of correlation on the assumption of normality is to be avoided. Clearly, even if the table be isotropic it need not be normal, but at least the test for isotropy affords a rapid and simple means for excluding certain distributions which are not even remotely normal. Table II. of Chap. V. might possibly be regarded as a grouping of normally distributed frequency if re- arranged as suggested in § 10 of the same chapter—it would be worth the investigator’s while to proceed further and compare the actual distribution with a fitted normal distribution—but Table IV. could not be regarded as normal, and could not be rearranged so as to give a grouping of normally distributed frequency. 13. If the frequencies in a contingency-table be not large, and also if the contingency or correlation be small, the influence of casual irregularities due to fluctuations of sampling may render it difficult to say whether the distribution may be regarded as essentially isotropic or no. In such cases some further con- densation of the table by grouping together adjacent rows and columns, or some process of “smoothing” by averaging the 326

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