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 III. Theory of sampling

Collection:: Economics Books

THEORY OF STATISTICS. The expression in the bracket is usually very nearly unity, for a normal distribution, and in that case may be neglected. Correlation coefficient.—If the distribution be normal, standard error of the cor- | Te relation coefficient for Se : (15) a normal distribution ad This is the value always given: the use of a more general formula which would entail the use of higher moments does not appear to have been attempted. As regards the case of small samples, cf. refs. 10, 28, and 31. Equation (15) gives the standard error of a coeflicient of any order, total or partial (ref. 33). For the standard error of the correlation-coefficient for a fourfold table (Chap. XI., § 10), see ref. 34: the formula (15) does not apply. Coefficient of regression.—If the distribution be normal, standard error of the co- EE efficient of regression 4, » =T2LN- "Tie T12_ (16) for a normal distribution 0) Jn 0, Nn This formula again applies to a regression coefficient of any order, total or partial: ¢.e. in terms of our general notation, £ denoting any collection of secondary subscripts other than 1 or 2, standard error of by, for | im a normal distribution | =o, A/n. Correlation ratio.—The general expression for the standard error of the correlation-ratio is a somewhat complex expression (¢f. Professor Pearson’s original memoir on the correlation-ratio, ref. 18, Chap. X.). In general, however, it may be taken as given sufficiently closely by the above expression for the standard error of the correlation coefficient, that is to say, standard error of correlation- | _ 1-7? (17) ratio approximately dey : As was pointed out in Chap. X,, § 21, the value of {=72—-1%is a test for linearity of regression. Very approximately (Blakeman, ref. 1), standard error of {= Wi JA -p2)2-(1-r22+1. (18) n For rough work the value of the second square root may be taken as nearly unity, and we have then the simple expression, standard error of { roughly = 2 a 19) 352 \ a

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