Inkassotarif für Asien, Afrika und Australien

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Monograph

Identifikator:: 890236992

URN:: urn:nbn:de:zbw-retromon-15675

Document type:: Monograph

Author:: Wehberg, Heinrich http://d-nb.info/gnd/1054450218

Title:: Die Bodenreform im Lichte des humanistischen Sozialismus

Place of publication:: München

Publisher:: Verlag von Duncker & Humblot

Year of publication:: 1913

Scope:: 1 Online-Ressource (XIII,170 Seiten)

Digitisation:: 2017

Collection:: Economics Books

Usage license:: Get license information via the feedback formular.

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Document type:: Monograph

Structure type:: Chapter

Title:: II. Die Bodenreform im Lichte des Freihandels. 1891

Collection:: Economics Books

CHAPTER XVI, NORMAL CORRELATION. 1-3. Deduction of the general expression for the normal correlation surface from the case of independence—4. Constancy of the standard- deviations of parallel arrays and linearity of the regression—5. The contour lines: a series of concentric and similar ellipses—6. The normal surface for two correlated variables regarded as a normal surface for uncorrelated variables rotated with respect to the axes of measurement : arrays taken at any angle across the surface are normal distributions with constant standard-deviation : distribution of and correlation between linear functions of two normally correlated variables are normal : principal axes—7. Standard-deviations round the principal axes—8-11. Investigation of Table II1., Chap. IX., to test normality : linearity of regression, constancy of standard-deviation of arrays, normality of distribution obtained by diagonal addition, contour lines—12-13. Isotropy of the normal distribution for two variables—14. Outline of the principal properties of the normal dis- tribution for n variables. 1. THE expression that we have obtained for the “normal” dis- tribution of a single variable may readily be made to yield a corresponding expression for the distribution of frequency of pairs of values of two variables. This normal distribution for two variables, or “normal correlation surface,” is of great historical importance, as the earlier work on correlation is, almost with- out exception, based on the assumption of such a distribution ; though when it was recognised that the properties of the correla- tion-coeflicient could be deduced, as in Chap. IX., without reference to the form of the distribution of frequency, a knowledge of this special type of frequency-surface ceased to be so essential. But the generalised normal law is of importance in the theory of sampling : it serves to describe very approximately certain actual distributions (e.g. of measurements on man) ; and if it can be assumed to hold good, some of the expressions in the theory of correlation, notably the standard-deviations of arrays (and, if more than two variables are involved, the partial correlation- coefficients), can be assigned more simple and definite meanings than in the general case. The student should, therefore, be familiar with the more fundamental properties of the distribution. 317

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