Essays of Benjamin Franklin

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Monograph

Identifikator:: 1008917265

URN:: urn:nbn:de:zbw-retromon-19129

Document type:: Monograph

Author:: Flückiger, Otto http://d-nb.info/gnd/117736708

Title:: Die Schweiz

Edition:: Zweite Auflage

Place of publication:: Zürich

Publisher:: Druck und Verlag von Schultheß & Co.

Year of publication:: 1914

Scope:: 1 Online-Ressource (VI, 243 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:: Bevölkerung

Collection:: Economics Books

CHAPTER XI. MISCELLANEOUS THEOREMS INVOLVING THE USE OF THE CORRELATION-COEFFICIENT. 1. Introductory—2. Standard-deviation of a sum or diflerence—3-5. In- fluence of errors of observation and of grouping on the standard- deviation—6-7. Influence of errors of observation on the correlations coefficient (Spearman’s theorems)—8. Mean and standard-deviation of an index —9. Correlation between indices — 10. Correlation- coefficient for a two- x two-fold table—11. Correlation-coefficient for all possible pairs of IV values of a variable—12. Correlation due to heterogeneity of material —18, Reduction of correlation due to mingling of uncorrelated with correlated material — 14-17. The weighted mean—18-19. Application of weighting to the correction of death-rates, ete., for varying sex and age-distributions—20. The weighting of forms of average other than the arithmetic mean. L. Ir has already been pointed out that a statistical measure, if it is to be widely useful, should lend itself readily to algebraical treatment. The arithmetic mean and the standard-deviation derive their importance largely from the fact that they fulfil this requirement better than any other averages or measures of dis- persion ; and the following illustrations, while giving a number of results that are of value in one branch or another of statistical work, suffice to show that the correlation-coefficient can be treated with the same facility. This might indeed be expected, seeing that the coefficient is derived, like the mean and standard-devia- tion, by a straightforward process of summation. 2. To find the Standard-deviation of the sum or difference Z of corresponding values of two variables X; and X,. Let 2, x), #, denote deviations of the several variables from their arithmetic means. Then if Z=X +X, evidently f=; + x, 210

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