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An Introduction to the theory of statistics

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Monograph

Identifikator:: 882692321

URN:: urn:nbn:de:zbw-retromon-5020

Document type:: Monograph

Author:: Agahd, Konrad http://d-nb.info/gnd/116256575; Schulz, Max von http://d-nb.info/gnd/1033198951

Title:: Gesetz betreffend Kinderarbeit in gewerblichen Betrieben

Edition:: Zweite Auflage, neub bearbeitet

Place of publication:: Jena

Publisher:: Verlag von Gustav Fischer

Year of publication:: 1904

Scope:: 1 Online-Ressource (X, 168 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:: Erster Teil. Betrachtungen zum Kinderschutzgesetz

Collection:: Economics Books

CHAPTER XIV SIMPLE SAMPLING CONTINUED: EFFECT OF REMOVING THE LIMITATIONS OF SIMPLE SAMPLING. 1. Warning as to the assumption that three times the standard error gives the range for the majority of fluctuations of simple sampling of either sign —2. Warning as to the use of the observed for the true value of p in the formula for the standard error—3. The inverse standard error, or standard error of the true proportion for a given observed proportion : equivalence of the direct and inverse standard errors when = is large— 4-8. The importance of errors other than fluctuations of ‘‘simple sampling ” in practice: unrepresentative or biassed samples—9-10. Effect of divergences from the conditions of simple sampling: (a) effect of variation in p and ¢ for the several universes from which the samples are drawn—11-12. (5) Effect of variation in p and ¢ from one sub-class to another within each universe—13-14. (¢) Effect of a correlation between the results of the several events—15. Summary. 1. THERE are two warnings as regards the methods adopted in the examples in the concluding section of the last chapter which the student should note, as they may become of importance when the number of observations is small. In the first place, he should remember that, while we have taken three times the standard error as giving the limits within which the great majority of errors of sampling of either sign are contained, the limits are not, as a rule, strictly the same for positive and for negative errors. As is evident from the examples of actual distributions in § 7, Chap. XIII, the distribution of errors is not strictly symmetrical unless p=¢=05. No theoretical rule as to the limits can be given, but it appears from the examples referred to and from the calculated distributions in Chap. XV. § 3, that a range of three times the standard error includes the great majority of the deviations in the direction of the longer “tail” of the distribution, while the same range on the shorter side may extend beyond the limits of the distribution altogether. If, therefore, p be less than 0°5, our assumed range may be greater than is possible for negative errors, or if p be a )Y x

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