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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Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Theory of sampling

Collection:: Economics Books

XIV.—REMOVING LIMITATIONS OF SIMPLE SAMPLING. 289 standard-deviation in some case of sampling exceeds the standard- deviation of simple sampling, two interpretations are possible : either that p and ¢ are different in the various universes from which samples have been drawn (i.e. that the variations are more or less definitely significant in the sense of § 13, Chap. XIII), or that the results of the events are positively correlated inter se. If the actual standard-deviation fall short of the standard- deviation of simple sampling two interpretations are again possible, esther that the chances p and ¢ vary for different individuals or sub-classes in each universe, while approximately constant from one universe to another, or that the results of the events are negatively correlated inter se. Even if the actual standard-deviation approaches closely to the standard- deviation of simple sampling, it is only a conjectural and not a necessary inference that all the conditions of * simple sampling ” as defined in § 8 of the last chapter are fulfilled. Possibly, for example, there may be a positive correlation » between the results of the different events, masked by a variation of the chances p and ¢ in sub-classes of each universe. Sampling which fulfils the conditions laid down in § 8 of Chap. XIII., simple sampling as we have called it, is generally spoken of as random sampling. We have thought it better to avoid this term, as the condition that the sampling shall be random—haphazard—is not the only condition tacitly assumed. REFERENCES. go generally the references to Chap. XIIL, to which may be aadaea— (1) PEARSON, KARL, ‘“ On certain Properties of the Hypergeometrical Series, and on the fitting of such Series to Observation Polygons in the Theory of Chance,” Philosophical Magazine, 5th Series, vol. xlvii., 1899, p. 236. (An expansion of one section of ref. 10 of Chap. XIII., dealing with the first problem of our § 14, i.e. drawing samples from a bag containing a limited number of white and black balls, from the standpoint of the frequency-distribution of the number of white or black balls in the samples, ) (2) GREENWOOD, M., “On Errors of Random Sampling in certain Cases not suitable for the Application of a ‘ Normal Curve of Frequency,’ Bio- metrika, vol. ix., 19183, pp. 69-90. (If an event has succeeded p times in n trials,what are the chances of 0, 1, . . . m successes in m subsequent trials! Tables for small samples.) EXERCISES. 1. Referring to Question 7 of Chap. XIII, work out the values of the significant standard-deviation o, (as in § 10) for each row or group of rows there given, but taking row 5 with rows 6 and 7, 19

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