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

XVIL.—SIMPLER CASES OF SAMPLING FOR VARIABLES. 349 «+ . . d, from the mean for a large sample from the entire record, we have 3" dogy igi d ga = R20 ) + JAP). Henra 1 or m= (0 7 To _ Sm = e {10) The last equation again corresponds precisely with that given for the same departure from the rules of simple sampling in the case of attributes (Chap. XIV. § 11., eqn. 4). If, to vary our previous illustration, we had measured the statures of men in each of » different districts, and then proceeded to form a set of samples by taking one man from each district for the first sample, one man from each district for the second sample, and so on, the standard-deviation of the means of the samples so formed would be appreciably less than the standard error of simple sampling ao/s/n. Asa limiting case, it is evident that if the men in each district were all of precisely the same stature, the means of all the samples so compounded would be identical : in such a case, in fact, oy =8,, and consequently o,,=0. To give another illustration, if the cards from which we were drawing samples had been arranged in order of the magnitude of X recorded on each, we would get a much more stable sample by drawing one card from each successive nth part of the record than by taking the sample according to our previous rules—e.g. shaking them up in a bag and taking out cards blindfold, or using some equivalent process. The result is perhaps of some practical interest. It shows that, if we are actually taking samples from a large area, different districts of which exhibit markedly different means for the variable under consideration, and are limited to a sample of =n observations ; if we break up the whole area into n sub-districts, each as homogeneous as possible, and take a contribution to the sample from each, we will obtain a more stable mean by this orderly procedure than will be given, for the same number of observations, by any process of selecting the districts from which samples shall be taken by chance. There may, however, be a greater risk of biassed error. The conclusions seem in accord with common-sense. (c) Finally, suppose that, while our conditions (a) and (3) of § 2 hold good, the magnitude of the variable recorded on one card drawn is no longer independent of the magnitude recorded on RAG N

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