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. 279 between two observed proportions by equation (6) of that chapter, this may be taken, provided » be large, as approximately the standard-deviation of true differences for the given observed difference. 4. The use of standard errors must be exercised with care. It is very necessary to remember the limited assumptions on which the theory of simple sampling is based, and to bear in mind that it covers those fluctuations alone which exist when all the assumed conditions are fulfilled. The formule obtained for the standard errors of proportions and of their differences have no bearing except on the one question, whether an observed divergence of a certain proportion from a certain other proportion that might be observed in a more extended series of observations, or that has actually been observed in some other series, might or might not be due to fluctuations of simple sampling alone. Their use is thus quite restricted, for in many cases of practical sampling this is not the principal question at issue. The principal question in many such cases concerns quite a different point, viz. whether the observed proportion = in th: sample may not diverge from the proportion p existing in the universe from which it was drawn, owing to the nature of the conditions under which the sample was taken, = tending to be definitely greater or definitely less than p. Such divergence between 7 and p might arise in two distinct ways, (1) owing to variations of classification in sorting the 4’s and os, the characters not being well defined—a source of error which we need not further discuss, but one which may lead to serious results [cf. ref. 5 of Chap. V.]. (2) Owing to either 4’s or as tending to escape the attentions of the sampler. To give an illustration from artificial chance, if on drawing samples from a bag containing a very large number of black and white balls the observed proportion of black balls was =, we could not necessarily infer that the proportion of black balls in the bag was approximately =, even though the standard error were small, and we knew that the proportions in successive samples were subject to the law of simple sampling. For the black balls might be, say, much more highly polished than the white ones, so as to tend to escape the fingers of the sampler, or they might be re- presented by a number of lively black insects sheltering amongst white stones: in neither case would the ratio of black balls to white, or of insects to stones, be represented in their proper pro- portions. Clearly, in any parallel case, inferences as to the material from which the sample is drawn are of a very doubtful and uncertain kind, and it is this uncertainty whether the chance of inclusion in the sample is the same for 4’s and o’s, far more than the mere divergences between different samples drawn in

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