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

THEORY OF STATISTICS. The frequency-distribution of the number of deaths per army corps per annum was Deaths, Frequency. 0 109 1 65 2 22 2 3 ‘ 1 whence o2=0'6079 o=078 —an almost exact agreement with the standard-deviation of simple sampling. 13. We may now turn from these verifications of the theoretical results for various special cases, to the use of the formule for checking and controlling the interpretation of statistical results. If we observe, in a statistical sample, a certain proportion of objects or individuals possessing some given character—say A’'s— this proportion differing more or less from the proportion which for some reason we expected, the question always arises whether the difference may be due to the fluctuations of simple sampling only, or may be indicative of definite differences between the conditions in the universe from which the sample has been drawn and the assumed conditions on which we based our expectation. Similarly, if we observe a different proportion in one sample from that which we have observed in another, the question again arises whether this difference may be due to fluctuations of simple sampling alone, or whether it indicates a difference between the conditions subsisting in the universes from which the two samples were drawn : in the latter case the difference is often said to be significant. These questions can be answered, though only more or less roughly at present, by comparing the observed difference with the standard-deviation of simple sampling. We know roughly that the great bulk at least of the fluctuations of samp- ling lie within a range of + three times the standard-deviation ; and if an observed difference from a theoretical result greatly exceeds these limits it cannot be ascribed to a fluctuation of “simple sampling ” as defined in § 8: it may therefore be signifi- cant. The “standard-deviation of simple sampling” being the basis of all such work, it is convenient to refer to it by a shorter name. The observed proportions of A’s in given samples being regarded as differing by larger or smaller errors from the true proportion in a very large sample from the same material, the 266

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