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. if p is, say, 1/3, and not 1/2 owing to the black balls, for some os tending to slip through our fingers. (Cf. Chap. XIV. S 4. 9. It is evident that these conditions very much limit the field of practical cases of an economic or sociological character to which formule (1) and (2) can apply without considerable modification. The formule appear, however, to hold to a high degree of approximation in certain biological cases, notably in the proportions of offspring of different types obtained on crossing hybrids, and, with some limitations, to the proportions of the two sexes at birth. It is possible, accordingly, that in these cases all the necessary conditions are fulfilled, but this is not a necessary inference from the mere applicability of the formule (cf. Chap. XIV. § 15). In the case of the sex-ratio at birth, it seems doubtful whether the rule applies to the frequency of the sexes in individual families of given numbers (ref. 9), but it does apply fairly closely to the sex-ratios of births in different localities, and still more closely to the ratios in one locality during successive periods. That is to say, if we note the number of males in a series of groups of » births each, the standard-deviation of that number is approximately a/mpg, where p is the chance of a male birth; or, otherwise, a/pg/n is the standard-deviation of the proportion of male births. We are not able to assign an a priors value to the chance p as in the case of dice-throwing, but it is quite sufficiently accurate for practical purposes to use the proportion of male births actually observed if that proportion be based on a moderately large number of observations. 10. In Table VI. of Chap. IX. (p. 163) was given a correlation- table between the total numbers of births in the registrationdistricts of England and Wales during the decade 1881-90 and the pro- portion of male births. The table below gives some similar figures, based on the same data, for a few isolated groups of districts con- taining not less than 30 to 40 districts each. In both tables the drop in dispersion as we pass from the small to the large districts is extremely striking. The actual standard-deviations, and the standard-deviations of simple sampling corresponding to the mid- numbers of births, are given at the foot of the table, and it will be seen that the two agree, on the whole, with surprising closeness, considering the small numbers of observations. The actual standard-deviation is, however, the larger of the two in every case but one. The corresponding standard-deviations for Table VI. of Chap. IX. are given in Qu. 7 at the end of this chapter, and show the same general agreement with the standard-deviations of simple sampling ; the actual standard-deviations are, however, again, as a rule, slightly in excess of the theoretical values. 269

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