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

284 THEORY OF STATISTICS. certain registration districts of England, in § 10 of Chap. XIII. p- 263. It will be seen that in the first group of small districts there appears to be a significant standard-deviation of some 6 units in the proportion of male births per thousand, but in the more urban districts this falls to 1 or 2 units; in one case only does s fall short of s,. In the table on p. 283 are given some different data relating to the deaths of women in childbirth in the same groups of districts, and in this case the effect of definite causes is relatively larger, as one might expect. The values of Js? — st suggest an almost uniform significant standard-deviation o,=0'8 in the deaths of women per thousand births, five out of the eight values being very close to this average. The figures of this case also bring out clearly one important consequence of (2), viz. that if we make » large s becomes sensibly equal to o,, while if we make » small s becomes more nearly equal to p,g,/n. Hence if we want to know the significant standard-deviation of the pro- portion p—the measure of its fluctuation owing to definite causes —n should be made as large as possible ; if, on the other hand, we want to obtain good illustrations of the theory of simple sampling n should be made small. If » be very large the actual standard- deviation may evidently become almost indefinitely large com- pared with the standard-deviation of sampling. Thus during the 20 years 1855-74 the death-rate in England and Wales fluctuated round a mean value of 222 per thousand with a standard-devia- tion of 0:86. Taking the mean population as roughly 21 millions, the standard-deviation of sampling is approximately 22 x 978 vo 3 106 =0052 This is only about one twenty-seventh of the actual value. 11. Now consider the effect of altering the second condition of simple sampling, given in § 8 (8) of Chapter XIII., viz. the condition that the chances p and ¢ shall be the same for every die or coin in the set, or the circumstances that regulate the appearance of the character observed the same for every individual or every sub-class in each of the universes from which samples are drawn. Suppose that in the group of n dice thrown the chances for m, dice are p; ¢,; for m, dice, p, ¢,, and so on, the chances varying for different dice, but being constant throughout the experiment. The case differs from the last, as in that the chances were the same for every die, at any one throw, but varied from one throw to another: now they are con- stant from throw to throw, but differ from one die to another as they would in any ordinary set of badly made dice. Required to find the effect of these differing chances.

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