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. Working from the observed proportion of green seeds, viz. 0:2532 instead of the theoretical 0:25, we have s= 7/025 x 0°75/7125 = 0:0051, and similarly the divergence from theory is only some 3/5 of the standard error, as before. It should be noted that this method must not be used as a test of association by comparing the difference of (4B) from (4)(B)/N with a standard error calculated from the latter value as a “theoretical number,” for it is not a theoretical number given a prior: as in the above illustrations, and (4) and (B) are themselves liable to errors of sampling. If we formed an association-table between the results of tossing two coins XV times, o= ,/&.}. 3 would be the standard error for the divergence of (4.8) from the a preore value n/4, not the standard error for differences of (4.5) from (4)(B)/N, (4) and (B) being the numbers of heads thrown in the case of the first and the second coin respectively. Case II.—Two samples from distinct materials or different universes give proportions of A’s p, and p, the numbers of observations in the samples being n, and =, respectively. (a) Can the difference between the two proportions have arisen merely as a fluctuation of simple sampling, the two universes being really similar as regards the proportion of A’s therein? (8) If the difference indicated were a real one, might it vanish, owing to fluctuations of sampling, in other samples taken in precisely the same way? This case corresponds to the testing of an association which is indicated by a comparison of the proportion of 4’s amongst B’s and fs. (¢) We have no theoretical expectation in this case as to the proportion of 4’s in the universe from which either sample has been taken. Let us find, however, whether the observed difference between p, and p, may not have arisen solely as a fluctuation of simple sampling, the proportion of 4’s being really the same in both cases, and given, let us say, by the (weighted) mean proportion in our two samples together, z.e. by py ELT Poly 0" nm +m, (the best guide that we have). Let ¢, €, be the standard errors in the two samples, then & = PoQo/ My & = PQo/ Ma If the samples are simple samples in the sense of the previous work, then the mean difference between p, and p, will be zero, 268

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