Die Schweiz

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Monograph

Identifikator:: 834699508

URN:: urn:nbn:de:zbw-retromon-88487

Document type:: Monograph

Author:: Zauschner, E.

Title:: Die Zollgesetze der österreichisch-ungarischen Monarchie nach dem gegenwärtigen Stande der Gesetzgebung nebst allen auf die Einhebung und Verwaltung der Zölle Bezug habenden Vorschriften und Erlässen

Place of publication:: Wien

Publisher:: Beck

Year of publication:: 1871

Scope:: 1 Online-Ressource (LVII, 525 S.)

Collection:: Economics Books

Usage license:: Get license information via the feedback formular.

XIIL.—SIMPLE SAMPLING OF ATTRIBUTES. 271 The actual difference is 3-0 per cent., or over 5 times this, and could not have arisen through the chances of simple sampling. If we assume that the difference is a real one and calculate the standard error by equation (6), we arrive at the same value, viz. 0-56 per cent. With such large samples the difference could not, accordingly, be obliterated by the fluctuations of simple sampling alone. Case III.—Two samples are drawn from distinct material or different universes, as in the last case, giving proportions of 4A’s p, and p,, but in lieu of comparing the proportion p, with py it is compared with the proportion of 4’s in the two samples together, viz. p,, where, as before, 2 TP tT np, OC mtn Required to find whether the difference between p, and p, can have arisen as a fluctuation of simple sampling, p, being the true proportion of 4’s in both samples. This case corresponds to the testing of an association which is indicated by a comparison of the proportion of 4’s amongst the B’s with the proportion of A4’s in the universe. The general treatment is similar to that of Case II., but the work is complicated owing to the fact that errors in p, and p, are not independent. If ¢, be the standard error of the difference between p, and Py We have at once a =6+6—2r,. qq 1 1 1 =pq r= rp ! Yn +m, on, Nn, +n, Ta being the correlation between errors of simple sampling in py and p,. But, from the above equation relating p, to Py and p,, writing it in terms of deviations in p, p, and 2 multiplying by the deviation in p, and summing, we have, since errors in p, and p, are uncorrelated, 2% q Ta rte nin 17% 177% Therefore finally & = Pd ny Yimin @ Unless the difference between py and p, exceed, say, some three times this value of ¢, it may have arisen solely by the chances of simple sampling.

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