An Introduction to the theory of statistics

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Monograph

Identifikator:: 893136298

URN:: urn:nbn:de:zbw-retromon-77125

Document type:: Monograph

Author:: Preisigke, Friedrich http://d-nb.info/gnd/116281871

Title:: Girowesen im griechischen Ägypten, enthaltend Korngiro, Geldgiro, Girobanknotariat mit Einschluss des Archivwesens

Place of publication:: Strassburg im Elsass

Publisher:: Verlag von Schlesier & Schweikhardt

Year of publication:: 1910

Scope:: 1 Online-Ressource (XVI, 575 Seiten)

Collection:: Economics Books

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345 THEORY OF STATISTICS. standard-deviation, and so on, or if we draw the successive samples from essentially different parts of the same record, the standard error will be greatly increased. For suppose we draw k, samples from the first record, for which the standard-deviation (in an indefinitely large sample) is oy, and the mean differs by d, from the mean of all the records together (as ascertained by large samples in numbers proportionate to those now taken); &, samples from the second record, for which the standard-deviation is o,, and the mean differs by d, from the mean of all the records together, and so on. Then for the samples drawn from the first record the standard error of the mean will be o/,/n, but the distribution will centre round a value differing by d; from the mean for all the records together: and so on for the samples drawn from the other records. Hence, if 0, be the standard error of the mean, XV the total number of samples, Ji Nat, = (iD) + 3k). But the standard-deviation o, for all the records together is given by N.o2 = 2(ka®) + Z(kd?). Hence, writing 2(kd?) = N.s;,, oh mir iol (9) n n This equation corresponds precisely to equation (2) of § 9, Chap. XIV. The standard error of the mean, if our samples are drawn from different records or from essentially different parts of the entire record, may be increased indefinitely as compared with the value it would have in the case of simple sampling. If, for example, we take the statures of samples of # men in a number of different districts of England, and the standard-deviation of all the statures observed is o,, the standard-deviation of the means for the different districts will not be a,/x/n, but will have some greater value, dependent on the real variation in mean stature from district to district. (b) If we are drawing from the same record throughout, but always draw the first card from one part of that record, the second card from another part, and so on, and these parts differ more or less, the standard error of the mean will be decreased. For if, in large samples drawn from the subsidiary parts of the record from which the several cards are taken, the standard- deviations are oy, 0, . . . . On and the means differ by d;, dos LK

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