Die Heimarbeit im Kriege

Bibliographic data

Monograph

Identifikator:: 1029343713

URN:: urn:nbn:de:zbw-retromon-72101

Document type:: Monograph

Author:: Schreiner, Olive http://d-nb.info/gnd/118795457

Title:: Die Frau und die Arbeit

Place of publication:: Jena

Publisher:: Eugen Diederichs

Year of publication:: 1914

Scope:: 1 Online-Ressource (180 Seiten)

Digitisation:: 2018

Collection:: Economics Books

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

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: I. Parasitimus

Collection:: Economics Books

Full text

No full text available for this image

: THEORY OF STATISTICS. variation on the standard-deviation of simple sampling is quite small, for, as calculated from equation (4), #=—(18 x 982 — 900) s=130/n/n as compared with 133/s/n. 13. We have finally to pass to the third condition (c) of § 8, Chap. XIIL, and to discuss the effect of a certain amount of dependence between the several “events” in each sample. We shall suppose, however, that the two other conditions (a) and (0) are fulfilled, the chances p and ¢ being the same for every event at every trial, and constant throughout the experiment. The problem is again most simply treated on the lines of § 5 of the last chapter. The standard-deviation for each event is (pg)! as before, but the events are no longer independent: instead, therefore, of the simple expression 0? =n.pg, we must have (cf. Chap. XL. § 2) o2=npq+2pq(rg +r t «oo Togt ooo) where, 7,4, 7,4, etc. are the correlations between the results of the first and second, first and third events, and so on—correlations for variables (number of successes) which can only take the values 0 and 1, but may nevertheless, of course, be treated as ordinary variables (¢f. Chap. XI. § 10). There are n(n —1)/2 correlation-coefficients, and if, therefore, 7 is the arithmetic mean of the correlations we may write a? =mnpg[l +7(n—-1)]. ; . (Bb) The standard-deviation of simple sampling will therefore be increased or diminished according as the average correlation between the results of the single events is positive or negative, and the effect may be considerable, as o may be reduced to zero or increased to m(pg)t. For the standard deviation of the propor- tion of successes in each sample we have the equation s2 = +r(n-1)] . (8) It should be noted that, as the means and standard-deviations for our variables are all identical, » is the correlation-coefficient for a table formed by taking all possible pairs of results in the n events of each sample. 286

Access restriction

Copyright

fullscreen: Die Heimarbeit im Kriege

Monograph

Chapter

Table of contents

Download

Monograph

Chapter

This page

Image fragment

Citation links

Citation recommendation