Geschichte der volkswirtschaftlichen Lehrmeinungen

An Introduction to the theory of statistics

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Monograph

Identifikator:: 1010911953

URN:: urn:nbn:de:zbw-retromon-20641

Document type:: Monograph

Author:: Gide, Charles http://d-nb.info/gnd/117543985; Rist, Charles http://d-nb.info/gnd/172332966

Title:: Geschichte der volkswirtschaftlichen Lehrmeinungen

Edition:: Nach der zweiten durchgesehenen und verbesserten Ausgabe, herausgegeben von Franz Oppenheimer

Place of publication:: Jena

Publisher:: Verlag von Gustav Fischer

Year of publication:: 1913

Scope:: 1 Online-Ressource (XXII, 828 Seiten)

Digitisation:: 2018

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Erstes Buch. Die Begründer

Collection:: Economics Books

2x) THEORY OF STATISTICS. another card, e.g. that if the first card drawn at any sampling bears a high value, the next and following cards of the same sample are likely to bear high values also. Under these circum- stances, if 7, denote the correlation between the values on the first and second cards, and so on, ES 5 == +25(rp +r + gC pe El Ba 0 There are n(n —1)/2 correlations; and if, therefore, r is the arithmetic mean of them all, we may write : Or on=—{1+7r(n-1)] . . (LLY As the means and standard-deviations of #;, x, . . . . #, are all identical, » may more simply be regarded as the correlation coefficient for a table formed by taking all possible pairs of the n values in every sample. If this correlation be positive, the standard error of the mean will be increased, and for a given value of » the increase will be the greater, the greater the size of the samples. If » be negative, on the other hand, the standard error will be diminished. Equation (11) corresponds precisely to equation (6), § 13, of Chap. XIV. As was pointed out in that chapter, the case when » is positive covers the case discussed under (a): for if we draw successive samples from different records, such a positive correlation is at once introduced, although the drawings of the several cards a? each sampling are quite independent of one another. Similarly, the case discussed under (6) is covered by the case of negative correlation, for if each card is always drawn from a separate and distinct part of the record, the correlation between any two «’s will on the average be negative : if some one card be always drawn from a part of the record containing low values of the variable, the others must on an average be drawn from parts containing relatively high values. It is as well, however, to keep the cases (a), (8), and (c) distinct, since a positive or negative correlation may arise for reasons quite different from those considered under (a) and (b). 15. With this discussion of the standard error of the arithmetic mean we must bring the present work to a close. To indicate briefly our reasons for not proceeding further with the discussion of standard errors, we must remind the student that in order to express the standard error of the mean we require to know, in addition to the mean itself, the standard-deviation about the mean, or. in other words, the mean (deviation)? with respect to the mean. 2h

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