Das Kapital: Der Produktionsprozeß des Kapitals

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Identifikator:: 1780159447

Document type:: Multivolume work

Author:: Marx, Karl http://d-nb.info/gnd/118578537

Title:: Das Kapital

Place of publication:: Berlin

Publisher:: J. H. W. Dietz Nachf., G. m. b. H.

Year of publication:: 1926-

Collection:: Economics Books

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Volume

Identifikator:: 1780159595

URN:: urn:nbn:de:zbw-retromon-188277

Document type:: Volume

Author:: Marx, Karl http://d-nb.info/gnd/118578537

Title:: Der Produktionsprozeß des Kapitals

Volume count:: 1.1928

Place of publication:: Berlin

Publisher:: J. H. W. Dietz Nachf., G. m. b. H.

Year of publication:: 1928

Scope:: XLVIII, 768 Seiten

Digitisation:: 2022

Collection:: Economics Books

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

Document type:: Multivolume work

Structure type:: Contents

Collection:: Economics Books

SUPPLEMENTS—GOODNESS OF FIT. 373 the reduction of which, its integration, can be effected in terms of x by methods described in text-books of the integral calculus. Everything turns, therefore, upon the computation of the function y. As we have seen, x? is determined by evaluating the standard deviations of the n variables and their correlations two at a time (the higher partials being deducible if the correlations of zero order are known). By an application of the method of p. 257, we have = {1 R2\"p ts V y1-3)% for the standard error of sampling in the content of the pth class ; while by a similar adaptation of the reasoning on p. 342 we reach J npg Eps No yo, for the correlation of errors of sampling in the pt* and ¢'® classes. With these data, x? can be deduced (the actual process of reduc- tion is somewhat lengthy, but the student should have no difficulty in following the steps given in pp. 370-2 of ref. 74, infra). Its value is =F nl n=0 Nin the summation extending to all n+ 1 classes of the frequency distribution. Values of the probability that an equally likely or less likely system of deviations will occur, usually denoted by the letter P, have been computed for a considerable range of x? and of n' =n + 1 =the number of classes, and are published in the Tables for Statisticians and Biometricians mentioned on p. 358. The arithmetical process is illustrated upon the two examples of dice-throwing given on p. 258. There are three points which the student should note as regards the practical application of the method. In the first place, the proof given assumes that deviations from the expected frequencies follow the normal law. This is a reasonable assumption only if no theoretical frequency is very small, for if it is very small the distribution of deviations will be skew and not normal. It is desirable, therefore, to group together the small frequencies in the “tail” of the frequency distribution, as is done in the second illustration below, so as to make the expected frequency a few units at least. In the case of the first illustration it might have been better to group the frequency of 0 successes with that of

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