An Introduction to the theory of statistics

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Monograph

Identifikator:: 882692321

URN:: urn:nbn:de:zbw-retromon-5020

Document type:: Monograph

Author:: Agahd, Konrad http://d-nb.info/gnd/116256575; Schulz, Max von http://d-nb.info/gnd/1033198951

Title:: Gesetz betreffend Kinderarbeit in gewerblichen Betrieben

Edition:: Zweite Auflage, neub bearbeitet

Place of publication:: Jena

Publisher:: Verlag von Gustav Fischer

Year of publication:: 1904

Scope:: 1 Online-Ressource (X, 168 Seiten)

Digitisation:: 2017

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Zweiter Teil. Kommentar zum Reichsgesetz, betreffend Kinderarbeit in gewerblichen Betrieben vom 30. März 1903

Collection:: Economics Books

XVL.—NORMAL CORRELATION. ) each of the two variables may be regarded as the sum, or some slightly more complex function, of a large number of elementary component variables, the intensity of correlation depending on the proportion of the components common to the two variables. Stature is a highly compound character of this kind, and we have seen that, in one instance at least, the distribution of stature for a number of adults is given approximately by the normal curve. We can now utilise Table IIL., Chap. IX, p. 160, showing the correlation between stature of father and son, to test, as far as we can by elementary methods, whether the normal surface will fit the distribution of the same character in pairs of indi- viduals : we leave it to the student to test, as far as he can do so by simple graphical methods, the approximate normality of the total distributions for this table. The first important property of the normal distribution is the linearity of the regression. This was well illustrated in fig. 37, p. 174, and the closeness of the regression to linearity was confirmed by the values of the correlation-ratios (p. 206), viz, 0-52 in each case as com- pared with a correlation of 0-51. Subject to some investiga- tion as to the possibility of the deviations that do occur arising as fluctuations of simple sampling, when drawing samples from a record for which the regression is strictly linear, we may conclude that the regression is appreciably linear, 9. The second important property of the normal distribution for two variables is the constancy of the standard-deviation for all parallel arrays. We gave in Chap. X. p. 204 the standard- deviations of ten of the columns of the present table, from the column headed 62:5-635 onwards ; these were— 2:56 2:60 2°11 2:26 2-55 2-26 2-24 245 2:23 2:33 the mean being 2:36. The standard-deviations again only fluctuate irregularly round their mean value. The mean of the first five is 2:34, of the second five 2-38, a difference of only 0:04: of the first group, two are greater and three are less than the mean, and the same is true of the second group. There does not seem to be any indication of a general tendency for the standard- deviation to increase or decrease as we pass from one end of the table to the other. We are not yet in a position to test how far the differences from the average standard deviation might arise in sampling from a record in which the distribution was 3925

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