Gleichberechtigung von Kapital und Arbeit

An Introduction to the theory of statistics

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Monograph

Identifikator:: 1014334349

URN:: urn:nbn:de:zbw-retromon-41140

Document type:: Monograph

Author:: Piechottka, Erwin

Title:: Gleichberechtigung von Kapital und Arbeit

Place of publication:: Berlin

Publisher:: Verlag von Hans Robert Engelmann

Year of publication:: 1921

Scope:: 1 Online-Ressource (64 Seiten)

Digitisation:: 2018

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Die Beteiligungssysteme

Collection:: Economics Books

XI.—CORRELATION : MISCELLANEOUS THEOREMS. 215 or from (9) ov Mie, §2 = TES = 20, + 0,2) (10) 9. Correlation between Indices—(Ref.11.) The following prob- lem affords a further illustration of the use of the same method. Required to find approximately the correlation between two ratios I =2X,|X,, Zy=X,/X,, X; X, and X, being uncorrelated. Let the means of the two ratios or indices be 7; 7, and the standard-deviations s; s,; these are given approximately by (9) and (10) of the last section. The required correlation p will be given by (X X. ¥psysy=3(y' - n)( - r,) XZ =x( =) “NTT MM, ( i ( Zy X Za ¥: Ar Neglecting terms of higher order than the second as before and remembering that all correlations are zero, we have MM, psi8y=—. yr (1 +307) - 1], Le =3: where, in the last step, a term of the order v,* has again been neglected. Substituting from (10) for s; and s,, we have finally— v2 = me {11 P= Jol + v5%)(25? + 25%) gab This value of p is obviously positive, being equal to 05 if vy =v, =7;; and hence even if X; and X, are independent, the in- dices formed by taking their ratios to a common denominator X will be correlated. The value of p is termed by Professor Pearson the “spurious correlation.” Thus if measurements be taken, say, on three bones of the human skeleton, and the measurements grouped in threes absolutely at random, there will, nevertheless, be a positive correlation, probably approaching 05, between the indices formed by the ratios of two of the measurements to the third. To give another illustration, if two individuals both observe the same series of magnitudes quite independently, there may be little, if

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