Volume XIV 
JULY, 1922 
NOS. 1 AND 2 
BIOMETRIKA 
THE STANDARD DEVIATIONS OF FRATERNAL 
AND PARENTAL CORRELATION COEFFICIENTS. 
By KIRSTINE SMITH, D.Sc, Lond. 
CONTENTS. 
Introduction ............... 1 
I. Fraternal Correlation ............. 2 
(a) The mean value ............. 3 
(h) The mean value of o-^ — the joresitwi^ilii'e standard deviation 3 
(e) The standard deviation of o-- • ■ . 4 
(d) Mean value and standard deviation of the product moment n .... 7 
(e) The product moment, nn(T^, of n and o-^ ........ 8 
(/) The standard deviation of the fraternal correlaticjn coefficient .... 8 
(g) Numerical evaluation of the formula for the standard deviation of a fraternal 
correlation coefficient ............ 9 
(A) Application of the formula to previous calculations of correlation . . .11 
II. Parental Correlation ............. 12 
(a) Mean value and standard deviation of the product moment n^^ . . . .13 
(6) The product moment, Hj^^^y^, of IIi.,, and o-- 15 
(c) The product moment, IIjj^.,^ o-'a, of and tr'-. ....... 16 
(d) The product inoment, Ilo-a^o-'-) of o"^ <wid o-" ........ 16 
(e) The standard deviation of the 2)arental correlation coefficient . . . .16 
(/ ) The standard deviation of the slopes of the regression curves . . . .17 
(g) Numei'ical evaluation of the formula for the standard deviation of a parental 
correlation coefficient ............ 18 
(A) Application of the formula to previous calculations of correlation ... 20 
Summary ............... 21 
Introduction. 
No attempts have been made as for as I know to calculate special formulae for 
the standai'd deviations of fraternal and parental correlation coefficients. The 
usual formula for tlie standard deviation of a correlation coefficient* which is 
deduced on the supposition that the values of the same variable are mutually 
uncorrelated is generally used also for this case, although it is only correct for a 
* Vide Pearson and Filon; Phil. Trans. Vol. 191 a, p. 229, 1898. 
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