No. 599] SHOETER ARTICLES AND DISCUSSION 



703 



%{xf 2 ). Since in a symmetrical intra-class correlation table the 

 variates are weighted in an (n — l)-fold manner the fraternal 

 correlation for males is given at once by direct summation from 

 the data table of Parker and Bullard by the formula, written for 

 simplicity in an entirely unreduced form, 



smxjy - m*J) _ {S[(n m -imx m )]y 



SjnUrhn-1)} \ S[n m (n m -D] J 

 r S[(n m - im xj)} _ /5[(, im -l)2W]V ' 



«w% - 1)] v - 1)] ; 



or substituting actual values 



r^ m2 = .323 ± .019. 



Apparently complex, the formula is really on closer inspection 

 very simple indeed. 



One altogether similar for the females gives the sororal corre- 

 lation 



r XflXji = .373 ± .018. 



Thus the correlation for the females is .050 ± .026 higher than 

 that for the males. 



For the cross correlations, that between number of nipples 

 borne by male and female pigs of the same litter, the constant 

 is given by 



S&jxjZixf)] _ S[n f Z(x m )] Sln^jx/)] 



r . _ S(n m n f ) S( tlf „,„ } X S { n m n f ) 



JSMCV'] _ (S[, lm Zl.r,-)\ y N[///-(j* m 2 )] _ (S[n f Z(x f )]Y 

 * Sirun,) \ S{n m n f ) ) \ S( nf n m ) \ Sfajn.) J 



r XmXf = .287 ± .020, 



a value apparently distinctly lower than that for either males 

 or females alone. 



If the correlation between the siblings be determined irre- 

 spective of sex the value is 



S [2(x)f _ ( S[( n - m (x)] V 

 = S[n(n - 1)] V Sjttfr-Q] I 

 " S[(n - l)S(a- 2 )] _ fS[(n - l)Z(z)] V' 

 5[n(n-l)] \ S[n(n-1)] J 



