174 Prof. K. Pearson and Mr. L. N. G. Filon. 



2. Normal correlation is first dealt with. It is shown that if 

 X = 0*67449 and n be the number of observations : 



Probable error of a coefficient r i2 of correlation = X — ~B 



v n 



Probable error of r 12 , for variations with definite values,* 



J 1 



= X 



1 + r 



Correlation of errors in two standard deviations = r 12 2 . 



Correlation of errors in a standard deviation and a correlation 

 coefficient = r^jV 2. 



Probable error of a regression coefficient for two organs 

 _ g x V 1— r 12 2 



where a x and <r 2 are the two standard deviations. 



Probable error of a regression coefficient for three organs 



_ JV_ <ri VI- r aa * — r v * — r 12 2 + 2 r 12 r 23 r 13 _ 

 \/ n a z 1— r 23 2 



Correlation between the errors in two correlation coefficients, i.e., 

 r 12 and r i3 



_ _ r 12 r 13 (1 — r 2 , 2 — r 13 2 — r 12 2 + 2 r M r^r 13 ) 



2(1— r 13 2 ; (l— nf) 



Correlation between the errors in two correlation coefficients, i.e., 

 r L 2 and r 34 



f (r 13 — r 12 r 23 ) (r 24 — r 23 r 34 ) -f (r 14 — r 34 r 13 ) (r 23 — r 18 r 13 ) 1 

 1 + (^13—^14^34) (r 24 — r l2 r 14 ) + (r 14 — r 12 r 24 ) (ro 3 — r 24 r 3t ) J 

 ~ 2(l-r 12 2 >(l-r 3i 2 ) 



3. Skew variation is next dealt with. First the probable errors and 

 correlations of the errors of the constants of the curve 



* This value for the " array " was erroneously given as that for the absolute 

 value of r ]2 in 'Phil. Trans.,' A, vol. 189, p. 345, but the statement was corrected 

 in ' Boy. Sue. Proc.,' vol. 61, p. 350. 



