XXIX] 



Jntrochiction 



li 



Illustration (i). Find the correlation between dullness and developmental 

 defects as indicated in the following table for 26,287 children. 





Without Defects 



AVith Defects 



Totals 



Not Dull ... 

 Dull 



22,793 



1,I8G 



1,420 

 888 



24,213 

 2,074 



Totals 



23,979 



2,308 



26,287 



Here t„ = ^^ = -078,898, 



Whence by interpolation from Table, p. 43 : 



T4= - 

 T|, = - 



•14712, 



•14G94, 

 •05977, 

 ■04262, 

 •06702, 

 ■00752, 

 1 ■41253, 



t/= •15945, 



T.,'= -15268, 



T,'= -05431, 



t; = - -05137, 



t; = - ■06755, 



T,/= -00017, 



A,. = 1-35442. 



Proceeding to apply the difference formula (xxxviii) for four further functions 

 we have 



T, = ^04770, t/ = -05221, 

 Ts = ^02985, T,' = ■02486, 

 T„ = - ^02530, T,' = - ■03185, 

 T,„ = - -03647, T,„' = - -03460. 

 Hence the equation for r is 



-026,854 = -023,458r + -022,435r=^ + -003,246rs 



+ -002,189»-' + -004,527?-' - -OOO.OOb-^ 

 + -002,490r + •000,742?'' + -000,806?-' 

 + -001,262r". 

 Whence we find r = 652 ± 009. 



Illustration (ii). Find the tetrachoric correlation for the four-fold table given 

 for Houses in course of Erection on p. xxxv. Here 



HI - «0 = To = ^{ = -260,080 ; |(1 - a,) = t/ = ^^^ = -009,157. 

 By simple linear interpolation, 



T, = -32442, t/ = -02468, 

 T,= -14753, T.,' = -04116, 

 T, = - 07766, t; = -04599, 



T, = - 11015, T4'= -03048. 



92 



