XXIX] 



Introduction 



li 



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

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



Here 



mtr = -078,898, 



•in-jsr 



t»' = «7 = -087,800, 

 Whence by interpolation from Table, p. 43 : 

 t, = -14712, 

 t„ = -14694, 

 t 3 = -05977, 

 r 4 =- 04262, 

 T , = - -00702, 

 To = - -00752, 

 h = 1-41253, 

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

 we have 



Tr = -04770, 

 t 8 = -02985, 

 t, = - -02530, 

 t„, = - -03647, 

 Hence the equation for r is 



•026,854 = -023,458r + -022,435r 2 + -003,246r 3 



+ •002,189r 4 + -004,527r 5 - -OOO.OOl?- 6 

 + •002.490?- 7 + 000,742r 8 + -OOO^Oer 9 

 + -0()l,262r 10 . 

 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 



| (1 - a,) = t = Jfff = -260,080 ; f(I - a,) = t 8 ' -jffr" -009,157. 

 By simple linear interpolation, 



t, = '32442, t,' = -02468, 

 t 2 = -14753, t/ = -04116, 

 t 3 =- -07766, t : ,' = -04599, 

 t 4 =- 11015, t 4 '= -03048. 



J/2 



