XXIX] 



Introduction 



li 



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

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



= -078,898, 



Here 



Whence by interpolation from Table, p. 43 : 



T,= '14712, 



T,= -14694, 



T :! = -05977, 



T 4 =- -04262, 



T S =- -06702, 



T 6 =- -00752, 



h = 1-41253, 



T/= -15945, 



T/ = -15268, 



T S '= -05431, 



T/ = - '05137, 



T 5 ' = - -06755, 



T,' = -00017, 



k = 1-35442. 



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

 we have 



T/ = -05221, 

 T,' = -02480, 

 T,' = - -03185, 

 T,; = - -03460. 



T. = -04770, 

 T S = -02985, 

 T, = - -02530, 

 T]0 = _ -03647, 

 Hence the equation for r is 



026,854 = -023,458?- + -022,435r 2 + "003,246^ 



+ 002,189r 4 + -004,527?-' - -OOO.OOb- 6 

 + 002,490?-' + 000.742?- 8 + -OOO.SOe?- 9 

 + -0()l,262r 10 . 



Whence we find ?= '652 + '009. 



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

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



i (1 - a,) = T O = Jff j = -260,080 ; $ (1 - ,) = T O ' = ^ T = -009,157. 



By simple linear interpolation, 



T, = -32442, 

 T 2 = -14753, 

 T 3 =--0776G, 



T,' = -02468, 

 T 2 ' = -04116, 

 T,; = -04599, 

 T/ = -03048. 



