XXIII— XXIV] 



Introduction 



xli 



When r t is zero in the population and not in the sample, the standard deviation 

 tr r of r = is given accurately by -= % a % ai> . 



Illustration (i). Tetrachoric r t for the Table 



is '652. Find approximately its probable error. 

 From Table XXIII : 



r = 6.5, X.- = '6785 ; r = "66, X >- = '6675. 

 .-. x,- = '6785- 0110 x -2 = -6763. 



Now 4(1+ a,) = '9211, 4(1 +«2> = '9122. 



Hence from Table XXIII, 



Xa, - l'»249 + 11 [754] = 1-8332, 



Xa, = 1'7623 + -22 [626] = 17761, 



X ai X ai = 3'2559. 



Xi cannot be found from Table V in this case as N is beyond its range. But it 

 equals 



•67449/V26287 = -67449/162-13 = -00416. 



Thus finally p.e. of r t = 00416 x -6763 x 32559 



= 009. 



Illustration (ii). Find the value of <r r for the table : 



Here 4(1 + a,) = '619 and 4 (1 + a 2 ) = -622. 



X 0i = 1-2712 + -9 [36] = 1-2744, 

 Xa , = 1-2748 + -2 [39] = 1 -2756. 

 0^ = ^X^1000 = -0514. 



In a similar manner the values for all the O o>'s in the table on p. xxxvii were 

 found. 



B. / 



