XXIII— XXIVJ 



Introduction 



xli 



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

 oo-, of r = is given accurately by -T=Xa,Xa.,- 



Illustration (i). Tetrachoric Vf for the Table 



22,79.3 

 1,186 



23,979 



1,420 



2,308 



24,2)3 



2,074 



26,287 



is -652. Find approximately its probable error. 

 From Table XXIII : 



r = -65, xr = "6785 ; /• = -66, x-- = '6675. 

 .-. Xr = -67S5--0110x-2 = -6763. 

 Now 1(1 +00 = -0211, i (! + «=) = ■9122. 



Hence from Table XXIII, 



Xa, = 1«249 + 11 [754] = 1-8332, 

 :)C^^ = 1-7623 + -22 [626] = 1-7761, 

 Xa.%a. = 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, = 00416 x -6763 x 32559 



= -009. 



Illustration (ii). Find the value of f,ar for the table : 



471 

 151 



148 

 230 



619 

 381 



622 



378 



1000 



Here ^(l+a,) = "619 and ^(1 + «,) = -622. 



X„^ = 1-2712 + -9 [36] =1-2744, 

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

 o<^. = Xa,Xa,/^/i000 = -0514. 



In a similar manner the values for all the „o-/s in the table on p. xxxvii were 

 found. 



