XXIII XXIVJ 



Introduction 



xli 



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

 O o> of r = is given accurately by ^=x ai Xa. 2 - 



Illustration (i). Tetrachoric r t for the Table 



22,793 

 1,186 



23,979 



1,420 

 888 



2,308 



24,213 

 2,074 



26,287 



is '652. Find approximately its probable error. 

 From fable XXIII : 



r = -65, xr = '6785 ; r = '66, Xr = "6675. 

 . -. Xr = -6785 - -01 10 x -2 = -6763. 



Now (l+o,) = '9211, J(l+s) = -9122. 



Hence from Table XXIII, 



X ai = 1 8249 + -11 [754] = 1-8332, 

 X a , = 1-7623 + -22 [626] = 1-7761, 

 Xa,Xa, = 3-2559. 



X\ cannot be found from Table V in this case as ^V is beyond its range. But it 

 equals 



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



Thus finally p.e. of r t = '00416 x -6763 x 3'2559 



= 009. 



Illustration (ii). Find the value of O o- r for the table : 



471 

 151 



622 



148 

 230 



619 

 381 



378 1000 



Here 



(1+0,) = '619 and $(1 +a a ) = '622. 

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

 Xai = 1-2748 + -2 [39] = 1 "2756. 

 0^ = ^,^/^1000 = '0514. 

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



found. 

 B. 



