VI 1 1 I X ] Introduction \x\\i\ 



When tho correlation is over '90 it is difficult to test the accuracy of the 

 result by the complete tetrachoric equation ; the terms converge so slowly that 

 it is scarcely possible to compute enough of them. On the other hand, if we take 

 material of which the correlation is known, say by the product-moment method, 

 it is again not easy to obtain adequate numbers in the cells not on the "cor- 

 relation diagonal." The above table is one for the correlation of binocular vision 

 and the vision of the better eye. The correlation coefficient worked by the product- 

 moment process on the full table was '9485. The above was the best fourfold table 

 we could make, i.e. the others gave two or three units only in one or other cell. 



We have ^ (1 - a h ) = '246,0137, \ (1 - a*) = -305,2392, 



and d/N = -225,5125. 



Thus we have h = '68709, k = '50939. 



Further # = '8709, <J>='1291, X = '0939, ^ = '9061. 



The value required of dfN occurs within the given (h, k) range only for r = '95 

 and r = '90. Accordingly we have 



'Q 77*1 f 245 > 878 l ^ .7sc a (-225,035 

 *'* = H69.7751 . + 7891,2249 . 



+ '0121 2249 2 ' 102 l + -0817 7751 ' 215 > 259 

 J ' 



or d/A^ -226,7594, for r = -95, 



= 211,0717, for r = -90. 

 Interpolating linearly for d/N= '225,5125, we have 



r- -90 + -05x111^ = -9460. 



This is as good a result as could possibly be anticipated for the agreement of a 

 product-moment and a tetrachoric coefficient, when we bear in mind that the accord- 

 ance depends on the existence of nine individuals only in the right-hand upper cell. 



To sum up we see that the table throughout the range of r gives very satis- 

 factory results with far less labour than the equation method, if we use second 

 differences for h and k and linear interpolation for r. There is not much to choose 

 in accuracy between the results from a central difference and from a forward 

 difference second order interpolation. For many purposes where two to three decimals 

 are adequate in the value of r the simple hyperbolic formula (a) is sufficient. 



(6) We will now proceed to illustrate the application of Tables VIII and IX to 

 determine all the cell contents of a contingency table of which the frequency dis- 

 tribution is supposed to be normal, and it is desired to test the accuracy of the 

 hypothesis. 



