152 
On Polychorle Coe^cients of Correlation 
An examination of the fourth column of Table XVI shows us that we have 
not for practical purposes seriously modified the columnar means by using r = "50 
instead of the individual value for each column. This is illustrated in Diagram III, 
where except in the case of the first array there is hardly daylight between the 
two series of points. 
-2 
c +1 
+2 
SI 
i; 
i; 
1 - 

1 
1 
1 
1 
1 
1 
• MEAN OF SON 
1 
1 r 1 1 1 
-2 -1 O +i +2 
Stature of Father in Indies. 
Diagram III. 
In Diagram III the hollow circles give the means with r obtained for each column, the nearly 
superposed dark circles the means with / = -5000. 
The solution of the problem therefore Mis back on Equations (x), (xvif) and 
(xv). We should still have to calculate t^, t^', 7"^ and Tp, but we should 
only need the three series of products Tp Tp, Tp Tp and ^g Tp ^g- Tp', and 
to obtain A-g. it would be adequate to use a value of r for which riss'jngs' had been 
found for the final interpolation. Still this involves very lengthy arithmetic, and 
we natiirally crave for a still easier process. The present full working out of a 
numerical example enables us for the first time- really to test the adequacy of an 
easier method of dealing with such polychoric tables which has been long in use 
as an approximate method in the Biometric Laboratory. 
(6) It is clear that if we could find the means of the columnar arrays, we 
could readily obtain the correlation and the regression line by aid of the correlation 
ratio corrected for class index. The whole problem accordingly turns on a ready 
means of reaching — at any rate — an approximate value of the mean of a columnar 
array. This array is the slice between two parallel planes of a normal correlation 
surface. 
In the case of a surface of zero correlation 
