Karl Pearson 
133 
I found 
x,= - -899r>, +-2428, +1-2674, 
y t = - 1-0066, +-2173, +1-4110, 
and 
S ^ " 
tit* 
Wa 
S 
'( 
•784,241, 
•776,941, 
r rCx = -8814, r yCv = -8856. 
Proceeding exactly as before by formula (xvii) we have 
_ --204,01275 
xy ~ -784,241 x -776,941 ~ 
For comparison I worked out the above 3 x 3 table by contingency. The 
contingency corrected for 3x3 cells is <f)' 2 = "076,0779, and therefore C = -2659, 
hence 
r. m = -2659/(-8814 x -8856) 
= "3406, l'egardless of sign. 
To sum up our results for this case we have : 
Bi-Serial 17 
Corrected 
Contingency 
Formula (xvii) 
6x2 
Table 
•340 and -343 
Gx4 
Table 
•3342 
•3171 
4x4 
Table 
•3242 
3x3 
Table 
■3406 
•3348 
The results are very satisfactory and show that for correlations of this 
magnitude our corrective factors work excellently when we use contingency to 
find Tq q . Formula (xvii) also gives fairly consistent results, but this is partially 
due to the relative smallness of r. For the smaller r the more nearly x st xy st 
may be replaced by x g x y t as is well shown in the case of the simple 2x2 table. 
On my scale of Intelligence seven categories are used ; there were in Mr Gilby's 
schools none of the A or Mentally Defective class, so that he only used six, B — O. 
We see that there is a high degree of correlation between the actual intelligence 
of a child and its class index. We must have 
For seven classes r>'97, 
„ six ,, r = '97, 
,, four „ r = "93, 
„ three „ ?- = -88. 
It is of interest to put beside these the frequencies of my General Health 
Scale and the resulting class index correlations. The scale had six classes : 
