Karl Pearson 
31 
Thus we have : v 2 = 8 \ (Ps _ Ps) * 
* i I P* 
In other words % 2 is to be found from the ordinary for the u+1 variates 
excluding the houses with zero cases. I had excluded these houses from my 
weighting formula, i.e. 
% A ps J 
which was, however, in error. The higher multiple cases are now we see not 
heavily weighted, but we are not to use the frequency of the zero case houses in 
evaluating our %' 2 . This is the effect of the double relation between the u+1 p's. 
An additional p is cast out of our result as compared with the ordinary frequency 
problem of goodness of fit. 
I have next to consider how far this correction modifies the results obtained 
in my papers for numerical cases. 
For enteric cases we have as on p. 412 of my Biometrika paper 
, _ (8398 - 3350) 2 ( 78- 56) 2 ( 2-1)* 
X ~ 3398 + 56 + 1 
= -678 + 8-643 + 1 = 10-321, 
hence we have for n' = 3, P = "006, or the odds are about 166 to 1 against such 
a large divergence from chance. 
For cancer cases we have from the returns on p. 432 
, = (2-f>) 2 (9^ (416) 2 (914) 2 
X 312-4 20 1-84 -086 
= -022 + 4 418 + 9-405 + 9 714 - 23-559. 
For ??' = 4, we have P = 0003 or the cancer house distribution is a very 
improbable one. 
If we deal with the experimental data that were obtained for probabilities on 
the same basis as the cancer statistics we have : 
S 2 1 
X ~ 313 + 29 + 2 
= -029 + -310 + -500 -= -839. 
Or, for ri - 3, the probability is over - 60. 
Thus although I made a bad algebraic slip the new values confirm practically 
the old and Dr Webb's cancer data suggest that there may very possibly exist 
a relationship between cancer and environment of some kind. 
Since my papers in Biometrika were written, my attention has been drawn to 
a Special Report on Cancer in Ireland which was issued in 1903 as a supplement 
