Karl Pearson and David Heron 
255 
Diagram XIII. 
(ii) 
0-10 
10-25 
25-45 
Over 
45 
Unvac- 
cinated 
\\ 
\\ 
V- - 
\ \ 
Sparse 
Very S})arse. 
Haemorrhagic. Confluent. Abundant. 
Severity of Attack. 
changes would have been made had we used as horizontal scale a Gaussian calculated 
on the new distribution of total severities. It will be seen on comparing Diagrams 
XIV and XV that no substantial difference is made in the fundamental result. 
Further to test the effect of concentration we have had tj the correlation ratio 
calculated by concentration at the means of the unselected scale of years since 
vaccination and by treating each array as a Gaussian ; the value found for it in 
the former case (when uncorrected for class-index correlation of severity) is '32, 
while in the latter case the three-rowed table gave t] = - 32 and "34, with a mean 
value "33*. Both these values would need the same class-index correction for 
severity, i.e. r xC = - 9502, which renders them "34 and '36 respectively. 
Further, to show that a wide range of hypotheses can be made without 
modifying the fundamental conclusion, we have again plotted the regression lines 
on the Yulean hypothesis of pseudo-ranks before and after equalising deaths and 
* Biometrika, Vol. vn. p. 257. The value of r found by concentrating at the Gaussian means of the 
marginal subranges is -31, quite close to the r\ values as corrected. 
