Miscellanea 
509 
It may be said that this skewuess might itself account for the results which Ur Turner 
considers opposed to current medical opinion and which he would account for by a curtailed 
normal distribution. Possibly it may, but I hold that this is very uidikely, and for the following 
reasons : 
(i) The severity is here measured by a time test, which invariably gives a skew distribution ; 
but if severity could be measured in some other quantitative manner, for example by intensity 
of eruption, mean rise of temperature or in some such fashion, we should most probably reach a 
more normal distribution. 
(ii) The effect of even the large amount of skewness indicated above on the correlation 
found by a fourfold division is, I think, not likely to be very large. It is too often assumed 
that the distribution must be very closely normal to give a good result by the fourfold table 
method. As a matter of fact, if the fourfold division falls on the "long tailed side" of the 
mode, as it does in these vaccination statistics, we get close values to the actual correlation even 
by the fourfold table method. To illusti-ate this 1 took the only correlation which was available 
on the data, namely the correlation between onset to eruption and eruption to bath. This 
correlation was found by the ordinary product moment process, which is independent of any 
hypothesis of normal distribution and came out = - -174 + '023. In other words, if severity of 
the disease be measured by a long period from eruption to bath, then a short period between 
onset and eruption is associated with severity. This is in accordance with the previous 
indication that the fatal cases have a short period from onset to eruption. 
I now formed a fourfold table from my exceedingly skew distribution, dividing between 
14 and 15 days from eruption to bath and between 3 and 4 days from onset to eruption. 
This gave : 
Onset to Eruption. 
a ■ 
o ^ 
0 days and less 
4 days and more 
Totals 
14 days and less ... 
15 days and more ... 
395 
138 
235 
51 
630 
189 
Totals 
533 
286 
819 
whence the correlation —•166 was deduced. It is clear that the skewness has not .sensibly 
influenced the value of the correlation as determined from this fourfold table. 
The divergence of the fourfold dividing lines from the median is certainly not quite as great 
in this case as in the vaccination problem, but it is difficult to go nearer the tails and get 
anything like a reliable result. Dividing between 4 and 5 days from onset to eruption, 
and 16 and 17 days from eruption to bath, I get: 
Onset to Eruption. 
4 days and less 
5 days and more 
Totals 
16 days and less ... 
17 days and more ... 
595 
112 
104 
8 
699 
120 
Totals 
707 
112 
819 
a • 
o ^ 
2-pq 
In this case the probable error of the frequency 8 is no less than 2, but a change of 2 
in the value of this frequency would change the value of r by about 20 p.c. Such a division is 
