544 
Tuberculosis and 8egregatio7i 
we are bound to reject these ratios as even approximate measures of segre- 
gation *. 
But it would not be satisfactory to leave the matter here and not provide some 
explanation of why this fourth segregation ratio, both before and after the annul- 
ment of the time-factor, leads to such high correlations. Luckily the matter is 
capable of a perfectly straightforward and obvious explanation, which would have 
been anticipated had Dr Newsholme had in mind the danger of "spurious cor- 
relation." 
What he is correlating are essentially ^/P and pij^. The latter may be 
written (pi/P)/{^/P). Now pi/P is practically constant during the period in 
question. Hence Dr Newsholme is correlating (p/P with l/{(f)/P), or a variate 
with its reciprocal. In other words we may anticipate something very closely 
approaching perfect correlation. The deviation from such correlation arises from 
the fact that Pi/P is not absolutely steady, although its variations are very probably 
nearly random. The assertion therefore that this fourth measure of segregation 
assists in demonstrating the close relation between the fall in the phthisis death- 
rate and institutional segregation is based on a fallacy which entirely overlooks 
" spurious correlation." 
It will be seen therefore that not one of Dr Newsholme's methods of reaching 
an approximate measure of the segregation is satisfactory, and they lead to con- 
tradictory and inconclusive results. Whether there is any really substantial 
relation between the prevalence of phthisis and institutional segregation we 
do not yet know. All we can say is that Dr Newsholme has entirely failed to 
demonstrate it, if it actually exists. 
(6) Before concluding this paper it may be of interest to judge how far it 
justifies the application of the method of variate difference correlation to such 
problems as are here dealt with. 
In the first place, the correlations of successive differences should approach 
steady values. This is generally — as the reader can judge by examining Tables I, 
II, IV and V — but not invariably, the case. The test cannot, however, be com- 
pleted, as the method ought not to be pressed to such high differences that the 
order of the difference is a large percentage of the original " population." 
We doubt whether it is advisable to carry differences beyond the 8th in a 
population of 38. 20 to 25 reduction in the population is as much surely as 
it is safe to allow where the original population is so small in number. It is true 
that a population of 38 itself is capable of exciting the derision of trained 
* Under the circumstances it is, perhaps, unnecessary to draw attention to Dr Newsholme's state- 
ment that "the specific result of pauper segregation must have been lower in Ireland than in England or 
Scotland " (p. 282). Free of the time-factor the correlations of phthisis deathrate and Dr Newsholme's 
fourth segregation ratio are higher in Ireland than in England or Scotland. This criticism as well as 
Dr Newsholme's original remark are of no importance, because the fourth segregation ratio correlation 
is entirely spurious. 
