560 
A Studij of the Effects of Diphtheria Isolation 
attacked. The regression is roughly linear and only very partially due to the high 
case-mortality in towns witli no isolation. It is probable that where there is 
a large amount of isolation, the care of patients falls largely into the hands of 
a few men with a more extensive experience of the disease, and that this reduces 
the case-mortality. 
Against this may be set the fact that the correlations between the absolute 
numbers of deaths and of cases isolated for constant numbers attacked are in- 
significant. The divergence between the two methods of approaching the problem 
is, however, explicable because the coefficients of variation of the absolute numbers 
are greater than unity, and the identity of the correlations reached by the two 
methods depends on the neglect of the squares and products of the coefficients 
of variation compared to unity. It may be asked: Why in this case we prefer 
the partial correlation found from the rates to that found from the absolute 
numbers ? We reply : Because the partial correlation coefficient for the absolute 
numbers depends on very high total correlations, and if these correlations be, as 
we have shown, non-linear, then the partial correlation coefficient not only loses 
its full meaning, but may, as experience has shown us, easily change its sign as 
well as its magnitude. We would suggest that in a minor sense total mortalities 
and total isolations are bound to give " restricted tables," for deaths and isolated 
cases are perforce less than the numbers attacked, and that in such "restricted" 
tables, there is a general tendency to skew correlation and to a spurious factor*. 
On the other hand it is true that case-mortalities and isolation-i'ates cannot 
exceed 100% fall short of 07o> but these limits are the same for every array 
and do not vary from array to array as in the previous case. On the whole we 
think it safe to say that isolation is associated with greater prevalence of the 
disease and with a lessened case-mortality. 
(5) Is there any significant Relation between Isolation- Rate and General 
Diphtheria Death-Rate ? We have seen (p. 553) that insignificant correlations exist 
between / and M, and it is difficult to understand how a spurious factor could 
have modified this result. In the first place the small values of Vpj and r^j^ on 
p. 555 show us that the value of pVjj^^ is sensibly the same as r„j^; thus, for a con- 
stant population there is no sensible association between diphtheria mortality and 
isolation. But now let us ask whether for a constant attack-rate, isolation does 
not lessen general diphtheria mortality. We have : 
Correlation First Period Second Period 
r,;,^ = Isolation-rate and Death-rate ... -|-'1532 -'01 19 
7',,, = Isolation-rate and Attack-rate ... -l-'4268 +-2905 
r^,/._, = Death-rate and Attack-rate ... 4- -6772 -(-■6879 
Hence 
j-j^j = Isolation-rate and Death-rate for] 
constant Attack-rate J 
- -204 ± -074 - -305 -I- -068 
See especially the illustrations of such "restricted" tables and their regression lines in a paper 
by Waite on Finger-Prints: Biometrika, Yol. x, pp. 421 — 478. 
