J. F. Tocher 
329 
(4) Variuhilities and their Differences. Problem (d). 
Do the re.sults for different parts of Scotland give any reason for supposing 
greater homogeneity or heterogeneity in one part than another? An endeavour 
can be made to answer this question after considering the variabilities in the 
distributions of the various characters. Under the character means, just dealt 
with, the sizes of the organs or characters were considered, differences in type 
noted, and the conclusion reached that the asylum population, as a whole, no 
matter what character is selected, is not a homogeneous one. An attempt will 
now be made to ascertain whether the separate district groups themselves can be 
described to be homogeneous; in other words, whether the groups in the various 
districts in Scotland are significantly more or less variable than the general 
asylum population. 
If a = the standard deviation of any character at any asylum, and 2' = the 
standard deviation of the same character in the remaining population, then the 
ratio 
liv 
is the relative local difference in variability for any asylum. The values of this 
ratio for each character have been determined using the formula* 
where N = (n + N') = number in the whole population, in place of 
Pearsons's full formula, which he shows to give the equivalent to 
2n'^2N') ■ 
The foregoing shorter formula has been used, on the assumption, warrantable in 
the present series, that the ratio ^ differs from ^ by a quantity so small that 
it may be put = ^without affecting the significance of the final result. In short, 
in this instance 
K2n 2n) 
is a good approximation. 
As expected, few districts show greater variability than the general population. 
Significantly greater variability occurs only in the character among the Inverness 
Pearson, Bioinetrika, Vol. v. p. 183. The case considered in this note is the probable error 
of the difference between the mean of a subsample and the mean of a sample, but the same reasoning 
is applicable to the difference between the standard deviations of subsample and sample. 
