316 
Anthrojmnett'p of Scottish Insane 
(where ?i= number of inmates at any asylum and iV^' = the remainder of the 
population of inmates) is the standard deviation of sampling of 7n — M'. This is 
the well-known expression for the standard deviation of the differences of two 
means, and the ratio 
is a measure of the deviation of the local means from the mean of the rest of the 
population relative to the standard deviation of sampling, or, shortly, is the 
relative local difference {RLD),n expressed in a way enabling its significance to be 
tested. Professor Pearson, whose many suggestions in the course of this investi- 
gation the writer desires here gratefully to acknowledge, points out that the 
biometrician is not warranted in usinor the ratio 
where J/ = general mean, and 2 = standard deviation for the whole population, N, 
(although this is sometimes done), since the local sample is included in the deter- 
mination of mean and standard deviation of the general population. In a note* 
kindly shown to the writer Professor Pearson shows that 
, (T- 2n\ n(M-my 
and is true whatever the magnitudes of N and n may be. In the present series 
where iV^ = 4381 and 3925 for males and females respectively, the term -^^-^^-^ ^ 
^ ^ N{N-n) 
becomes small and may be neglected, so that the standard deviation of sampling of 
1)1 — M' is given by (and can be conveniently calculated by using) the expression 
and the ratio applicable to the present data is thus 
The values of this ratio, if the samples are piu-ely random ones, are simply the 
abscissal values of the normal curve whose equation is 2/ = 1/V27r . and the 
corresponding ordinal values divide the curve into areas proportional to the 
probabilities of greater or lesser values occurring in future samples. For graphic 
representation in the lollowing maps, the relative local differences have been 
grouped in the following manner. (See also Table VIII.) All values between 
— 'o and + "5 have been placed into one class, class 0, the central ordinate of the 
class corresponding to the abscissal value of the normal curve, x = Q. All values 
between +'5 and + I'o ; I'o and 2-5; 2-5 and S'o belong to the positive classes 
■" Since published. Biometrika, Vol. v. pp. 181—183. 
