318 
Anthropometry of Scottish Insane 
1, 2, and 3 respectively, the central abscissa of each class being once, twice, and 
three times the standard deviation of sampling respectively. It should be noted 
that the central abscissa of each class does not divide the class into two equal 
areas ; it merely notes the centre of the range of the class. The last positive 
class is class 4, including values greater than 3"5 times the standard deviation of 
sampling. In a similar manner four negative classes have been instituted with 
the corresponding limits ; class - 1 : — 5 to — 1 "5 ; class — 2 : — To to — 2'5 ; class 
— 3 : — 2'5 to — 3"5 ; class — 4 : greater than — 3".5. The object of this grouping is 
to arrange the relative local differences in the order of their significance, separating 
those which are fair samples of the general population from those which clearly 
are not. The following classes of relative local differences are thus created. 
(Table VIII.) 
TABLE VIII. 
1 
2 
3 
4 
The local mean, compared with the 
general mean is 
Class 
Eaiige of class in terms of 
<"'~")/Vi-?('-") 
Probabilities at extremes of range of 
each class. Percentage cases with 
greater deviations 
Upper Limit 
Lower Limit 
Very much smaller 
-4 
- 3'5 upwards 
0 
•0233 
Probably significantly le.ss 
-3 
-2-5 to -3-.5 
■0233 
■6210 
Less, but not quite significantly less 
_ 2 
-1-5 to -2 -.5 
■6210 
6^6807 
Very slightly less ... 
-1 
- -5 to -1-5 
6^6807 
30^8537 
Quite insignificantly different 
0 
+ -5 to - -5 
30-8537 to 50* and 50 to 30-8537 
Very slightly greater 
1 
+ -5 to 1-5 
6-6807 
30-8537 
Greater, but not quite significantly greater 
2 
1-5 to 2-5 
■6210 
6-6807 
Probably significantly greater 
3 
2-5 to 3-5 
■0233 
■6210 
Yery much greater ... 
4 
3'5 upwards 
0 
■0233 
Relative local differences falling beyond + 2 and — 2 may be regarded as 
probably significant since the number of asylums is small (22), and since the 
probability that a greater deviation than that occurring at the furthest extreme 
on the range of this class is about 1 in 81, while the value for the central abscissa 
of this class is about 1 in 22. The figures in the fourth column obviously express 
the probable number of deviations from the general mean (per cent.) in future 
samples for the uppei' and lower limits of each class. 
The distribution constants of each character for the whole population being 
used as a basis, the constants for each character iti the various districts throughout 
Scotland will now be discussed. The relative differences between the local means 
and the rest of the population for each character are first considered. 
* 50= P, for centre of this class, 
