220 
A First Study of the Burmes.e Skull 
Let us now compare the characteristics of the extreme groups A and C. 
In order to do this we need to compare any difference in the means with the 
probable error of tliat difference, to see whether it is significant or not. And for 
the probable error we need to know the standard deviation of each character 
within the race to which it belongs. Our numbers are altogether too slight to fur- 
nish us with this standard deviation; I have therefore adopted as next best thing 
the standard deviations as found in some other race, on the assumption, confirmed 
by previous experience*, that though the S.D.'s vary from race to race, they are 
at least of about the same order. Our probable error of means based on these 
borrowed S.D.'s will necessarily be only approximate, and we shall not be able to 
test the likely significance of a difference in means by asking definitely whether it 
is more or less than about 2-5 times the probable error. More latitude must be 
allowed than usual, especially when one sex seems to show a significant difference 
and the other not; a truer standard deviation might alter the probable error so 
as to make the two sexes indicate the same thing. 
The standard deviations of the Egyptians (Naqada Racef) have been bor- 
rowed for as many characters as are given there; this is our longest measured series, 
and its standard deviations are therefore subject to the smallest probable errors. 
For characters not measured by Fawcett, I have taken from the Moorfields English 
Crania studied by Macdonnell \ the S.D.'s of such characters as he added to Fawcett's 
list, and from Benington's Congo series§ the S.D.'s of the nose measurements which 
were his new contribution. The standard deviation of weight |j (W. in grs.) was taken 
from an Egyptian series of which 50 of each sex were weighed by A. G. Davin for 
comparison with Mbriori crania. Finally, that of 100 {B — H)jL was calculated from 
the S.D.'s of the component indices, and that of the premaxillary height (PH), 
which is approximately equal to the upper-face height (G'H) minus height of nose 
(NH), by means of the S.D.'s of these two characters. 
On the following page is a table showing the excess or defect of Group C means 
as against those of Group A, with the approximate probable errors of the differences. 
The characteristics which influenced oi;r merely appreciative grouping are well 
brought out by this table. The greater width of the cheek-bones in Group A is 
indicated by the longer bi-zygomatic breadth (J) and the greater upper-face breadth 
(GB), the differences exceeding five times the probable error in both cases for both 
sexes. Again, as regards the nose, the width of the pyriform aperture in Group A 
exceeds that in Group C by more than five times the probable error in males, and 
by seven times in females; about the nasal height there is no such clear verdict, 
with a barely significant difference in the males, the C's exceeding, while the A's 
have a very definite excess for the females. In any case the relative proportions 
of the nose are not left in doubt, since the A's have a significantly higher nasal 
index in both. 
* See Tables of Interracial Variability in Benington's Paper, Biomcirilca, Vol. viii. pp. 323 and 324. 
I Fawcett's paper in Biometrika, Vol. i. jj. 438. 
t Biomefrika, Vol. v. pp. 92, 93. § Biometrika, Vol. viii. pp. 298, 299. 
II Not yet published. 
