426 Variation and Correlation of Skull Measurements 
DETERMINATION OF THE MEANS AND VARIABILITY OF THE SEVERAL 
MEASUREMENTS. 
In Table I are exhibited the means of the several measurements, the 
standard deviations, the coefficients of variation and the differences 
between the two sexes, with their respective probable errors. These values 
were determined by the usual biometric formule (Davenport, 04). As 
one would expect, the mean values in the males are always higher than in 
the females. Since in the present investigation the total number of 
measurements of both sexes was not large, it is important to compare the 
differences between the sexes with the corresponding probable errors in 
order to see whether or not the differences here found are to be considered 
significant. ‘Table I shows clearly that in all cases the differences are 
greater than three times the probable errors. The maximum difference 
occurs in the nasal bone; ten times the probable error, and the minimum 
occurs in the width of the cranium, five times the probable error. This 
indicates that the characters under consideration are really greater in 
the male. The maximum percentage differences occurs in the nasal bone 
(7.5 per cent) and minimum in the width of the cranium (1.4 per cent) 
while the remaining differences are nearly similar (3.1 per cent to 3.9 
per cent). 
From the percentage differences here found it would seem probable ~ 
that if we compared the mature male and female skulls having the same 
total length, the length of the nasal bone in the male would be longer 
than that in the female, and since the length of the entire skull depends 
on the combined length of the nasal bone and the fronto-occipital length, 
it would follow that the fronto-occipital length or the length of the 
cranium, would be less in the male than in the female. In order to test 
this conclusion in any individual case it is necessary to determine whether 
or not the total length of the skull and of the nasal bone on one hand, 
and the total length of the skull and fronto-occipital length on the other 
hand, are closely correlated. This point will be more fully discussed after 
the coefficients of correlation have been determined. 
(a) Range of variates and rate of increase of the various characters 
associated with changes in the size of the entire skull—The two extremes 
of the various characters, as well as the rate of increase of those characters 
associated with the increase in the length of the entire skull, is somewhat 
different according to sex as is shown in Table II. 
As is shown in Table II, the absolute range between the two extremes 
is always slightly greater in male than in female except in the case of the 
