cephalic indices, for no less than 0-4008 of this would remain, if we destroyed all organic relationship between the lengths on which these indices are based.
Example (d). To find the spurious correlation between the indices femur/ humerus and femur [tibia.
The following results have been calculated* from measurements made by Koganei on Aino skeletons. (See ‘ Mittheilungen aus der medicinischen Facultat der K. J. Universitat, Tokio,’ Bd. I. Tables.)
I hare kept the sexes apart although there are but few of each.
$ Skeletons. Number = 40 to 44. Measurements in centimetres. Femur, F : mx = 40'845, = 1-957, = 4’792. Tibia, T : m^=- 31*740, <r2 = 1-577, v2 = 4-970. Humerus, H : m3 = 29*593, = 1-337, = 4‘517. The following' coefficients of correlation were calculated directly: Fem ur and tibia : r12= 0*8266. Femur and hum erus: = 0"8585. Tibia and humerus : r23= 0*7447.
From these were deduced by the formulae of this p ap erf:— Index, F/T : in = 128-75, S12 = 3-7075, V12 = 2-8795. Index, F/H : iX3 — 137"92, 2 13 = 3-4084, Y 13 = 2’4714. Index, T/H : i23 = 107*02, S23 = 3*6675, V23= 3-4271. Hence we find for the correlation of the indices F/H and T/H : * p = 0-5644. But the spurious correlation, if the bones had been grouped at random would have been p0 = 0-4557.
- I hare to thank Miss Alice Lee for a considerable part of the arithmetic work
of this example.
f The values for the indices are not in absolute agreement with those to be deduced from the lengths, for it was not always possible to use the same skeleton for femur and humerus as for tibia and humerus, i.e., sometimes one or other bone was missing. For the same reason, the constants for the absolute lengths do not agree entirely with those given for Ainos in my paper on “ Yariation in Man and W oman” in ‘ The Chances of Death and other Studies in Evolution,’ vol. 1, p. 303), for the simple reason that I there used every available bone, and not every available pair, as here.
