45^ AMERICAN ANTHROPOLOGIST [s. s., I, 1899
By introducing in the negative elements of this sum the values for
r i2» r is • • • from (6), we obtain
(8)p* = /*i*(i -^123 . . - >*i3* . • - 2/- 138 . . r 132 . . r J2 — . .), or in a shorter form
P 2 = Mj 2 [1 — 2(r la . . p . r lb . . p . r ab )], in which sum a and £ must be made to assume all the values from
2 to/.
IV
I have treated, according to this method, the measurements of the 57 skulls of adult male Sioux Indians to which I referred above (page 453). I have compared length (/) and breadth (6) of skull with its height (//), the bizygomatic diameter of the face (#), and with the capacity of the skull. For the last purpose I have made a reduction which seemed necessary, because the capacity of the skull is a cubic measure, while all the others are linear measures. For this reason I have compared the latter with the cubic root of the capacity of the skulls (c). The averages and variabilities of these measurements are as follows :
c I b h z
Average (mm.) 112.9 181. 7 143.5 l 33° 141. 6
Standard variability. ... + 2.6 + 6.3 + 5.6 + 4.7 + 6.3
The following coefficients of correlation were found :
I. Coefficients of Single Correlation.
Determined by :
c 1 b h z
Average c +°-54 +0.67 +044 -f 0.49
Average 1 + 0.54 -f- 0.24 -j- ° 36 + ° 39
Average b + 0.67 + 024 0.00 + 0.6 1
Average h +0.44 + 0.36 0.00 .... +0.19
Average z +0.49 +0.39 -f-0.61 -j-c.19 ....
It appears from this table that the correlations of the diam- eters with the capacity are strongest, while that between length and breadth is one of the lowest values in the table. This con- dition is still more strongly brought out when double, triple, and quadruple correlations are considered.
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