Godfrey H. Thomson 
361 
hierarchies, though such perfection as the above would be unlikely to arise from 
chance. 
Second Example. For a second example I have therefore chosen a hierarchy 
formed thus by the chance sampling of group factors, without any general factor, 
and moreover one which shows considerable departure from perfection of hierarchical 
order, it being the least perfect of those which I have up to the present formed in 
this way. The mode of construction of the variates is given in detail in Roy. Sac. 
Proc. A. xcv. (April 1st, 1919) on page 402, and the theoretical correlations on 
page 403 of that article. The latter show a certain degree of hierarchical order, 
though not very high, the true mean columnar correlation R for all pairs of 
columns being 0'59. 
Dice were now thrown to form 20 measures of each of the ten variates, 
First the magnitudes of the group factors (which it will be recalled were in that 
article named after the cards of a playing pack) were decided by throwing dice, 
with the following results. 
TABLE III. 
Number identifying 
the subject 
Ace 
2 
3 
4 
Name of Group Factor 
5 6 7 8 9 
10 
Kn 
Q 
K 
1 
6 
1 
6 
6 
5 
5 
4 
4 
2 
3 
1 
1 
4 
2 
2 
4 
3 
2 
6 
4 
3 
0 
6 
2 
5 
3 
3 
3 
5 
r 
1 
4 
6 
3 
1 
4 
3 
6 
4 
3 
2 
4 
6 
6 
2 
5 
5 
5 
6 
6 
4 
5 
5 
4 
5 
5 
5 
5 
4 
2 
2 
5 
2 
4 
I 
I 
4 
4 
5 
6 
5 
6 
2 
6 
1 
4 
5 
6 
6 
4 
2 
5 
4 
7 
1 
1 
3 
4 
6 
4 
6 
6 
2 
3 
2 
5 
4 
8 
1 
3 
2 
2 
5 
3 
4 
4 
1 
2 
2 
9 
1 
f) 
1 
5 
3 
2 
2 
1 
3 
5 
4 
1 
10 
6 
1 
3 
2 
1 
2 
4 
5 
1 
4 
4 
3 
2 
11 
2 
4 
4 
2 
4 
3 
2 
1 
3 
3 
2 
3 
2 
12 
6 
3 
6 
1 
1 
2 
1 
1 
1 
2 
1 
1 
6 
13 
6 
1 
6 
5 
5 
1 
6 
1 
3 
4 
4 
3 
1 
14 
5 
6 
1 
2 
5 
5 
2 
3 
5 
2 
1 
4 
5 
15 
5 
2 
6 
2 
2 
5 
5 
1 
6 
6 
1 
2 
5 
16 
6 
2 
6 
4 
4 
6 
3 
6 
4 
6 
2 
2 
3 
17 
2 
1 
6 
3 
3 
1 
2 
6 
2 
6 
1 
2 
5 
18 
4 
1 
2 
4 
2 
4 
3 
G 
4 
6 
6 
3 
5 
19 
6 
2 
6 
3 
1 
2 
2 
5 
4 
5 
3 
1 
4 
20 
3 
3 
2 
5 
2 
6 
2 
3 
6 
6 
2 
4 
6 
Using these numbers, we can make up the scores for the gr'oup factor portion 
of each of the ten tests describedjn the article quoted. There results (see Table IV). 
The proper number of dice, as described in the article quoted, were then 
thrown for each test and for each subject to represent the specific factors, and the 
scores of these dice added to the scores given in the last table, the resulting total 
being the complete score for each subject in each test (Table V). 
From the dice scores the observed correlations between the variates can be 
Biometrika xii 24 
