Godfrey H. Thomson - 363 
TABLE VI. 
Tlie Observed Hierarchy. 
X-, 
Xg 
x^ 
A'2 
^6 
X-i 
A'4 
Xfi 
■^10 
• 
•72 
•47 
•64 
•53 
■50 
•34 
■45 
•21 
•09 
•72 
• 
•48 
•43 
•75 
■48 
■32 
•67 
- ^26 
•10 
•47 
•18 
• 
•51 
•46 
■45 
■50 
•46 
- -02 
■24 
x-„ 
■64 
•43 
•51 
• 
•58 
■60 
•20 
, •IS 
•29 
■08 
Xo 
•53 
•75 
•46 
■58 
• 
■63 
•26 
•33 
•05 
- -11 
Xe 
•50 
•48 
■45 
■60 
•63 
• 
•22 
•29 
- ^16 
•18 
Xi 
•34 
•32 
•50 
•20 
•26 
•22 
• 
■41 
•38 
■15 
■*3 
•45 
•67 
■46 
■15 
•33 
■29 
•41 
• 
- -20 
■08 
X^ 
•21 
- -26 
- ^02 
•29 
■05 
- ^16 
•38 
- -20 
• 
- -11 
.<'8 
•09 
•10 
•24 
•08 
- ■ll 
•18 
•15 
•08 
- •u 
• 
The pairs of columns which pass the Hart and Spearman correctional standard 
give the following values : 
TABLE VIL 
Columns 
passing 
standard 
Observed columnar 
correlation R 
True columnar 
correlation 
The Hart and Spearman 
corrected columnar 
correlation R' 
2 & 7 
0^73 
0-75 
0-76 
6 & 7 
0^63 
0^89 
M5 
2 & 3 
0^70 
0^60 
vol 
2 & 6 
0^81 
0^88 
ro6 
3 & 6 
0^66 
0^83 
ro4 
Means 
0^71 
0-79 
1 -00 
True mean columnar correlation of 
the whole table and not merely 
of the pairs of columns selected 
by the correctional standard 
Dr Hart and Professor Spearman would therefore claim the hierarchy as being 
a sample of a perfect' one. The true mean columnar correlation for the whole 
table is 0^59, the Hart and Spearman correctional standard selects pairs of columns 
whose true mean columnar correlation is 0^79, and the mean value of these when 
corrected according to their formula rises to unity. This example goes far, I think; 
towards shaking confidence in their criterion. 
It must, I think, be partly chance which makes it so peculiarly unfavourable to 
their work : but I give it as it came. Reall}' a vei-y large number of such examples 
is necessary, and not all of these could be expected to be so unfavourable. The 
only other example which I have attempted I have carried far beyond 20 cases 
24—2 
