A. Ritchie-Scott 
125 
Then 
+ 2S?„^i2 0-uO'l2-Sll . 12 
When = = 
1 we have the mean r, r,^, and if there are I r's 
2 So"!!^ + 2ScriiCTi2i?ii.i2 
.(147). 
.(148), 
which for convenient computation may be written 
2 ^11-11 ^ ■ 12 
In finding the mean weighted r we may regard as the mean of uncorrelated 
values of r of equal weight each having the s.D. CTq. Hence ct^ 
and ^1 
2' 
i.e. the weights are proportional to the reciprocals of the squares of the s.D.'s. 
Putting this value in (147) we have 
2 _ 
9"^ ^11 • 12 
(^nO'i2 
.(149). 
§ 14. Details of tables and summary of numerical results. 
I. The first table examined was taken from Pearson and Heron's paper "On 
Theories of Association," Bioynetrika, vol. ix, p. 220, Table XIV, and is a Gaussian 
surface for r = -5 adjusted to give whole units in the cells. 
I 
2 
3 
4 
5+6 
7 
8 
Total 
1 
7 
20 
5 
2 
34 
2 
21 
14,5 
79 
36 
10 
9 
1 
301 
.3 
6 
94 
85 
54 
19 
22 
4 
284 
4 
2 
32 
39 
31 
12 
17 
4 
137 
5+6 
18 
28 
25 
11 
18 
5 
105 
7 
11 
22 
24 
12 
22 
7 
98 
8 
2 
6 
8 
5 
13 
7 
41 
Total 
.36 
322 
264 
180 
69 
101 
28 
1000 
The frequency in heavy type contains the mean of the surface. 
A. Table I divided so that the mean falls in cell 7122,. 
1 +2 
3+4 
5+6+7+8 
Total 
1+2 
193 
122 
20 
335 
3+4 
134 
209 
78 
421 
5+6+7+8 
31 
113 
100 
244 
Total 
358 
444 
198 
1000 
