Miscellanea 
311) 
I have tested the results on an instance given in Professor Pearson's original memoir, namely 
the age and auricular height in Girls, correlation table pp. 34 and 54. 
The means of the arrays in the full table are as follows : 
Even Grouping 
Number of 
Grouping 
III 
11 
I 
Age 
3— 4 
4— 5 
5— 6 
6— 7 
7— 8 
8— 9 
9— 10 
10— 11 
11— 12 
12— IS 
13— Ik 
14— 15 
15— 1G 
16— 17 
17— IS 
18— 19 
19— 20 
20— 21 
21 22 
22—23 
Mean Auricular 
Height 
115- 25 
116- 9643 
117- 4722 
119- 1000 
120- 3026 
121- 6340 
121- 7246 
122- 8160 
123- 1427 
123- 8908 
124- 8622 
125- 7146 
126- 1565 
126-5340 
126- 9132 
127- 0205 
129-5577 
123-8214 
126-5000 
125-25 
Number of 
Cases 
1 
7 
18 
40 
76 
125 
177 
235 
261 
309 
263 
198 
214 
162 
95 
61 
13 
7 
8 
2 
Uneven Grouping 
Number 
IV 
VI VII 
These were grouped in seven ways in three of which the groups were of equal width, and the 
other four give an attempt at equal frequency : the method of grouping is set out by means 
of columns headed in Roman numerals. The age distribution differs significantly from the 
norma], the constants being /3i = "0013, j3 2 =2 , 7101, but it would perhaps have been better to 
have selected a less normal distribution : still it represents the ordinary ' cocked hat ' statistics 
that tend to occur. 
The regression is certainly not very linear, the growth apparently ceasing at about 18-19. 
The values of rj' 2 (the raw value), H 2 (the value after using Professor Pearson's correction) and 
rj 1 (the value after attempting to use the X' J correction) are given in the following table. 
Number 
of 
Grouping 
Number 
of 
Groups 
V 
H- 
1 - \ 2 from 
Normal Curve 
V 2 
V 
v" 
V 
I 
20 
■09183 
•303 
•08414 
•08489 
•291 
•08494 
•291 
11 
10 
•08657 
■294 
•08290 
•08595 
•293 
•08510 
•292 
III 
K 
•07701 
•278 
•07535 
•08786 
•296 
•08635 
•294 
IV 
9 
•08836 
■297 
•08510 
•08953 
•299 
V 
6 
•08342 
•289 
•08136 
•08913 
•299 
VI 
5 
•08218 
•287 
•08053 
z 
•08885 
•298 
VII 
2 
•06203 
■249 
•0615V) 
•09739 
1 
■312 
