Karl Pearson 
253 
X array 
/, 2\ , 
» p = w„ 1 - ^ + 2 
Observed w^, 
Theoretical nip 
(mp - vl„f 
n"p (nip - mpY 
25 
10-8548 
28-333 
26-049 
5-2167 
56-6262 
30 
22-6613 
29-523 
30-785 
1-5926 
36-0904 
35 
9-8710 
34-375 
35-521 
1-3133 
12-9636 
40 
5-9355 
42-500 
40-257 
50310 
29-8615 
45 
16-7581 
44-000 
44-993 
•9860 
16-5235 
50 
26-5967 
50-800 
49-729 
1-1470 
30-5064 
55 
10-8548 
55-500 
54-465 
1-0712 
11-6277 
60 
14-2984 
59-600 
59-201 
-1592 
2-27631 
65 
14-2984 
62-200 
63-937 
3-0172 
43-1411 
70 
7-9032 
70-000 
68-673 
1-7609 
13-9167 
75 
3-9677 
72-500 
73-409 
■8263 
3-2785 
S{n"^, (Dip - mpf\ = 256-81196. 
balancing of errors. For (i) his theoretical m^'s differ considerably from mine 
owing to the divergence in our values of standard deviations, correlation and 
regression, and (ii) he has used a different value to mine for fip, and what I believe 
to be an erroneous value of a^Yi,, — namely too low a value. It appears to be thus 
a mere chance that we should reach the same result. 
Illustration II. Auricular Height of School Girls. 
Slutsky takes this example from my memoir on Skew Correlation*, and it is 
a peculiarly good illustration for the following reasons: 
(i) The regression line is distinctly skew. In my paper Yp, the mean deviation 
in auricular height from the mean auricular height of the general population of 
girls who differ from the mean age of the general population by Xp, is given 
by the cubic 
Yp = -296,076 + -722,886 x Xp- -029,580X^,2 - -002,223X^3, 
and the goodness of fit of this regression line is to be tested. 
(ii) The frequency distribution of the ages of the 2272 girls is : 
Age ... 
3—4 
4—5 
5—6 
6—7 
7—8 
8—9 
9—10 
10—11 
11—12 
12—13 
13—14 
Frequency 
1 
7 
18 
40 
76 
1.52 
177 
235 
261 
309 
263 
Age ... 
14—15 
15—16 
16—17 
17—18 
18—19 
19—20 
20—21 
21 22 
22—23 
Frequency 
198 
214 
162 
95 
61 
13 
7 
8 
2 
This is not normal. We find for its constants : 
Mean age = 12-7007 years, /3i = -001,335, 
o-,, = 3-064,819 years, = 2-710,593. 
The probable error of is about -045 and thus cannot be the result of sampling 
from Gaussian material. ^-^ is sufficiently near zero to mark the distribution as 
substantially symmetrical. 
* Drapers' Company Research Memoirs. Biometric Scries il. p. 34. Cambridge University Press. 
