254 
" Goodness of Fit " in Statistics and Physics 
The distribution can accordingly be described by a symmetrical limited range 
curve of my Type LI : 
The values of the constants being found we have 
y = 283-7415 
,13-264,696/ 
This curve was drawn on a large scale and the frequencies for each age 
integrated with the following results: 
Age 
Frequency 
Age 
Frequency 
Observed 
Calculated 
Observed 
Calculated 
3—4 
1 
1-5 
13—14 
263 
275 
4—5 
7 
7-5 
14—15 
198 
246 
5—6 
18 
19 
15—16 
214 
197 
6—7 
40 
41-5 
16—17 
162 
143-5 
7—8 
76 
76 
17—18 
95 
91-5 
8—9 
125 
123-5 
18—19 
61 
53 
9—10 
177 
178 
19—20 
13 
26 
10—11 
235 
227-5 
20—21 
7 
9 
11—12 
261 
265-5 
21 22 
8 
7 
12—13 
309 
282-5 
22—23 
2 
1-5 
The goodness of fit of the calculated to the observed array frequencies was tested. 
I found X" = 25-4769 giving P = -146, or such a sample would occur about once 
in seven trials. The fit therefore is a fairly reasonable one, and the above values, 
not the observed ones, have been used for the array frequencies. Clearly they 
effectively smooth the random sampling. 
(iii) The standard deviations of the arrays have been given by me*, and it 
has been shown that the arrays are very far from homoscedastic. The value 
of Tj is -303,024, which combined Avith gives for the mean square standard 
deviation of the arrays in squared 2 mms. units 
V = 10-835,433. 
I now somewhat diverged from the plan of my memoir on skew regression. 
I sought the best fitting straight line to the weighted squares of the standard 
deviations, i.e. I made 
u = 8 {n„ (a„2 - Ax - 5)2} 
a minimum, where nj, is the frecjuency of the pth array of auricular heights for 
girls of age x, and a,, is the standard deviation of this array. In working this 
I omitted the first and last arrays as t][uite unreliable. I found A = -436,706, 
giving for the line 
_ _ -436,706 (a; - x), 
or oj," = •436,706* + 5-290,970. 
* Loc. cU. p. 34, Table and Plate I, Diagram II. 
