250 
" Goodness of Fit " In Statistics and Physics 
"a; V-"- ' xy) 
which admit of easy calculation when once we have determined that characters 
of the sampled population m^,, v^, a^, f„j or may be replaced by the like 
characters calculated not from a single array but from the whole material of the 
sample. I am inclined to believe that 
2 _ AT i Vx.vY "~ {Vx.yY 
^ 1 - 7? 2 
^ 'I x.y 
would be an effective measure of x^, where, however, we must not put ->;^,.,^ = rj^^y 
in the numerator for we are actually measuring the improbability of the deviations 
of -q.j.^y from i.e. of from nip. But such a form would be of Uttle use unless 
we knew the sampled population. It indicates, however, how risky is the problem 
of replacing only certain of the sampled population values of the constants by 
those of the sample. 
In any given case it appears best to draw the scedastic curve, i.e. plot o-,j to 
Hj,. This curve may be fitted with either a straight hne or parabola of the second 
order, according as the array variabihty decreases or increases in one or both 
directions from some fairly central array. This is perfectly easy, but care must 
be taken to weight the standard deviations of the arrays with their frequencies. 
Very rarely as T have pointed out previously are the data ample enough to justify 
anything but a linear scedastic curve. If this line be practically horizontal then 
we can take a%^^ = (1 — rj'^-r.y) throughout. I propose to illustrate the whole 
process on the two examples selected by Slutsky. 
Illustration I. Prices of Rye in Samara. 
The example is given in Slutsky's recent paper* and is as follows: 
Correlation between 'prices of rye at monthly intervals. 
Price of rye in Samara a month earlier 
Copecks 
per pud 
25 
SO 
S5 
40 
45 
50 
55 
60 
65 
70 
75 
Totals 
cS 
25 
3 
5 
1 
f) 
B 
30 
6 
13 
2 
21 
■35 
3 
3 
2 
8 
40 
1 
2 
1 
4 
45 
1 
2 - 
10 
2 
15 
50 
2 
19 
4 
1 
26 
55 
3 
2 
2-5 
1-5 
9 
60 
2 
5-5 
5 
12-5 
O 
65 
1 
1 
3-5 
5 
1 
11-5 
70 
1 
4 
1 
6 
_o 
75 
1 
1 
2 
Ph 
Totals 
9 
21 
8 
4 
15 
25 
9 
12-5 
12-5 
6 
2 
124 
* "On the Criterion of Goodness of Fit of the Regression Lines and on the Best Method of Fitting 
them to the Data." Journal of tlic R. Statistical Society, Vol. lxxvii. p. 81. 
