Karl Pearson 
251 
The data are not very suitable, but I use them because Slutsky has done so. 
Their unsuitabihty arises (i) from the smallness of the total population, but 
especially (ii) from the marked signs of heterogeneity obvious in the marginal 
totals. If y be the vertical, x the horizontal variate I obtain, assuminrj that the 
column headinf/s represent central values, the following constants for the distribution : 
in^ = 47-1572 copecks per pud, - 13-7769, 
?»y = 47-0363 copecks per pud, 13-6852, 
r„ - -953,545, 
Regression hne : y^. = -947,205^' -f 2-3687. 
My values of Oj., Oy, r^.,j, and of the regression line constants, difl'er very considerably 
from Slutsky's. I have not used Sheppard's correction which would, however, 
only have emphasised our differences. I have not reworked Slutsky's first method 
with these changes because I do not think it is the correct method, i.e. he uses 
observational values for o'j,^ , and thus I cannot say whether the above values 
w^ould improve his bad fit (i.e. P = 0-02), but I have adopted my own value 
4 
using for the mean value ct„" (1 — = 16-9965. Slutsky takes for the 
value of CT^ , on the assumption of homoscedastic arrays, the mean of the observed 
standard deviations of the arrays, i.e. 
(".^.; = 3-8022 
according to his values, or he takes 
a\ =-- 14-4567. 
This value is, I think, theoretically incorrect, the mean value of a'^,j^. = (1 — 
and this must be the homoscedastic value. Clearly Slutsky's value is too small. 
The point remaining is the value of I should naturally determine it from 
the frequency curve for the marginal ;r-totals, but the extreme irregularity of the 
marginal a-totals — due partly to paucity of data, but more to probable hetero- 
geneity — makes any such process unsatisfactory. I have therefore taken = to 
the observed array frequency — a result with which I am thoroughly dissatisfied, 
but which appears to be the only course. We have then the table on p. 253. 
, 256-81196 
T^^^^ . ^' = ^^^-^'-^^- 
Looking this out in the Tables for Goodness of Fit we find for n' = 11 + 1 = 12, 
P=-18. 
Thus we see that the fit is passable, although not brilliant, much better than 
Sbitsky's P - -02. 
Slutsky also gives by his second method = 15-1 and P = -18 for the fit on 
the hypothesis of homoscedasticity, but I think this can only arise from a curious 
