Feb. a8, 1916 
Correcting for Soil Heterogeneity 
1041 
plots are repeated at sufficiently frequent intervals, they will undoubtedly 
be a great aid in determining the correction for soil differences. How¬ 
ever, where field tests of this kind are carried out on even a moderate 
scale, the use of check plots adds very materially to the labor and expense 
of the experiment. For example, in 1914 we grew 150 one-fortieth acre 
plots. From a study of the field it seems clear that any adequate system 
of checks would have required 1 check plot to every 5, or about 30 
additional plots. The labor involved in handling these would have been 
considerable; and judging from the literature on the subject, the value 
of the results might still be very doubtful. 
For several years this Station has been carrying on variety tests of oats. 
The object of these tests is to obtain some measure of the productiveness 
of new strains or varieties produced in the plant-breeding work. These 
new strains are always tested along with a number of standard com¬ 
mercial varieties. The method adopted in this work (13) is to grow four 
systematically repeated plots of each variety. The size of each plot is 
33 feet square, or one-fortieth of an acre. The four plots thus make a 
total of one-tenth of an acre devoted to each variety. These plots have 
always been grown on a more or less rectangular piece of ground. (See 
fig. 4.) The fields for these tests have been chosen for their apparent 
uniformity. However, the resulting yields have always indicated that 
certain portions of the field were much better or worse in respect to soil 
fertility than the average of the field as a whole. In certain cases two 
or more of the four plots of a variety come to lie, say, in certain of these 
more fertile spots. This tends to produce an unduly high average for 
that variety. 
In order to obtain a correcting value for these different soil conditions, 
it occurred to us to determine first the probable yield of each plot by the 
contingency method. This may be done as follows: Take a theoretical 
field divided into plots as in figure 1. Let a, 6, c ..../ represent the 
observed yields of the respective plots, of which the mean yield is p . 
Then, assuming all plots to be planted with the same variety and con¬ 
ditions other than the soil to be uniform, we can obtain the most probable 
yield of, say, plot a by multiplying the sum ac by the sum aj and dividing 
by the total al. Proceeding in this way for each plot, we can obtain a 
calculated yield a', bc f ... for each plot. The mean of these cal¬ 
culated yields will be the same as the mean of the observed yield—viz, p. 
It is clear that these so-called calculated yields correspond to what 
Pearson (12) in his work on contingency has designated by v UVJ or the 
value for each square on the hypothesis of independent probability. 
The difference between the observed and calculated yields would then 
correspond to what Pearson calls a subcontingency. 
The “calculated” yields obtained by this contingency method repre¬ 
sent the most probable yields of the respective plots based on the distri¬ 
bution of the observed yields. This method of estimating the probable 
