jan. 12,1924 Adjusting Yields for Soil Heterogeneity 89 
from their respective means, or this equation may be converted to abso¬ 
lute values, A = 1.027 T — 0.027. The predicted A's then may be calcu¬ 
lated for the corresponding values of T. Thus, for row 6, series 1, T = 
115.4 per cent, or 1.154. 1.154X 1.027—1.185, 1.185 — 0.027= 1.158, the 
predicted yield of row 6. The actual yield, 15.4 pounds, divided by 1.158 
= 13.3 pounds, the adjusted yield of row 6. The “Adjusted yields, basis 
of 3-row plats” in column 6 of Table II are the averages of the yields 
corrected in this way. Here again the means are modified slightly, but 
the gain in reliability as measured by the decrease in the probable errors 
is about half. Moreover, the method used here is based upon the deter¬ 
mined regression and involves no arbitrary assumption, which was not 
the case for the data in column 5. 
In practice it will be easier and sufficiently accurate to obtain the pre¬ 
dicted percentage yields graphically from the regression line drawn as in 
figure 2, but to a reasonably large scale. 
OTHER CONSIDERATIONS 
The planting arrangement used in the experiment described is in no 
way fundamental to the method of adjustment proposed. In fact, it 
would have been better from the standpoint of theory if the replicates 
of the different items had been distributed more widely. Neither is it 
necessary to have as many replicates as in this case. It is necessary to 
have plats of such size and frequency as will give a reasonable 
approximation of the productiveness of each seed class. The replicates 
should be distributed systematically to cover the experimental field as 
uniformly as possible, and in such a way that the sequence is not the same 
in the different series. Thus, representing the seed classes by 1, 2, 3, 4, 
etc., the first may be planted 1, 2, 3, 4, etc., the second, 1, 3, 5, 7, etc., the 
third, 1, 4, 7, 10, etc., and the fourth, 1, 5, 9, 13, etc., or any similar 
system that will give a different sequence in each series. The index of 
productiveness for each 5-row group under such a system would be in 
terms of the average of 20 row^s located in different parts of the field, and 
the final mean of four adjusted replicates w^ould be weighted according to 
the yield of as many as 80 row r s in a large experiment properly arranged. 
Moreover, although not all strains will be used equally in correcting each 
of the others unless the number of replications is the same as the number 
of strains in the experiment, nevertheless the basis will be an average of a 
large number of strains in each case, thus reducing the chances of distor¬ 
tion due to the specific response of a single variety. 
It is recognized that the extreme variability of the soil in the experi¬ 
ment discussed in some ways made the data particularly amenable to the 
correction used. On the other hand, probably many experimental fields 
are equally, though not similarly, variable. The rapidity of the variation 
in the case considered, as brought out in figure 1, made conditions decid¬ 
edly adverse for adjustment. It w r as this rapid variation that made the 
3-row plats better than the 5-row plats for predicting. A field with a 
gradual change in productiveness from one side to the other, but with neg¬ 
ligible fluctuations around this trend, would be ideally suited to adjust¬ 
ment on the basis of a moving average, although in such a case the opti¬ 
mum number of rows to be averaged probably would be larger. 
The important points are that adjustment on the basis of the deter¬ 
mined regression is not arbitrary and that no extra land or field labor is 
required. The computations of the indices and correlation are simple, and, 
