Jan. 12 ,1924 
Adjusting Yields for Soil Heterogeneity 
85 
6, series 1 (Table I) was divided by 1.122 , the ratio of the yield of rows 
5 and 7 (26.5 pounds) to the sum of the average yields of strains 2 and 
3 for the entire experiment (23.6 pounds) which were grown in rows 5 
and 7 of series 1. The yield of each row was adjusted similarly and 
the adjusted yields then were averaged. The means are given under the 
heading “Adjusted yields, basis of 2-alternate-row plats” in column 5 of 
Table II, for comparison with the actual yields. 
EFFECTS OF .CORRECTION 
Inspection of Table II shows that all of the means have been modified 
one way or the other. Many of the modifications are so slight as to be 
entirely negligible, whereas others appear to have some significance. 
There is a consistent difference, however, in the probable errors of the 
two sets of means, those of the relative yields being lower in every case.. 
The mean of the probable errors for the actual yields, 1.757 bushels, is 
reduced to 1.287 for the relative yields, a reduction of 0.47 bushel or 
26.75 P er cent. This represents a real gain in the degree of accuracy 
with which comparisons can be made between the strains. 
As will be shown later, the assumption of a 1:1 ratio between the 
variations in yield of the plats of two alternate rows and that of the 
row between them was not warranted entirely. It was sufficiently 
accurate, however, to eliminate one-fourth of the variation as evidenced 
by the smaller probable errors. 
EXTENSION OF METHOD 
As previously noted, the method used was not entirely satisfactory. 
In the first place, the extreme variability of the soil made the use of 
such short rows questionable. These conditions combined to make the 
plat yields fluctuate rather widely with the result that sometimes a 
yield, actually too low as judged by its ratio to the mean for the strain, 
was decreased still further because the adjacent rows yielded more than 
their mean. Part of this may have been due to competition, but much 
of it was a result of random fluctuation. Finally, a planting arrange¬ 
ment in which the replicates were distributed more uniformly would 
have been better. Objections inherent in the calculations are subject 
to elimination. Other methods, therefore, were tried, and their effects 
noted. 
OTHER BASES FOR ADJUSTING 
If the mean actual yields of the different strains represented approxi¬ 
mately their respective productiveness, it was reasonable to assume 
that the ratio of the actual yield of a plat of any given number of rows 
to the computed average yield of a group of rows of equal number and 
kind would be an approximate index of the productivity of the soil 
in which the given plat was grown. On this hypothesis, indices of pro¬ 
ductiveness were computed for plats of three and five adjacent rows, 
in addition to those for the plats of two alternate rows already consid¬ 
ered. In order to make the indices continuous, the moving average 
commonly used in time series was utilized. The method of computa¬ 
tion may be indicated from the data in Table I for the 3-row plats. 
Thus, the 3-row index (column 8) centered on row 7, series 1, was ob¬ 
tained by dividing the total yield of 39.7 pounds (column 5) for rows 
6 to 8, inclusive, by 37.9 pounds, the total yield of two average rows 
of Strain No. 1 plus one average row of Strain No. 3 (Table II, column 3). 
