nsto 
86 
Journal of Agricultural Research voi. xxvn, No. 2 
The quotient, 104.7 per cent, is the percentage yield, or index of pro¬ 
ductiveness for a plat centered on row 7. It should be noted that 
these indices were not computed by averaging the percentage yields of 
the individual rows. 
the) efficiency of the different checks 
The efficiency of the plats of different sizes as a basis for adjustment 
was studied through their correlation and regression relations to the per¬ 
centage yields of the individual rows, and through the reduction in the 
variability of the latter which was accomplished by adjusting to the differ¬ 
ent kinds of checks. 
For convenience, the individual rows will be considered as variable A , 
the plats of two alternate rows as variable B> and the 3 and 5 row plats as 
T and C, respectively. The constants reported for these plats were com¬ 
puted from correlation tables in which the class interval was 5 per cent 
with class centers at . . . 95.05, 100.05, 105.05, etc. The table for r AT is 
shown in figure 2. 
The coefficients of correlation of A with B , T, and C, and the regression 
of A on these variables, the gross standard deviations of the different kinds 
of plats, and the net standard deviations of A for constant B , T, and C are 
shown in Table III. All of these indicate the superiority of the 3-row 
moving average for adjusting yields. The net standard deviation of A 
with one variable constant is the same as the standard error of estimate 
for the coefficients of regression of A on that variable and shows the 
amount of variation that will remain in A after adjusting it on the basis 
of that regression. The relative fit of the 3 and 5 row plats to the indi¬ 
vidual rows for series 1 and 6 and series 2 and 7 is shown graphically in 
figure 1. The fit of the plats of two alternate rows is not shown, but may 
be estimated readily from the individual row values. 
The reliability of the correlation coefficients and the constants derived 
from them rests upon the assumption that the relations between the vari¬ 
ables are rectilinear. That the latter assumption is warranted as regards 
the relations of the individual rows with the 3-row plats is shown clearly in 
figure 2, in which the means of A for the corresponding values of T are 
shown by the plus sign (+). The regression line for A on T also is shown 
in figure 2. 
Table III .—Coefficients of correlation of A with B, T, and C; coefficients of regression 
of A on B, T, and C; gross standard deviations, in percentages, of A, B, T, and C; and 
partial standard deviations of A for constant B, T, and C,for a single row and for the 
mean of 4, 10, and 22 rows 
Variable. 
Coefficients of— 
Percent¬ 
age <7 of 
variable in 
column 1. 
Percentage (T A for the mean of the num¬ 
ber of rows stated, when the variable 
in column i is made constant. 
Correlation, A with 
variable in column i. 
Regres¬ 
sion A on 
variable in 
column 1. 
1 row. 
4 rows. 
10 rows. 
22 rows. 
I 
3 
4 
16.805 
14.170 
14.100 
12.440 
5 
6 
a 8.403 
6.005 
4.265 
4.729 
7 
a 5*315 
3 * 79 ^ 
2.698 
2.992 
8 
a 3*5 8 3 
2.560 
1.819 
2.016 
O.69951bO.0230 
.86i6± .0116 
.8266± .0143 
0.830 
1.027 
1.117 
12.009 
8- 53° 
9 - 4 S 8 
o Gross O' a- 
