82 
Journal of Agricultural Research 
Vol. XXVII, No. 2 
its mean, X on an average deviates r x y — times one unit, from its mean. 
The deviation is in the same direction if the regression is positive (r= -f), or 
in the opposite direction if it is negative. Similarly, reg YX = r x y “ * Thus, 
when any row X deviates from its mean by x units, the magnitude 
x^r x Y is the predicted deviation of the associated Y row from its mean. 
Letting the actual deviations of rows Y from their mean be represented 
by y and the predicted deviations by y v the y/s are the closest estimates of 
the y ’s that it is possible to obtain, knowing the x’s and assuming a recti¬ 
linear relationship. 
Let y-y t = y 2 , the error of estimate or residual. There are, of course, 
N y 2 s in N paired observations. Their mean is zero and their standard 
deviation is given by the equation av 2 = oyV 1 — r 2 XY - This is the “ standard 
error of estimate,” and its value is less for the y t 's than for any similar 
values predicted on the basis of x. 
adjusting yields to checks 
The assumption underlying the methods that have been generally 
used in adjusting the yields of test plats to those of nearby checks has 
been equivalent in effect to assuming an entirely arbitrary correlation 
between the two kinds of plats. Let c x and c 2 be the yields of two adjacent 
checks, C the mean yield of all checks, and Y and Y a the actual and 
adjusted yields of the test. Then, adjusting for the checks on each side 
2Y 
according to the equation, . — C = Y a , is equivalent to adjusting on 
c i i c 2 
the basis of an assumed regression coefficient of +1. When only every 
third or fifth plat is a check and the regression is supposed to decrease 
proportionately with the distance from the checks, the assumption 
is even more arbitrary. That such methods of adjustment frequently 
have reduced the variability of the test plats materially is ample evi¬ 
dence of the fundamental soundness of some means of correcting for soil 
heterogeneity. 
Without a detailed review of the literature, Stadler’s 7 discussion of 
the value and limitations of adjusting to checks may be cited as approx¬ 
imating in general the conclusions of other investigators. These may 
be summed up briefly in the statement that adjusting sometimes is 
beneficial and sometimes it is not. Stadler also discusses some of the 
conditions under which adjustment was more and less effective in his 
experiments. These may be grouped into conditions that would tend 
to increase and those that would tend to decrease the significant correla¬ 
tion between the check and the test plats. It is clear that the practice 
of adjusting to check plats is unwarranted when there is no correlation 
between the yields of the tests and the checks. It is equally clear that 
an adjustment to the checks on the basis of the actual regression of the 
test plats on the check plats is warranted and of value. On this basis 
it would be desirable to have frequent check plats in every experiment 
and to use them for adjusting the yields only in those cases in which 
there was a significant correlation between their yields and those of the 
test plats. Because of the area required, this is not practical unless the 
7 Stadler, L. J. experiments in field plot technic for the preliminary determination of com¬ 
parative yields in the .small grains. Mo. Agr. Exp. Sta. Research Bui. 49, p. 72, 1921. 
