CORN AND HOG CORRELATIONS 
45 
best fits the observed facts, an approach can be made to a quantita- 
tive solution, which, it is believed, gives a better grasp of the situa- 
tion as a whole, as well as in detail, than can be obtained from any 
mere discussion of the correlations. 
THE METHOD OF PATH COEFFICIENTS 
The first step in the use of this method is the construction of a 
diagram in which the supposed causal relations among the variables 
are represented by arrows. Each correlation can be represented 
symbolically as the resultant of the paths of influence leading from 
one variable to the other or to both from a common cause. This 
gives as many simultaneous equations as there are correlations, 510 
in the present case, for the solution of the path coefficients. Addi- 
tional equations are furnished in ^ 
those cases, such as the determina- 
tion of corn crop by acreage and 
yield, in which it is known that one 
variable is completely determined 
by two or more of the others. In 
the present case it would be theoret- 
ically possible to find coefficients 
for more than 510 different paths of 
influence. This number doubtless 
would not be too many for a com- 
plete solution. It would be hope- 
less, however, to deal with so large a 
number of unknown quantities, and 
even if it were practicable the use 
of so complicated a system would 
defeat the purpose of the analysis, 
the object of which is to obtain as 
accurate an explanation of the 
correlations as possible with a mini- 
mum complexity in the causal rela- 
tions. The problem then resolves 
itself into the discovery of a simple system of relations, which shall 
give a reasonably close approximation to the 510 correlations. 
A path coefficient, measuring the importance of a given path of 
influence from cause to effect, is defined as the ratio of the standard 
deviation of the effect, when all causes are constant except the one in 
question, the variability of which is kept unchanged, to the total 
standard deviation of the effect. Figure 26 represents a system in 
which the variations of two quantities X and Y are determined in 
part by independent causes represented by A and D, and in part by 
common causes, represented by B and C. These common causes 
may be correlated with each other through more remote causes, 
which are not represented in the figure but whose resultant is the 
correlation coefficient, r B c It is assumed that all the relations are 
linear. In practice, slight departures from linearity do not invalidate 
the analysis. Combination of effects by multiplication, as in the 
relations of acreage and yield to crop, or slaughter and weight to pork 
production, are sufficiently close to being additive where the vari- 
ability of the quantities is small in comparison with their mean 
values. 
Fig. 26.— A diagram illustrating the path coeffi- 
cients in the case of two variables {X and Y), 
determined in part by correlated common causes 
(B and C) 
