SERIES CORRELATED WITH NET EARNINGS 253 
respect to the items just mentioned, and an average result is 
calculated, it does not necessarily follow that the average rate 
of net earnings is large when gross earnings rates are large or 
when total expense rates are small, or that it is small when inverse 
conditions obtain. Neither does it follow that when the average 
rate of gross earnings is large or small, the average rate of net 
earnings is large or small, because nothing is said about total ex- 
pense, and, of course, this is the important “missing link” in the 
equation of relations. 
Now the facts are, as shown in Chapters V, VI, and VII, that 
ratios of gross earnings, of total expense, and of net earnings for 
member banks, by districts, vary from district to district and 
from year to year. Such variations are of two types: the respec- 
tive ratios vary among themselves, and with respect to each other. 
That is, for the experience studied, gross earnings, total expense, 
and net earnings do not stand in the simple relation given above— 
8—-6=2 and 6 —4==2. They are rather of the following type: 
8—6=2 and 7-4=3. Accordingly, with variation character- 
izing all three series, comparisons of them individually and one 
with another can be made only by using some form of an average 
as a standard. And when this is done, the relations found to 
obtain are true only “on the average.” For the collective experi- 
ence compounded into an average figure, the simple relations be- 
tween high or low gross earnings, high or low total expense, and 
high or low net earnings, or vice versa, do not necessarily hold. 
This much is apparent with respect to the correlations found to 
obtain between different series, as developed in previous chapters. 
But more of this presently. 
Average net earnings, as has already been noted, are residuals, 
depending upon the relations between average gross earnings and 
average total expense, each of these averages summarizing condi- 
tions varying with respect to the member banks by districts and 
by years. Moreover, both average gross earnings and average 
total expense ratios are functionally related to operating condi- 
tions, and these vary among the respective banks. It is apparent, 
therefore, that in studying by districts (1) the norms and trends 
in the ratios of net earnings themselves, relative to appropriate 
average conditions within the districts or for the country as a 
whole, and (2) the correlations of net earnings with other series, 
variation rather than strict uniformity rules: and, further, that