GROSS EARNINGS IN DISTRICT I 279 
between gross earnings ratios and those of total expense and of 
net earnings, is to select for the respective series suitable aver- 
ages with which the ratios in the correlated series may be com- 
pared. Those chosen are the yearly averages of the banks in 
the various volume (earning assets) groups. 
Having selected standards of reference for the series to be 
correlated, as for instance gross earnings and total expense, the 
process of manipulating the data is as follows: (1) For each 
volume group, determine the percentage amounts and directions 
by which the ratios in the correlated series for each of the banks 
in 1924 deviate from the 1924 group average. (2) Select classes 
of uniform widths into which are placed the paired variables 
(deviations) for each bank, the resulting distribution being of 
the double-frequency type. (3) Repeat this process for each 
of the volume (earning assets) groups and combine the fre- 
quencies, thus securing a distribution for all banks in the year 
1924. (4) Repeat processes (1) to (3) for the year 1925. (5) 
Combine the distributions for the two years. 
The frequencies in Table 159 show the results of carrying out 
these steps for paired ratios of gross earnings and of total 
expense to earning assets, and supply the bases for the sum- 
maries at the right and at the bottom of the table. These are 
obtained as follows: (1) total the number of instances in the 
respective lines and columns; (2) add and then average the 
amounts in each line so as to get the average percentage disper- 
sion for the factor in the stub, used as the independent variable; 
(3) algebraically add and then average the amounts in each 
line so as to get the net average percentage deviation for the 
factor in the caption treated as the dependent variable, and (4) 
reverse processes (2) and (3) so as to get the average percentage 
dispersion of the factor in the caption when used as the independ- 
ent variable, and the net average percentage dispersion for the 
factor in the stub when treated as the dependent variable. The 
results of steps (2) and (3) supply measures of regression of total 
expense on gross earnings; those of step (4) measures of regres- 
sion of gross earnings on total expense. 
Similar analysis was made of the relations between ratios 
of gross and of net earnings, the results of carrying through the 
processes for the two paired series being summarized in 
Table 160.