APPENDIX I 
379 
the influence of gross earnings on net earnings is greater than 
that given by (7), which expresses the most probable effect for 
all the banks. Similarly, the negative mean v of Group 4, 
— 1.0 + 0.3, indicates that the influence of gross earnings on net 
earnings in that group is smaller than that given by (7), if the 
influence of total expense is assumed everywhere to be the same. 
Thus far in this analysis, an approximate measure of the rela- 
tive influence of gross earnings and of total expense on net earn- 
ings is secured. It has also been shown that the probability is 
great that either one or the other of the following propositions 
is true: (1) if the law of variation of net earnings with gross 
earnings is the same for banks in all groups, then the probability 
is about 1,000 to 7 that the law of variation of net earnings with 
total expense is different for banks in the different groups; (2) 
if the law of variation of net earnings with total expense is the 
same for banks in all groups, then the probability is also large 
that the law of variation of net earnings with gross earnings is 
different for banks in the different groups. 
One method of proving which of the two above propositions 
is the more true is to treat each of the four groups separately, 
in a manner similar to that followed for the entire 408 banks. 
This has been done. The constants K,, K,, E’;, and E’, in the 
general equations (1) and (2), for each of the groups, together 
with the probable errors, are shown in Table IV. 
The outstanding facts in this table are, first, that the law of 
variation of net earnings with gross earnings is practically the 
same in all groups; that is, the constant E, = 4 0.77 + 0.04, ap- 
proximately, and is the same as that given by equation (7) based 
upon all banks. Second, the law of variation of net earnings 
with total expense varies widely from group to group; that is, 
the constant E,” has a minimum numerical value of 0.33 in Group 
4 and a maximum numerical value of 0.62 in Group 3. The differ- 
ence between these two values is nearly 3 times their probable 
errors, significant indication that total expense influences net 
earnings more in banks in which it is low—it is these which tend 
to increase—than in banks in which it is high—it is these which 
tend to decrease. Moreover, the difference between any two 
group values of E. (with the possible exception of those for 
3 The difference is about eleven times the probable error of E from Solution 
IL viz., * 0.026.