SERIES CORRELATED WITH EXPENSES 233 
understood, Table 139 is presented, showing the distribution of 
the district-year frequencies for two of the series paired with 
total expense. The table also contains the positions of the ratios 
in 1925 in all districts, and of those for all years in the Boston 
istrict. 
The relation between ratios of total expense and ratios of in- 
vestments is generally inverse; that between ratios of total expense 
and ratios of gross earnings is direct. While not all of the 
frequencies for series showing inverse and direct correlation are 
distributed as are those in Table 139, conformations are generally 
of these types, net earnings heing one series, paired with total 
expense, about which the nature of the association is clearly in 
doubt. 
But an analysis of the relations of different types of banking 
data to variable total expense need not be restricted to correlat- 
ing district deviations. It may be pushed further with the intent 
of discovering and measuring the type and extent of the associa- 
tion between year-to-year changes in the ratios of a number of 
series paired with ratios of total expense. Specifically, it is de- 
sired to know whether, with increasing or with decreasing ratios 
of total expense, net changes of a like or of an inverse nature 
occur in those of other banking series. Such an inquiry is under- 
taken not for the purpose of establishing cause-and-effect relations 
between such series, but only with the intent of measuring the 
type and degree of the association, if any, which is present. 
Ratios of total expense are again treated as the independent 
variable. In earlier chapters, where this process was carried out 
with total expense as the dependent variable, it was found that 
by directions and by percentage amounts of change ratios of total 
expense were positively or negatively associated with variable 
changes in a number of other series. In the case now being 
studied, the process, as noted, is the reverse, interest being cen- 
tered in the directions and net percentage amounts of change in 
different series accompanying variable changes in direction and 
amount in ratios of total expense. 
Table 140 shows the net year-to-year changes in the ratios in a 
number of series paired with changes of a like nature in ratios 
of total expense. The classification of the changes in the ratios 
of total expense is secured by a method analogous to that already