SERIES CORRELATED WITH EXPENSES 237 
A frequency grouping of the percentage year-to-year changes 
in the correlated series will serve to illustrate the detail from 
which certain of the net amounts in Table 140 are secured. The 
nlain figures in Table 141 relate to the frequencies for all of the 
changes for all of the districts; the bold type figures refer to the 
respective districts, as named in the Federal Reserve Act, for 
the changes between 1924 and 1925; and the letters indicate the 
different pairs of years in the Boston district. It will be observed 
that the alignments of the changes in the single pair of years 
in all districts, and in all year-to-year changes in one district, 
follow generally that for the combined experience in all districts. 
The discussion immediately above relates to the types and 
measures of correlation obtaining between deviations and net 
year-to-year changes in district ratios of total expense to earning 
assets and similar ratios in other series of bank data. Another 
basis upon which correlations between such series may be deter- 
mined is available. It has already been determined that while 
ratios of expense and of other indexes of bank operation vary 
among the respective Federal Reserve districts, a single ratio each 
year for each series being compounded out of the records for the 
entire membership in each district, these variations for individual 
series, rather than being haphazard, are characterized by clearly 
defined norms, and that those for certain paired series are cor- 
related positively or negatively. The nature of this association, 
with ratios of total expense treated as the dependent and each 
of a number of other series as the independent variable, has al- 
ready been determined. In the matter which immediately fol- 
lows, variations by districts being taken from the averages for 
the country as a whole, the order of the correlated variables is 
reversed. Specifically, and with respect to ratios of gross earn- 
ings, for instance, the questions to be answered are of the follow- 
ing order: Do districts having ratios of expense above (or below) 
the country levels have ratios of gross earnings above (or below) 
the country level, or vice versa? Moreover, what is the nature of 
the relations between the percentage amounts of such deviations? 
Similar questions may be asked respecting each of the other series 
of ratios. 
It has already been learned that districts having high or low 
gross earnings ratios, respectively, have high or low ratios of total