SERIES CORRELATED WITH EXPENSES 239 
expense, and that the higher or lower the ratios in the first series, 
the higher or lower are those in the second series. But is the 
reverse of these conditions true? The answer to this question, 
and to similar questions for other series, is found in Table 142. 
From this table it is seen that ratios in certain series are closely 
correlated with those of total expense. Generally speaking, the 
relations are as follows: (1) when ratios of expense are high or 
low—that is, above or below the level for the country as a whole 
—ratios of investments and of net earnings to earning assets are 
low or high; that is, the correlations are negative; (2) when ratios 
of expense are high or low, those of time deposits and of gross 
earnings to earning assets are also high or low—that is, they are 
positively correlated; and (3) the greater the deviation from type 
in the matter of total expense, the greater the deviation in ratios 
of investments and of gross earnings to earning assets. The net 
percentage amounts of deviation in the ratios in these series are 
positively correlated with similar deviations in ratios of total 
expense. 
That these relations markedly characterize the bulk of the 
frequencies dealt with, at least for certain of the series, is ap- 
parent from the alignment of the distributions shown in Table 
143, the association between total expense and gross earnings 
ratios being strikingly consistent. Space is not available in 
which to record the paired frequencies for all of the correlated 
series. In general, however, the type of distribution is accu- 
rately summarized in the net amounts given in Table 142. 
Moreover, as shown in Table 143, the type of relations found 
for deviations for all districts all years tends to obtain for 
all years for the Boston district, and for the year 1925 for all 
districts. 
A table, summarizing the types of relations measured in dif- 
ferent ways found to obtain between variable ratios in a number 
of series (the dependent variables) and ratios of total expense 
(the independent variable) will bring together our findings in 
these respects and supply, with other tables already presented, 
the bases for the generalizations on pages 249-250. Such a table 
is that found on page 250. Chart 48 shows graphically the rela- 
tions between ratios of total expense and net earnings to earning 
assets.