SERIES CORRELATED WITH GROSS EARNINGS 219

inversely correlated. Net decreases in ratios of demand deposits
to total deposits accompany both increases and decreases in ratios
of gross earnings to earning assets, but the decreases are greater
on the average and for each dispersion group when gross earnings
 ratios are increasing than when they are decreasing. Moreover,
 both for direct and for inverse correlations by direction of
change, the percentage amounts of change are positively correlated.
 That is, for instance, the greater the percentage rise or
fall in gross earnings ratios, the greater the net percentage rise
or fall in ratios of total expense. These series are positively correlated
 both by direction and by amount of year-to-year change.
But the greater the percentage rise or fall in gross earnings ratios,
the greater the net percentage fall or rise in ratios of demand
deposits to earning assets. In the latter series, correlation by
type of change is inverse; by percentage amount of change it
is direct.
The results shown in Table 133 summarize the changes of the
ratios in the twelve districts for the seven years. The ratios in
the various districts, while having their own peculiarities, as
is evident from matter presented in earlier chapters, are sufficiently
 alike in their dispersion from district and country averages
 and in their year-to-year changes to suggest common norms
and trends. Moreover, when the series are correlated, uniformities
 of a direct or of an inverse nature obtain. Are the correlations
of ratios for individual districts for the various years, and of
those for different years for a single district, the same in general
as those for all districts and all years? This condition was found
to obtain for the correlations of total expense and of net earnings
 with gross earnings for the Boston district for the years 1919
to 1925 and for all districts for the year 1925, the correlated
series being deviations from district averages. Does it obtain
between the same series, for this restricted experience, when the
pairs of items are year-to-year percentage changes? The answer
to this question is found in Table 134, which shows by position
the frequencies for (1) all districts and all years, (2) the Boston
 district for each of the years 1919-1925, and ( 3) each of the
districts for the change between 1924 and 1923.
From this table it is seen that (1) year-to-year changes in the
ratios of total expense and of net earnings are positively correlated
 with year-to-year changes in gross earnings ratios: (2) the