There’s a lot of interesting data in $4 to $1: Public Library Benefits and Budgets, Volume 1, Libraries by Size (currently around $16 paperback and $8 ebook or $32 site license, if you buy it by Friday, October 18, 2013)–data that can help you understand the picture of public libraries across the country as well as how your own library measures up.
One key figure is the correlation between circulation per capita and spending per capita: Libraries that spend more do more.
The correlation is strong (that is, the Pearson’s Coefficient is at least 0.50) for all size categories of public libraries and for the nation as a whole (0.59).
Where is it strongest?
Among 828 libraries serving 40,000 to 99,999 people (legal service area population, not registered borrowers).
As you’ll see on page 150 of the book, that correlation is 072–a very strong correlation.
[Which libraries have the lowest correlation? In fact, only one size category falls below 0.61: The very smallest libraries, those serving fewer than 1,000 potential patrons, with 0.51 correlation. That's not surprising--with such small patron groups and correspondingly small budgets, you'd expect a wide range of results.]