## Give Us a Dollar: A budget table in detail

Before regaling (?) you with more commentary on the close-up picture of America’s public libraries in FY2010, as provided through several hundred tables in Give Us a Dollar and We’ll Give You Back Four (2012-13)–also available as a DRM-free PDF or a library-ready hardback–it might make sense to step through one or two of the tables in detail to help show how it works.

There are mostly what I call benchmark tables and budget tables (each budget table printed as a single table combining two logical tables to save space).

The benchmark tables have rows based on the measure of a certain metric–e.g., for circulation per capita, the top row is 24+, the second row is 17-23 (which means “17.00 to 23.99”) and the bottom row is 0-1 (that is, 0-1.99). Other columns show the percentage of libraries in that row, the cumulative percentage from the top down, the median benefit ratio for the libraries in that row (the number at which half the libraries are at least that high and half are no higher), and the median expenditures per capita for that row.

The budget tables have rows based on expenditures per capita, and the rows are the same in all budget tables–e.g., \$73-\$399[.99] as the top row, \$5-\$11[.99] as the bottom.

The 16 libraries with \$400 or more per capita spending and the 144 with less than \$5.00 were omitted. Those 16 libraries must be doing some remarkable work in their communities…

Columns show the 25%ile, median and 75%ile for a given metric–that is, respectively, the point at which one-quarter of the libraries fall at or below that number, the point at which half fall at or below and half fall at or above, and the point at which three-quarters fall at or below the number.

Let’s step through one such table–the table for circulation per capita in Chapter 11, which covers libraries serving 6,800 to 8,699 people. (This table also appears in the commentary coming in the November Cites & Insights, along with a scatterplot that shows why I rely on tables rather than graphs for this book.) If you’re wondering, 6,800 to 8,699 is, as with every chapter (3-19), roughly 510 libraries (actually 503 in this case) and roughly one-seventeenth of the full set of 8,659 libraries covered in tables. Eight chapters cover smaller libraries, eight cover larger ones–these libraries, which I think of as “larger small libraries,” are the halfway point.

Here’s the table:

 \$/cap Circulation per cap 25% Med 75% \$73-\$399 13.23 16.99 24.19 \$53-\$72 9.81 15.48 20.85 \$43-\$52 8.07 11.18 15.76 \$36-\$42 8.07 10.40 13.71 \$31-\$35 6.99 9.97 12.21 \$26-\$30 5.78 7.98 11.00 \$21-\$25 5.27 6.98 9.05 \$17-\$20 4.58 6.05 8.69 \$12-\$16 2.57 4.11 5.35 \$5-\$11 1.66 2.78 3.82 Overall 4.86 8.10 13.29

What does this tell us? First, half the libraries in this size category circulated 8.10 items per capita (potential borrowers, not just actual registered patrons) or more, half 8.10 or less. The lowest quarter circulated 4.86 or less; the highest, 13.29 or more.

But those are the overall numbers. In this case, it’s consistently true that the median circulation goes up as expenditures per capita rise. (That’s always true in general, but in some groups of libraries there are row pairs where it’s not, frequently because there are very few libraries in a given expenditures bracket.) So:

• Half the worst-funded libraries (\$5-\$11.99 per capita) circulated 2.78 per capita or less, and half of those circulated 1.66 or less–and the busiest quarter circulated 3.82 or more.
• Add a little money, add a little circ, but with a lot of overlap. Thus, for libraries spending \$12-\$16.99 per capita, the lowest quarter circulated less than the lowest half of the \$5-\$11 libraries, but the highest half circulated significantly more: 4.11 or more for half the libraries and 5.35 or more for the busiest quarter.
• A little more money, a little more circ: three-quarters of the libraries spending \$17-\$20.99 circulated more items per capita than the halfway point for \$12-\$16.99 (that is, the 25%ile is 4.58, compared to 4.11 as the median on the lower row), and the halfway point is almost 50% higher than for the less-well-funded libraries.
• And so on, step by step: Overall, when you add funding, you get more circulation per capita–probably due in part to longer hours and a fresher collection. It’s not neat: There’s always overlap, even at the top. But it’s consistent.

That’s the budget table. Because it’s dealing with percentiles, some may find it confusing, but it shows how your library fits in. In this case, if you’re in a library that serves 7,500 people, spends \$165,000 (excluding capital expenses) and circulates 60,000 items, you’re in the second quarter for similarly-funded similar-size libraries: Definitely in the top half (6.98 and above), definitely not in the top quarter (9.05 and above). Your circulation level would be almost exactly average if you were spending, say, \$195,000…but since you seem to be a relatively efficient library, you could reasonably aim for, say, 75,000 circulation, or even try to get to the top quartile for that better funding at 82,500 or more.

That’s one table out of hundreds in the book.