## Give Us a Dollar: Case Study—Part 4

This concludes the story of Fourbuck Public Library in New York (a mythical library based on the average of two real libraries) and how it might benefit from a revised version of Give Us a Dollar and We’ll Give You Back Four. If you find this revised version more useful, please let me know.

Earlier portions appeared Monday, Tuesday and Wednesday, June 11-13, 2012.

## Deeper and Different?

As I was stepping through this case study, I found myself thinking of a very different approach to the heart of the book—basically, everything after Chapter One. The different approach would rely almost entirely on derived numbers, numbers that should be comparable across very different libraries. It would have fewer but much longer chapters.

Here’s what I have in mind. I need feedback as to what is likely to work best, and whether this model or the current book should be the basis for refinement.

### Fourbuck’s Data

With the new model, almost every book purchaser would want to send me email asking for the library’s data line. While everything in the data line can be readily calculated from 2009 IMLS reports, there are more derivative figures and it’s easier to just get the bunch.

Here’s what Fourbuck would get back from me (collapsed into a few lines instead of one line per label-data pair):

St: NY Key: NY999X LSA: 10,768 Exp: \$280,057 Vis: 48,019
Ref: 3,590 Circ: 94,886 ILL: 23,625 Attend: 2,922 PC: 5
PCUse: 6,189 \$/Cap: \$26.01 Ben/Cap: \$140.21
Hrs: 2,559 PC: 5 Circ/c: 8.81 BenR: 5.39 Att/c: 0.27
PC/c 0.57 Ref/c: 0.33 Vis/c: 4.46 Circ/hr: 37.1 Vis/hr: 18.8

I’ve omitted most of the derived benefit amounts and partial benefit ratios, added two new derived figures (circulation per hour and visits per hour), and moved things around—mostly so the last 10 data elements appear in the same order as they do in tables.

After a revised Chapter 1, the book would consist of two very long chapters (and possibly shorter commentary chapters). The first of the two chapters would discuss libraries by size (legal service area), using expenses per capita as a secondary axis. The second would discuss libraries by state, using size as a secondary axis. (Should the secondary axis, that is, the rows for each table, be ten size categories or 18? Advice?) I’ll just step through the portion of the possible Chapter 2 that’s relevant to Fourbuck.

### 2. Libraries by Size

Instead of the ten size categories used by HAPLR or the eleven used in other sources, both of which yield widely different numbers of libraries per section and tend to overemphasize the few hundred very large library systems, this study would use size brackets chosen based on the actual data, designed to have roughly 500 libraries in each bracket.

For 2009 data, given the exclusions I’ve already made, that means 18 size brackets, with none having fewer than 493 or more than 506 libraries. (For the number-minded among you, that’s 500 plus or minus 7.) A real-world equal-size breakdown necessarily emphasizes smaller libraries, since most US public libraries are small. So, for example, the Fourbuck library, with an LSA of 10,768, is in the 10th of 18 brackets (starting from the smallest), a bracket including 505 libraries serving 8,700 to 11,199 people.

The secondary axis, operating expenditures per capita (\$ per cap), appears to work well with ten divisions. Given 2009 data, those divisions are the ones used in the preliminary edition (e.g., \$82 and up, \$61 to \$81.99, etc.).

This methodology should mean that a typical row of data in a table (except the richest one) should cover roughly 50 libraries, although that number will vary widely (in the example shown here, it varies from 41 to 60).

So far, here’s what I think would appear in each of 18 sections of the new Chapter 2, subject to feedback, refinement, addition of commentary and possible addition of correlations and graphs if they appear to add something. There are six tables (the chapter would begin with six tables covering all libraries). Except for the first, which shows the number of libraries and percentage for each dollar bracket, each table shows two metrics—and shows not only the median library but the 75%ile (that is, bottom of top quarter) and 25%ile (top of bottom quarter). Let’s step through the actual tables that are relevant to Fourbuck and see what we find.

 \$ per cap Count % \$82+ 34 7% \$61-\$81 47 9% \$46-\$60 41 8% \$38-\$45 60 12% \$32-\$37 55 11% \$27-\$31 56 11% \$22-\$26 45 9% \$17-\$21 60 12% \$12-\$16 57 11% \$5-\$11 50 10% Overall 505

Table X.1 Expenditure distribution of libraries serving 8,700 to 11,199 people

Table X.1 is the only table showing number of libraries. Fourbuck notes that it’s in one of the smaller groups—and also, significantly, that 58% of libraries in this size group have better funding. (Should there be a cumulative % column here to make that calculation trivial?)

 \$ per cap Hours Personal Computers 25% Med 75% 25% Med 75% \$82+ 2,912 3,151 3,536 14 19 27 \$61-\$81 2,626 2,812 3,276 10 14 19 \$46-\$60 2,743 2,968 3,276 7 13 19 \$38-\$45 2,444 2,721 2,970 7 10 17 \$32-\$37 2,488 2,717 2,964 8 19 14 \$27-\$31 2,366 2,756 3,120 7 12 14 \$22-\$26 2,080 2,496 2,912 6 8 13 \$17-\$21 2,028 2,285 2,600 6 8 11 \$12-\$16 2,040 2,288 2,601 7 10 14 \$5-\$11 1,848 2,167 2,382 5 7 10 Overall 2,236 2,678 3,000 7 10 15

Tabke X.2 Hours and personal computers in libraries serving 8,700 to 11,199 people

Fourbuck is open just slightly longer than most libraries with its funding level—but it’s not in the top quartile. More to the point, libraries with better funding are open a lot more hours, which almost automatically means more service to the community. Adding another two or three hours per week would put Fourbuck at the median point for libraries of this size, but more would be better.

And look at the other metric! Fourbuck is really short of internet-connected personal computers for public use: Just half of the median for all libraries of its size and in the bottom quarter of libraries even with its mediocre funding. Even most libraries on starvation diets (\$5-\$11) have more PCs.

 \$ per cap Circulation/cap Benefit Ratio 25% Med 75% 25% Med 75% \$82+ 12.9 19.6 24.7 2.4 2.8 3.5 \$61-\$81 9.5 13.4 18.6 2.6 4.0 4.6 \$46-\$60 7.7 10.0 14.6 2.8 3.7 4.8 \$38-\$45 7.0 9.2 11.4 3.4 4.1 5.3 \$32-\$37 6.0 7.4 9.5 3.6 4.5 5.3 \$27-\$31 4.7 6.3 8.9 3.5 4.7 5.3 \$22-\$26 4.6 6.0 7.7 3.6 4.6 5.8 \$17-\$21 3.9 5.1 6.8 4.4 5.3 6.7 \$12-\$16 2.5 3.5 4.7 4.3 5.4 6.9 \$5-\$11 1.8 2.6 3.6 4.8 6.3 8.4 Overall 4.2 6.9 10.5 3.5 4.6 5.7

Table X.3 Circulation per capita and benefit ratios for libraries serving 8,700 to 11,199 people

This is one of those tables that speaks to better funding fairly directly—look at the pattern of median circulation per capita as funding changes. Fourbuck’s actually in reasonable shape: Better than median for all libraries its size and well into the top quarter for libraries with its funding. Bump that funding up a little and it would still be nearly in the top quarter—but it would probably do better with more hours. (Ten circulations per capita’s a good starting target, and it’s not out of reach.)

The benefit ratio for Fourbuck is above average for its mediocre funding but not in the top quarter—but benefit ratio is one place where you really don’t want to be at the top. Note that the median for the whole size group rounds to 5.

 \$ per cap Attendance/cap PC use/cap 25% Med 75% 25% Med 75% \$82+ 0.6 1.0 1.5 1.5 2.7 4.1 \$61-\$81 0.4 0.6 0.8 0.9 2.0 2.7 \$46-\$60 0.3 0.5 0.7 1.0 1.6 2.5 \$38-\$45 0.3 0.4 0.6 0.9 1.4 1.8 \$32-\$37 0.2 0.4 0.5 0.9 1.3 2.1 \$27-\$31 0.2 0.3 0.4 0.8 1.2 1.8 \$22-\$26 0.1 0.3 0.4 0.6 1.0 1.5 \$17-\$21 0.2 0.2 0.4 0.5 0.8 1.1 \$12-\$16 0.1 0.2 0.2 0.4 0.7 0.9 \$5-\$11 0.1 0.1 0.2 0.4 0.6 1.0 Overall 0.2 0.3 0.6 0.6 1.1 1.8

Table X.4 Attendance and PC use per capita for libraries serving 8,700 to 11,199 people

More money, more and better programs, more program attendance—although few of the libraries in this size category, even the well-funded ones, do really well on this metric. At 0.27, rounded to 0.3, Fourbuck’s just about average for program attendance, but could do a lot better. (Should this—and some other metrics—show two decimal places?)

As for PC use—well, when the PCs aren’t there, it’s hard for them to be used heavily. Fourbuck’s in the bottom quarter even for its funding level, barely half of the median level.

 \$ per cap Reference/cap Visits/cap 25% Med 75% 25% Med 75% \$82+ 0.6 1.4 2.2 9.9 13.8 18.3 \$61-\$81 0.5 0.7 1.4 6.7 10.1 12.5 \$46-\$60 0.2 0.7 1.0 4.9 6.9 10.2 \$38-\$45 0.3 0.6 0.9 5.5 6.9 9.0 \$32-\$37 0.4 0.7 1.0 4.7 6.4 8.7 \$27-\$31 0.2 0.4 0.7 3.8 4.9 7.5 \$22-\$26 0.2 0.3 0.6 3.1 3.8 5.7 \$17-\$21 0.2 0.4 0.7 2.8 3.9 5.2 \$12-\$16 0.1 0.2 0.6 1.8 2.6 4.3 \$5-\$11 0.1 0.3 0.7 1.4 2.0 2.7 Overall 0.2 0.5 0.9 3.1 5.4 8.2

Table X.5 Reference questions and visits per capita for libraries serving 8,700 to 11,199 people

Here, Fourbucks is in reasonably good shape for its funding level, and reference is one area where the numbers are tricky. Fourbucks is roughly average for its funding (but below average for its size) on reference, above average for its funding (but below average for its size) on visits per capita. You already know the refrain: Longer hours, more programs, more PCs, probably more money for fresher materials, and visits will go up along with circulation.

 \$ per cap Circulation/hour Visits/hour 25% Med 75% 25% Med 75% \$82+ 38.5 57.4 87.0 31.9 38.2 57.4 \$61-\$81 30.3 47.6 55.4 20.8 29.5 43.1 \$46-\$60 23.2 34.6 51.0 16.6 21.1 35.8 \$38-\$45 26.0 32.3 41.1 18.8 24.4 31.9 \$32-\$37 21.6 25.8 36.0 16.4 25.2 31.5 \$27-\$31 16.6 24.5 33.6 13.2 18.9 25.8 \$22-\$26 17.5 24.0 28.2 10.1 15.2 22.4 \$17-\$21 17.0 21.0 28.9 10.9 16.4 22.8 \$12-\$16 10.0 14.2 21.9 7.8 12.0 19.4 \$5-\$11 8.5 11.8 16.6 7.3 9.7 12.3 Overall 16.6 25.8 37.0 11.8 20.3 29.5

Table X.6 Circulation and visits per hour for libraries serving 8,700 to 11,199 people

These new metrics are interesting, as you might expect them to vary less dramatically than circulation and visits per capita. That’s true—but there are still substantial variations. Circulation per capita for the median library in each funding group varies by a ratio of 7.5 to one (and the wealthiest libraries have 2.8 times the circulation per capita of the group as a whole), while the ratio is 4.9 to one for circulation per hour (and 2.2 to one for the wealthiest compared to the group as a whole). Well-funded libraries attract more usage per hour, in addition to being open longer hours. Similarly for visits per hour: The ratio of best-funded median to worst-funded median is 2.6 to one, where it’s 6.9 to one for visits per capita.

That’s the set. I haven’t included correlations or graphs, and it’s not clear how many decimal places should appear. I’m also not sure whether there are other metrics that really should be included, such as benefit per capita. Remember that this set of tables (and similar state-by-state tables, but arranged by size rather than funding) would replace the other tables, not add to them.

Would this set of tables be more useful to Fourbuck and other libraries in arguing for better funding? Your feedback is needed. Does the project as a whole make sense? Again, your feedback is needed. If you’ve purchased the book, please respond to the survey. In any case, your feedback to mailto:waltcrawford@gmail.com is welcome.