A recent article in *AL Direct* entitled The Smartest Readers presents some simple library rankings based on that stalwart library measure, circulation per capita. Rankings like these are, at least to me, a reminder of a perennial conundrum concerning the meaning of per capita library measures. For more than a century librarianship has puzzled over how to evaluate these statistics. Do per capita data tell us whether or not libraries are doing a good job? What amounts of materials made available or levels of services delivered are sufficient for libraries with specific missions and serving communities of a particular size and makeup?

Mainly, libraries have to rely on their own ingenuity to interpret per capita or per constituent data (like per student, faculty, employee, subscriber, stakeholder, and such). About the only official guidance they have gotten over the decades is advice about comparing (benchmarking) their data with appropriate peer libraries. Lacking some more objective gauge of statistical performance, libraries end up applying what might be called the *more-is-better rule*. Indeed, this convenient and popular assumption is at the heart of library ranking schemes like the LJ Index, HAPLR, the Bibliotheksindex BIX, and the ARL Index.

So it’s natural that ALA librarian Karen Muller, author of the article, would sort the data from high to low. And she limits the comparisons to roughly similar libraries, those serving communities of 100,000 or more, although she chose that group in order to cross-check her top 20 list with *Amazon.com’s* rankings of Most Well-Read Cities.

But here’s an interesting tidbit I have to offer on this topic: If statistics-based advocacy is our aim, we can put a better foot forward by advertising the performance of *smaller libraries* moreso than larger ones. As a group, *smaller libraries* almost always outshine the largest libraries on per capita measures.

Let’s see how this works. For comparison purposes I gathered 2009 IMLS data for a group of smaller public libraries to match the size of the group that Muller used in her article. She analyzed the 549 largest U.S. public libraries and my group consists of the 551 U.S. libraries serving communities of 15,000 to 20,000.1

Chart 1A below is a scatterplot of the data that Muller analyzed showing circulation and community population together.2 Notice that the circles in the chart are clustered toward the left since these libraries serve communities ranging from 100,000 to nearly 5 million. Most of the community populations are between 100,000 and 200,000, which accounts for this clustering.3

Chart shown here omit some outlying data points. Click charts for complete views. Move cursor over circles in complete views to see individual library data.

Chart 1B shows libraries from chart 1A that make the top 20 rankings based on their circulation per capita measures. These are the same libraries that appear in Muller’s top 20 list (see footnote #2). Note also that horizontal lines in charts 1A and 1B indicate the median circulation per capita values for the groups.

Charts shown here omit some outlying data points. Click charts for complete views. Move cursor over circles in complete views to see individual library data.

Charts 2A and 2B show the same circulation measures for libraries with populations ranging from 15,000 to 20,000.

Charts shown here omit some outlying data points. Click charts for complete views. Move cursor over circles in complete views to see individual library data.

Notice in the charts that the median circulation per capita is higher for the smaller libraries (charts 2A and 2B) than for the larger libraries (charts 1A and 1B). For example, for the two top 20 lists (charts 1B and 2B), the median circulation per capita value is 23.1 for large libraries and 26.6 for the smaller libraries.

Now let’s try another measure, volumes of print materials per capita. Chart 3A shows this statistic for large libraries and 3B does so for the top 20 large libraries ranked on the statistic.

Charts shown here omit some outlying data points. Click charts for complete views. Move cursor over circles in complete views to see individual library data.

Granted, in some instances a couple of large libraries might outperform all smaller libraries on a given measure, as Boston Public Library does with its 15.0 volumes per capita measure. (Click on chart 3B above to see larger chart. On that chart move cursor over the circle located in the top row and center column of the grid.) Yet charts 4A and 4B demonstrate that smaller libraries, as a group, consistently perform better. Again, median values shown in the charts exceed those for the larger libraries. Plus, the distribution of circles tells this story too. More circles in chart 4A extend higher on the vertical scale than in chart 3A. For example, only 5 larger libraries reported volumes per capita of 8 volumes or higher (chart 3A) while 16 smaller libraries did (chart 4A). And only 11 larger libraries exceed 6 volumes per capita compared to 48 smaller libraries that do.

Finally, for one more measure, total library staff per 1,000 community population, we see these same patterns in charts 5A through 6B. Medians are higher for smaller libraries and, overall, circles in charts 6A and 6B extend higher than in 5A and 5B. (When comparing charts 5A to 6A and 5B to 6B be sure to take note of the vertical axes value labels, as the scales differ on each.)

The bar charts shown here illustrate the differences between the two groups on median values of the per capita measures.

Click for larger image.

Of course, we have to look at several more than three library measures to declare this a trend. But I bet you that it is. Actually, I’m sandbagging here because certain pioneers of public library performance statistics documented this phenomenon as early as 1973. In their landmark study that analyzed per capita measures Ernest DeProspo, Ellen Altman, Kenneth Beasley, and Ellen Clark wrote:

*A statistical comparison of libraries of different sizes…suggests that small libraries give a greater return per dollar spent, and that the economy of scale normally expected in larger institutions is not evident.*4

Weird, isn’t it?

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1 Using 2009 IMLS data, public libraries in communities of 10,000 or less number 5,388, and those in communities from 10,000 to 20,000 number 1,400. So, the smallest comparably sized segment I could find is the group serving communities from 15,000 to 20,000, which consists of 551 libraries, excluding libraries outside of the 50 U.S. states.

2 Charts 1A, 3A, and 5A present data for 539 U.S. public libraries in the 50 states serving communities of 100,000 or more. The listing at the bottom of chart 1B (click chart above to see complete image) matches the table in Muller’s article exactly. This suggests that figures in the article are from 2009 IMLS data, although the article says they are from 2008.

3 The horizontal axis of Chart 1A and a couple others in this post use “logarithmic scaling.” This gives more space to smaller data values toward the left of the charts and makes the arrangement of values to the right more condensed. Thus, the axis values get progressively higher, left to right. The axis value labels indicate this progression clearly. (Without logarithmic scaling circles representing the smaller large libraries would be jammed next to the 100,000 axis gridline.)

4 DeProspo, E. R., Altman, E., Beasley, K. E., and Clark, E. C. (1973). *Performance measures for public libraries,* Chicago: Public Library Association, p. 22. Red emphasis added.

Hi Ray:

Interesting stuff. I’ve done some analyses of the productivity of Norwegian public libraries – at http://pliny.wordpress.com/2011/07/06/pl-2411/

and the bigger tend to do better than the smaller.

Tord Høivik (Plinius)

Thanks so much for your comments, Tord. I responded on your blog–basically saying how intriguing this is! I wonder what might explain these different statistical patterns in our two countries?