I Think That I Shall Never See…

This post is about a much discussed question: How did the Great Recession affect U.S. public libraries? I’m not really going to answer the question, as that would amount to a lengthy journal article or two. But I am going to suggest a way to approach the question using data from the Institute of Museum and Library Services (IMLS) Public Libraries in the United States Survey. Plus I’ll be demonstrating a handy data visualization tool known as a trellis chart that you might want to consider for your own data analysis tasks. (Here are two example trellis charts in case you’re curious. They are explained futher on.)

As for the recession question, in the library world most of the discussion has centered on pronouncements made by advocacy campaigns: Dramatic cuts in funding. Unprecedented increases in demand for services. Libraries between a rock and hard place. Doing more with less. And so forth.

Two things about these pronouncements make them great as soundbites but problematic as actual information. First, the pronouncements are based on the presumption that looking at the forest—or at the big picture, to mix metaphors—tells us what we need to know about the trees. But it does not.

In the chart below you can see that the Great Recession had no general, across-the-board effect on public library funding. Some libraries endured severe funding cuts, others more moderate cuts, others lost little or no ground, while the majority of libraries actually had funding increases in the aftermath of the recession.

IMLS0611_CumChangeOpExp_500

Bars to the left of the zero line indicate libraries with decreases; bars to the right, increases.
Change of -10% = 10% decrease. Change of 10% = 10% increase.
Click for larger image.

In the chart note that 35% of libraries had 5-year inflation-adjusted cumulative decreases of one size or another. Of these libraries, about half (18% of all libraries) had decreases of 10% or greater and half (17% of all libraries) had decreases less than 10%. 65% of libraries had cumulative increases of any size. Of libraries with increases, two-thirds (43% of all libraries) had increases of 10% or greater and one-third (22% of all libraries) with increases less than 10%. By the way, expenditure data throughout this post are adjusted for inflation because using unadjusted (face-value) figures would understate actual decreases and overstate actual increases.1

The second problem with the advocacy pronouncements as information is their slantedness. Sure, library advocacy is partial by definition. And we promote libraries based on strongly held beliefs about their benefits. So perhaps the sky-is-falling messages about the Great Recession were justified in case they actually turned out to be true. Yet many of these messages were contradicted by the available evidence. Most often the messages involved reporting trends seen only at a minority of libraries as if these applied to the majority of libraries, as the advocacy pronouncements I mentioned do.

A typical example of claims that contradict actual evidence appeared in the Online Computer Library Center (OCLC) report Perceptions of Libraries, 2010. Data in that report showed that 69% of Americans did not feel the value of libraries had increased during the recession. Nevertheless, the authors pretended that the 31% minority spoke for all Americans, concluding that:

Millions of Americans, across all age groups, indicated that the value of the library has increased during the recession.2

In our efforts to support libraries we should be careful not to be dishonest.

But enough about information accuracy and balance. Let’s move on to some nitty-gritty data exploration! For this I want to look at certain trees in the library forest. The data we’ll be looking at are just for urban and county public library systems in the U.S. Specifically, the 44 libraries with operating expenditures of $30 million or more in 2007.3 The time period analyzed will be 2007 to 2011, that is, from just prior to the onset of the Great Recession to two years past its official end.

Statistically speaking, a forest-perspective can still compete with a tree-perspective even with a small group of subjects like this one. Here is a graph showing a forest-perspective for the 44 libraries:

Median Coll Expend

Median collection expenditures for large U.S. urban libraries.  Click to see larger graph.

You may recall that a statistical median is one of a family of summary (or aggregate) statistics that includes totals, means, ranges, percentages, proportions, standard deviations, and the like. Aggregate statistics are forest statistics. They describe a collective as a whole (forest) but don’t tell us that much about the individual members (trees).

To understand subjects in a group we, of course, have to look at those cases in the data. Trellis charts are ideal for examining individual cases. A trellis chart—also known as a lattice chart, panel chart, or small multiples—is a set of statistical graphs that have been arranged in rows and columns. To save space the graphs’ axes are consolidated in the trellis chart’s margins. Vertical axes appear in the left margin and the horizontal axes in the bottom or top margin or both.

Take a look at the chart below which presents data from agricultural experiments done in Minnesota in the 1930’s. It happens that the data shown there are famous because legendary statistician R. A. Fisher published them in his classic 1935 book, The Design of Experiments. Viewing the data in a trellis chart helped AT&T Bell Laboratories statistician William Cleveland discover an error in the original data that went undetected for decades. The story of this discovery both opens and concludes Cleveland’s 1993 book Visualizing Data.4

The primary message of Cleveland’s book is one I’ve echoed here and here: Good data visualization practices can help reveal things about data that would otherwise remain hidden.5
Trellis Chart Example

Trellis chart depicting 1930’s agricultural experiments data.
Source: www.trellischarts.com.  Click to see larger image.

At the left side of the chart notice that a list of items (these are barley seed varieties) serves as labels for the vertical axes for three graphs in the top row. The list is repeated again as axes labels for the graphs in the second row. On the bottom of the chart repeated numbers (20 to 60) form the horizontal scales for the two graphs in each column. A trellis chart layout provides more white space allowing the eye to concentrate on the plotted data alone, in this case circles depicting experimental results for 1931 and 1932. And the chart’s side by side arrangement of smaller graphs makes it easy to compare different cases (aka research subjects) on a single measure. The chart below shows this using library data:

Demo trellis chart

Trellis chart example with library collection expenditures data.  Click for larger image.

This chart presents collection expenditures as a percent of total operating expenditures from 2007 to 2011. The cases are selected libraries as labeled. Notice how prominent the line shapes are. Like the humped lines of Atlanta, Baltimore, Cuyahoga Co., and Hawaii. And the bird-shapes of Brooklyn and Hennepin Co. And the District of Columbia’s inverted bird.

Trellis charts make it easy to find similarities among individual trends, such as the fairly flat lines for Baltimore Co., Broward Co., Cincinnati, Denver, and King Co. Nevertheless, the charts presented here are more about identifying distinct patterns in single graphs. Each graph tells a unique story about a given library’s changes in annual statistics.

Incidentally, I’ve added a slight adaptation to the trellis charts I’ll be presenting here to accommodate cases with exceptionally high data values. Instead of appearing in alphabetical order with the other libraries shown, graphs for cases with high values are located at the far right as shown in this one-row example:

Trellis Chart Adaptation

Row from trellis chart with high value graph shaded and in red.
 Click for larger image.

Notice that the graph at the right is shaded with its vertical axis labeled in red, whereas the vertical axes labeling for the non-shaded graphs appear at the left margin in black. In this post all shaded/red-lettered graphs have scaling different from the rest of the graphs in the charts. Using extended scaling just for libraries with high values allows the rest of the libraries’ graphs to use scales that make the trend line shapes more pronounced.6

Now let’s look for some stories about these 44 urban and county libraries beginning with total operating expenditures:

Oper Expend Chart #1

Chart #1 interactive version

Oper Expend Chart #2

Chart #2 interactive version

Total Operating Expenditures.  Click charts for larger images. Click text links for interactive charts.

Take a moment to study the variety of patterns among the libraries in these charts. For instance, in chart #1 Brooklyn, Broward County, Cleveland, and Cuyahoga Co. all had expenditure levels that decreased significantly by 2011. Others like Denver, Hawaii, Hennepin Co., Houston, Multnomah Co., and Philadelphia had dips in 2010 (the Great Recession officially ended in June of the prior year) followed by immediate increases in 2011. And others like Boston, Orange Co. CA, San Diego Co., and Tampa had their expenditures peak in 2009 and decrease afterwards.

Now look at collection expenditures in these next two charts. You can see, for instance, that these dropped precipitously over the 4-year span for Cleveland, Los Angeles, Miami, and Queens. For several libraries including Atlanta, Baltimore, and Columbus expenditures dipped in 2010 followed by increases in 2011. Note also other variations like the stair-step upward trend of Hennepin Co., Houston’s bridge-shaped trend, the 2009 expenditure peaks for King Co., Multnomah, San Diego Co., and Seattle, and Chicago’s intriguing sideways S-curve.

Coll Expend Chart #1

Chart #1 interactive version

Coll Expend Chart #2

Chart #2 interactive version

Collection Expenditures.  Click charts for larger images. Click text links for interactive charts.

Again, with trellis charts the main idea is visually scanning the graphs to see what might catch your eye. Watch for unusual or unexpected patterns although mundane patterns might be important also. It all depends on what interests you and the measures being viewed.

Once you spot an interesting case you’ll need to dig a little deeper. The first thing to do is view the underlying data since data values are typically omitted from trellis charts. For instance, I gathered the data seen in the single graph below for New York:

NYPL Coll Expend

Investigating a trend begins with gathering detailed data. Click for larger image.

The example trellis chart presented earlier showed collection expenditures as a percent of total operating expenditures. This same measure is presented in the next charts for all 44 libraries, including links to the interactive charts. Take a look to see if any trends pique your curiosity.

Coll Expend as pct chart #1

Chart #1 interactive version

Coll Expend as pct chart #2

Chart #2 interactive version

Percent Collection Expenditures .  Click charts for larger images. Click text links for interactive charts.

Exploring related measures at the same time can be revealing also. For example, collection expenditure patterns are made clearer by seeing how decreases in these compare to total expenditures. And how collection expenditures as a percentage of total expenditures relate to changes in the other two measures. The charts below make these comparisons possible for the 4 libraries mentioned earlier—Cleveland, Los Angeles, Miami, and Queens:

Multiple collection measures

Chart #1 interactive version

Multiple measures with data values

Chart #2 interactive version

Understanding collection expenditure trends via multiple measures. Chart #1, trends alone. Chart #2, data values visible.  Click charts for larger images. Click text links for interactive charts.

The next step is analyzing the trends and comparing relevant figures, with a few calculations (like percentage change) thrown in. Cleveland’s total expenditures fell continuously from 2007 to 2011, with a 20% cumulative decrease. The library’s collection expenditures decreased at nearly twice that rate (39%). As a percent of total expenditures collection expenditures fell from 20.4% to 15.6% over that period. Still, before and after the recession Cleveland outspent the other three libraries on collections.

From 2007 to 2010 Los Angeles’ total expenditures increased by 6% to $137.5 million, then dropped by 18% to $113.1 million. Over the 4-year span this amounted to a 13% decrease. For that same period Los Angeles’ collection expenditures decreased by 45%.

By 2010 Miami’s total expenditures had steadily increased by 38% to $81.8 million. However, in 2011 these fell to $66.7 million, a 17% drop from 2010 level but an increase of 13% over the 2007 level. Miami’s collection expenditures decreased by 78% over from 2007 to 2011, from $7.4 million to $1.6 million.

Total expenditures for Queens increased by 17% from 2007 to 2009, the year the Great Recession ended. However, by 2011 these expenditures dropped to just below 2007 levels, a 2% cumulative loss over the 4 years and a 19% loss from the 2009 level. From 2007 to 2011, though, Queens collection expenditures declined by 63% or $7.3 million.

Talk about data telling stories! Three of the 4 libraries had percent of total expenditures spent on collections decrease to below 6% in the aftermath of the recession. To investigate these figures futher we would need to obtain more information from the libraries.

As you can see, trellis charts are excellent tools for traipsing through a data forest, chart by chart and tree by tree. Obviously this phase takes time, diligence, and curiosity. Just 44 libraries and 5 years’ worth of a half-dozen measures produces a lot of data! But the effort expended can produce quite worthwhile results.

If your curious about other interesting trends, the next two sets of charts show visits and circulation for the 44 urban and county public libraries. Looking quickly, I didn’t see much along the lines of unprecedented demand for services. Take a gander yourself and see if any stories emerge. I hope there isn’t bad news hiding there. (Knock on wood.)

Visits

Chart #1 interactive version

Visits chart #2

Chart #2 interactive version

Visits.  Click charts for larger images. Click text links for interactive charts.

Circ Chart #1

Chart #1 interactive version

Circ Chart #2

Chart #2 interactive version

Circulation.  Click charts for larger images. Click text links for interactive charts.

 
—————————

1   The 2007 through 2010 expenditure data presented here have been adjusted for inflation. The data have been re-expressed as constant 2011 dollars using the GDP Deflator method specified in IMLS Public Libraries in the United States Survey: Fiscal Year 2010 (p. 45). For example, because the cumulative inflation rate from 2007 to 2011 was 6.7%, if a library’s total 2007 expenditures were $30 million in 2007, then for this analysis that 2007 figure was adjusted to $32 million.
   Standardizing the dollar values across the 4-year period studied is the only way to get an accurate assessment of actual expenditure changes. A 2% expenditure increase in a year with 2% annual inflation is really no expenditure increase. Conversely, a 2% expenditure decrease in a year with 2% annual inflation is actually a 4% expenditure decrease.
2   Online Computer Library Center, Perceptions of Libraries, 2010: Context and Community, p. 44.
3   In any data analysis where you have to create categories you end up drawing lines somewhere. To define large urban libraries I drew the line at $30 million total operating expenditures. Then, I based this on inflation adjusted figures as described in footnote #1. So any library with unadjusted total operating expenditures equal to or exceeding $28.2 million in 2007 was included.
4   See anything unusual in the chart? (Hint: Look at the chart labeled Morris.) The complete story about this discovery can be found here. Page down to the heading Barley Yield vs. Variety and Year Given Site. See also William S. Cleveland’s book, Visualizing Data, pp. 4-5, 328-340.
5   Using ordinary graphical tools statistician Howard Wainer discovered a big mistake in data that were 400+ years old! His discovery is described in his 2005 book, Graphic Discovery: A Trout in the Milk and Other Visual Adventures. Wainer uncovered anomalies in data appearing in an article published in 1710 by Queen Anne’s physician, John Arbuthnot. The original data were registered christenings and burials collected in England from 1620 to 1720 at the orders of Oliver Cromwell. See Wainer, H. Graphic Discovery, 2005, pp.1-4.
6   The chart below illustrates how a larger scale affects the shapes of a trend line. The scale in the left graph ranges from $25M to $100M, while the scale of the right graph ranges from $25M to $200M. Because the left graph scaling is more spacious (smaller scaling), its trend line angles are more accentuated.

Different Axes Example

Click for larger image.

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