Tuesday, February 27, 2007

PL 12/07: Productivity and size in public libraries

Filed under: statistics — plinius @ 8:51 pm

The relationship between productivity and size is an important question in library development. In Norway, as in other Nordic countries, smaller branch libraries are closing down – often against strong local protests.

The recent (2006) Norwegian White Paper on libraries – Library Reform 2014 – argues that larger units are needed to serve the new generation of users: urban, web proficient and highly educated. The White Paper argues for a minimum staff of six to eight persons – which corresponds to a service population of 15 to 20 thousand persons.

But is it true that larger libraries more productive than smaller ones? To what extent can the public library sector benefit from economies of scale? And how should productivity be measured?

To answer these questions, we turn to public library statistics.

The following is the extended abstract of a paper submitted to the 7th Northumbria International Conference on Performance Measurements in Libraries and Information Services, which will be held as an IFLA Satellite Meeting in Stellenbosch, Aug. 13-16, 2007.


The proper use of public money: an improved measure of productivity in public libraries based on Norwegian statistics


The sub-headings conform to the instructions for authors

Libraries are productive entities. They produce a variety of goods and services – and consume resources in order to do so. A library’s production – or output – is the sum of its products. A library’s productivity is its output relative to its input.

This research paper introduces an alternative indicator of productivity, based on available public library statistics, and compares it – conceptually and empirically – with the widely used (traditional) indicator Loans/Staff-year.


We investigate the behaviour of both indicators in the population of Norwegian municipal libraries in 2005. We use standard statistical parameters (correlations, medians, quartiles) combined with visual analysis of scatter-diagrams to show that the new indicator gives, indeed, more meaningful and precise results.

In Europe, the most widely used measure of productivity in public libraries seems to be the number of loans divided by the size of the staff. By staff, we mean the number of person years, or FTEs, rather than the number of employees as such. We use, in other words, the following

Indicator of productivity = Loans per FTE (or simply L/F)

This indicator has, however, been criticized for its exclusive focus on lending. Libraries are involved in a wide range of activities. The staff must divide its time between many tasks.

The library can only maximize its “lending productivity” by neglecting other important services: reference, reader’s advisory, user education, home page development, etc. On the input side, most librarians would also say that the volume of lending depends heavily on the quality of the collection – not only on the working hours invested.

Findings – part 1

We first consider the productivity of Norwegian public libraries in 2005, using the traditional indicator. We find, indeed, that productivity increases with municipal size – but only up to about ten thousand inhabitants. Beyond that level, the typical (median) L/F stabilizes at about fourteen thousand loans per person-year.

Scatter diagrams and correlation coefficients show – in addition – that the linear relationship between L and F is only moderately strong. The traditional indicator of productivity suffers – that is – from high variability. When we divide the municipalities into groups based on population size, we find higher correlation values (between L and F) in the set of large than in the set of small municipalities:

* 10 thousand inhabitants or more: R = 0,60
* 5-10 thousand inhabitants: R = 0,54
* less than 5 thousand inhabitants: R = 0,46

From a statistical point of view, this is not surprising. Local particularities are more likely to affect small than large communities. When many small units are aggregated, local variations cancel each other out, making general patterns more visible. Larger libraries are also likely to be more standardized and hence more similar in their capacity to transform resource input into service output.

Findings – part 2

In the second part of the paper we show that an alternative indicator of productivity – adapted from Finnish library statistics – is less exposed to these random variations. Conceptually, Productivity equals Output/Input. In Finland, Output is measured by the sum of loans and visits (LV). Input is measured by the sum of salaries and media purchases (SM). We may interpret the ration LV/SM as the number of transactions (loans or visits) generated or supported by a given allocation of funds to user oriented inputs (staff and media).

We apply the “Finnish” indicator to the Norwegian data – and find the same general relationship as before. Productivity increases with municipal size up to about ten thousand inhabitants. But the correlations between LV and SM are higher than in the first case: 0,73 rather than 0,60 for municipalities with more than ten thousand inhabitants.

Grouping municipalities by population size is standard procedure in most analyses of library statistics from the local level. The underlying idea is: bring similar units together – and keep different units apart. But municipalities may, of course, be similar on other dimensions than sheer size.

Findings – part 3

In the third part of the paper we look more closely at the categorization of municipalities by size. In Norway, the Central Bureau of Statistics provides good data for two important socio-geographic variables

* the percentage of the population that lives in densely settled areas
* the geographical centrality of each municipality (“travel distance to nearest metropolitan center”)

When we bring these two variables into the analysis, the correlation coefficients – and the visible “linearity” of the scatter diagrams – increase further. In municipalities near urban centers – with at least ten thousand inhabitants in densely settled areas, we find

* a marginal level of productivity of 62 new transactions per 1 000 NKr (appr. 125 euros)
* a correlation between LV and SM of 0,78 (R*R = 0,61)

The scatter diagram (based on LV and SM) for these 67 libraries reveals not just a linear, but a proportional relationship between LV and SM. Marginal productivity equals average productivity – with no visible economies of scale.

Conclusion: The “Finnish” indicator LV/SM = (Loans + Visits)/(Salaries+Media expenditure) seems to be a more stable, and hence better, indicator of productivity than the traditional L/V = Loans/FTE. This result is also confirmed by data from earlier years.

Practical implications

The methods outlined in sections 1 and 2 above are applicable in all regions with detailed library statistics. Libraries, library systems and countries that use L/F to measure productivity should be encouraged to compare the two indicators with their own data – and choose the more effective one.

The results in section 3 suggest that comparative studies of public libraries should not use population size alone as their main background variable. Other geographic factors should also be introduced as explanatory variables.


The statistical results are definitely new – and we have not, so far, encountered studies using a similar approach to public library productivity in the research literature.



Tord Høivik (2005). Comparing libraries. From official statistics to effective strategies. Paper for the IFLA Satellite Meeting Management, marketing, evaluation and promotion of library services, based on statistics, analyses and evaluation in your own library, held in Bergen, August 9-11, 2005



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