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APPENDIX D
THE ARL LIBRARY INDEX
(SOURCE: Mandel, Carol A., and Mary P. Johnson, ARL Statistics
1979-80, Association of Research Libraries, Washington, D.C., 1980,
pp. 23-24.)
The data tables at the beginning of the ARL Statistics display
figures reported by ARL member libraries in 22 categories that, with
the exception of the measures of interlibrary loan activity, describe
the size of ARL libraries in terms of holdings, expenditures, and
personnel. The rank order tables provide an overview of the ranges.
and medians for 14 of these categories, or variables, among ARL
academic libraries as well as quantitatively comparing each library
with other ARL member institutions. However, none of the 22 variables
provides a summary measure of a library's relative size within ARL or
characterizes the ARL libraries as a whole.
The ARL Library Index has been derived as a means of providing
this summary characterization, permitting quantitative comparisons of
ARL academic libraries, singly and as a group, with other academic
libraries. Through the use of statistical techniques known as factor
analysis, it can be determined that 15 of the variables reported to
ARL are more closely correlated with each other than with other
categories. Within this group of 15 variables, some are subsets or
combinations of materials. When the subsets and combinations are
eliminated, 10 variables emerge as characteristic of ARL libary size.
These are: volumes held, volumes added (gross), microform units held,
current serials received, expenditures for library materials,
expenditures for binding, total salary and wage expenditures, other
operating expenditures, number of professional staff, and number of
nonprofessional staff.
These 10 categories delineate an underlying dimension, or factor,
of library size. By means of principal component analysis, a
technique that is a variant of factor analysis, it is possible to
calculate the correlations of each of the variables with this
hypothetical factor of library size. From this analysis a weight for
each variable can be determined based on how closely that variable is
correlated with the overall dimension of library size defined by all
10 categories. A high correlation indicates that much of the
variation in ARL library size is accounted for by the variable in
question, implying a characteristic in which ARL libraries are
relatively alike. The component score coefficients, or weights, for
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the 1979-80 ARL academic library data are as follows:
Volumes held
Volumes added (gross)
Microforms held
Current serials received
Expenditures for library materials
Expenditures for binding
Expenditures for salaries and wages
Other operating expenditures
Number of professional staff
Number of nonprofessional staff
.12108
.11940
.07509
.12253
.12553
.11266
.12581
.10592
.12347
.11297
From these weights an individual library can compute an index
score that will indicate its relative position among ARL libraries
with respect to the overall factor of library size. The data for each
of the 10 variables are converted to standard normal form and
multiplied by the appropriate weight. The resulting scores are
expressed in terms of the number of standard deviations above or below
the mean index score for ARL academic libraries. Thus, the formula*
for calculating a library's 1979-80 index score is as follows:
.12108 (log of volumes held - 6.2916~/.2172
+.11940 (log of volumes added gross - 4.8412~/.2025
+.07509 (log of microforms - 6.0950~/.1763
+.12253 (log of current serials - 4.3432~/.2341
+.12553 (log of expenditures for materials - 6.2333~/.1636
+.11266 (log of expenditures for binding - 5.0480~/.2475
+.12581 (log of total salaries - 6.46751/.2103
+.10592 {log of operating expenditures - 5.67731/.2635
+.12347 (log of professional staff - 1.8281~/.1968
+.11297 {log of nonprofessional staff - 2.1512~/.2046
The index scores for the 99 academic libraries that were members
of ARL during 1979-80 are shown on the following page. It is
important to emphasize that these scores are only a summary descrip-
tion of library size, distributing ARL libraries along a normal curve,
based on 10 quantitative measures that are positively correlated with
one another in ARL libraries. The scores are in no way a qualitative
assessment of the collections, services, or operations of these
libraries.
*For calculation on a hand calculator, the formula can be mathemati-
cally simplified to: (.55746 x log of volumes held) + (.58963 x log of
volumes added gross) + (.42592 x log of microforms) + {.52341 x log of
current serials) + {.76730 x log of expenditures for materials) +
{.45Sl9 x log of expenditures for binding) + {.59824 x log of total
salaries) + (.40197 x log of operating expenditures) + (.62739 x log of
professional staff) + (.55215 x log of nonprofessional staff) -
26.79765.