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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 219

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220 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.