Library Services in Theory and Context

Chapter 16: Measurement and Quantification

Introduction

So far we have largely ignored problems of measurement. We did so because we were primarily concerned with the theoretical task of defining a conceptual framework rather than the practical difficulty of doing things. In day-to-day activities, however, it is very helpful to be able to measure things: doing so can add a sense of proportion. In this chapter we shall review the progress that has been made in measurement with respect to library services. We shall also consider some of the problems.

Although there were some earlier examples of measurement and quantification in libraries, the late 1960s mark a convenient turning point. The first serious monograph on the subject was published in 1968¹ and it was around then that the literature begins to reflect the results of quantitative techniques being applied to libraries by different groups in different places. By the mid-1970s this activity was no longer novel.² By the late 1980s it has been broadly absorbed and diffused.

Reflecting on this corpus of literature, on the topics which have been selected for study, on the weaknesses and gaps, and on the significant but limited extent of practical implementation, one suspects that progress in this field is probably very similar to progress in to other areas of social service. The conditions, at any rate, would appear to be similar:

• staff strive to provide a range of different services to multiple constituencies with differing interests;
• service, not profit, is the objective, and there is no single measure of overall effectiveness;
• intangible benefits and externalities abound;
• there are role uncertainties for personnel concerning professional as opposed to administrative roles; and
• political control over service priorities is unevenly distributed among the segments of the population being served.

A labor-intensive, not-for-profit activity in which intangible benefits are provided to individuals is necessarily a complex system even though it may not be a large one.³

The approach of this chapter will be to review those areas in which most work has been done, then to identify some areas in which more work needs to be done.

Bibliometrics: the structure of published literature and of its usage

"Bibliometrics" is the term used to denote the quantitative study of phenomena of "documentary discourse," such as authorship, publication, reading, and citation.⁴ This area includes studies of: the growth of the literature on a given subject;⁵ patterns in the distribution of publishing productivity by individual authors ("Lotka's Law");⁶ how articles on any subject are dispersed across journals ("Bradford's Law of Scattering");⁷ the "obsolescence" of literature;⁸ the epidemiology of ideas as reflected in technical literature;⁹ and the study of networks and patterns in scholarship as evidenced by analyses of who cites whom.¹⁰

There is almost endless scope for mathematical modeling in this area. The data—usually the references at the end of articles—are readily available to all and, increasingly, in machine readable form. Hence, experiments can be replicated or extended indefinitely. Hitherto, the precise formulation of the distributions found, and whether they are really the same as each other, has been a fertile area.¹¹

It is convenient to identify two principal sorts of modeling:

1. Descriptive analysis. The identification and explication of patterns is an area in which the foundations of librarianship merge with the foundations of other social sciences. There are affinities with mathematic linguistics and, seemingly, broad tracts of quantification pertaining to human behavior. This area was advanced and popularized by Derek de Solla Price and others interested in the science (and sociology) of science. Notions such as the "invisible college" (clusters of mutually citing scholars),¹² and "technological gate-keepers" (individuals through whom a disproportionately large amount of communication flows),¹³ and the use of citation analysis to write history¹⁴ and to predict Nobel Prize winners¹⁵ can hardly fail to intrigue.

Since this work is primarily descriptive, it is of questionable usefulness. We cite it, however, on the grounds that it provides insights and that mathematical modeling of parts of what is a very complex area could form the basis for applied research.

2. Prescriptive models. Some researchers have examined bibliometric studies and endeavored to explore their implications for library management decisions. The principal example of this concerns scattering, obsolescence, and the determination of optimal library size.

Bradford's Law of Scattering, which is a measure of the dispersion over all available journals of articles on any given subject, is normally formulated as a cumulative, ranked distribution. The few journals which contribute most of the articles on a topic constitute the "core" or "nuclear zone." Other titles which contribute less are ranked and added, individually or in clusters ("zones"), in order of decreasing number of articles contributed. Expressed this way, Bradford's Law of Scattering can properly be regarded as a law of diminishing returns with respect to the number of titles held in a given subject area.

Obsolescence, the fall-off in use of materials as they age, can similarly be regarded as a law of diminishing returns with respect to the length of time material is retained in a library's collections. (For this and scattering see chapter 10.)

A significant breakthrough in library operations research was the realization that, taken in conjunction, these two laws of diminishing returns provide some insight into the elusive concept of optimal library size. Making important assumptions about the degree of scattering, the rate of obsolescence, the behavior of library users, and the value of users' time, one can, in theory, prescribe the least-cost journal collection capable of meeting any given percentage of 'the demands on a given subject. Priority in this area (sometimes referred to as "the p% library") appears to belong to Cole,¹⁶ but a number of other researchers have rediscovered or refined this and related approaches.¹⁷ The same problem occurs in the case of file size in computer-based bibliographical information storage and retrieval systems. What combination of range of titles and range of years should be stored for computerized literature searches to provide what percentage of completeness of coverage? What combination should be retained in primary storage for the initial search as opposed to secondary storage (or manual systems) for extended searches?

There are three principal difficulties in this approach: (a) An unrealistically homogeneous demand is generally assumed. Overlapping, nonhomogeneous subsets of demand are difficult to handle; (b) The models remain incomplete and optimization impossible until one can determine the impact on the user population of different values of p. What proportion of demand should we endeavor to satisfy and how does the choice of p influence the demand? (c) An entirely probabilistic solution may be politically unsatisfactory for the librarian who may prefer instead to minimize the regret which could result from irate library users seeking material that was either not purchased or, worse, discarded because future demand had been expected to be negligible.

On account of the incompleteness of our knowledge of library-user interactions, it seems likely that bibliometric analysis will come to be useful not so much in prescribing what should be done but rather in helping us to understand the dynamics involved; in predicting the probable consequences of decision-making; and, by helping identify atypical situations, in identifying malfunctions and interesting anomalies in operational systems.

Far less developed are explanations of the causes of the patterns that are observed.

Logistics of documentary delivery

The study of the logistics of library services may be less elegant than bibliometrics, but the results can and have been implemented with success. The aspects most commonly studied are: the distribution of demand over a collection;¹⁸ the growth in collection size;¹⁹ the distribution of lengths of time involved in book usage and inter-usage intervals; standards of service, for example, "immediate availability," which usually signifies the probability of library users finding what they want when they want it;²⁰ the impact of policy variables, for example, how many different titles should be provided? How many copies of each? How long should they be retained? How long should the loan period be? Should overdue books incur fines? How far is photocopying a reasonable substitute for lending? How far is dependence on interlibrary loan an acceptable substitute for acquisition? How should a network of backup interlibrary loan facilities be organized?

This area contains two documented examples of implemented operations research studies.

Example 1: National Lending Library, U.K.

The design and development of the National Lending Library for Science and Technology at Boston Spa, Yorkshire, England (now known as the Document Supply Center) is a classic case of the use of common sense and simple quantification.

The British government, inspired by the progress of Russian technology in the form of Sputnik, decided to build a new national library, not a conventional library but a library for libraries. This was to be a back-up facility which would collect British and foreign scientific literature and make it available by interlibrary loan. The whole enterprise was aggressively unconventional. Few people agreed that a modern science and technology library should be set up in a remote rural location; should prefer manual to computerized methods; and, for the most part, have no catalog. The design and development were, however, based firmly on the collection and analysis of factual data. The result was rapid and spectacular success. It now also serves as a back-up facility for libraries in North America and worldwide.²¹ Central to the whole plan was the elementary use of queuing theory. In a concise and lucid paper, Urquhart and Bunn summarized the best available data on the interlibrary loan demand in Britain and demonstrated that, for the great majority of journal titles, there was no statistical justification for interlibrary loan provision separate from the main national reference libraries.²² They then used queuing theory to calculate the number of copies needed to maintain at least 95 percent availability on demand with either regionalized or centralized provision. The inescapable conclusion that centralized provision was not only more economical at low levels of demand but increasingly more economical at higher levels of demand ran entirely contrary to the conventional wisdom of the British library profession at that time.

Example 2: Variable loan policies, University of Lancaster

In 1968, the University Librarian at the University of Lancaster, England, was worried by complaints that users could not find the books they sought. The library had its own small in-house research unit to which the problem was referred. The study proceeded by adopting "immediate availability when needed" as a measure of service and by identifying the relationship between the four variables associated with the availability of any given title: pattern of demand; number of copies; loan period; and probability of a copy being available.

For any given level of demand, the probability of a copy being available is directly related to the number of copies and inversely related to the length of loan period. Hence, the loan period and the duplication policy should be related both to the level of demand and to each other. As with the National Lending Library, it is essentially a queuing problem. At Lancaster, however, analytical solutions based on queuing theory were abandoned in favor of programming a computer to simulate the borrowing and returning of books.

It was estimated that users could find the books they wanted about 60 percent of the time. Three alternative strategies were compared for increasing this success rate to about 80 percent: selective duplication of popular titles; shortened loan periods for undergraduates; and a "variable" loan policy whereby the loan period depended directly on the demand for the document not the status of the borrower. The last was deemed superior in cost-effectiveness and was implemented.²³ The expected improvement in service resulted but also provoked a dramatic and largely unanticipated increase in demand which the adaptive properties of the system helped meet. This work has been replicated in detail at Case Western Reserve University²⁴ and implemented elsewhere. A by-product has been the use of the modeling to create library management games for professional education in librarianship, though their impact has been small.²⁵

Morse's pioneering treatise, Library Effectiveness: A Systems Approach,²⁶ was largely concerned with the logistics of book availability and drew heavily on queuing theory and on a Markov model of book obsolescence in analyzing book availability at the Massachusetts Institute of Technology Science Library. His work has since been extended by Chen.²⁷ Meanwhile, Kantor has clarified and extended the analysis of factors interfering with book availability by explicitly incorporating the adequacy of the library's collections and users' failures to find items which were in their correct places as additional factors.²⁸

Another topic in library logistics is the use of mail delivery of books as an alternative to bookmobiles. A treatment of this topic by Hu et al. serves to illustrate the problems of externalities, the secondary consequences of library use.²⁹ Children may be the majority of the users. Fostering the use of books by children is generally agreed to be good for their education in general and their verbal skills in particular. These benefits clearly ought not to be ignored, yet nobody seems to know how to incorporate them. This remains a major problem in planning library services in a society that is very highly dependent on verbal skills.

Telecommunications

The rise of networks of hundreds of libraries interconnected on-line with bibliographical data bases (outstandingly, with OCLC in Dublin, Ohio) has inspired a new interest in modeling multilibrary relationships.³⁰ For the most part, the structure of the problems remains substantially the same as before computerization. What is new is the greater formality, the increased availability of data, and the emphasis on telecommunications. One can expect this to be a fertile area for quantitative analysis.

Hierarchies and networks

Libraries almost unavoidably tend to fall into formal or informal networks—with hierarchical structures being especially common. In universities it is normal to have main and departmental libraries. In the public library systems there is generally a hierarchy of two or three levels with headquarters, regional centers, and neighborhood branches. In all cases, other libraries as a source of interlibrary loans constitute an additional layer. Inside each library there is generally a three-stage hierarchy: reserve and/or "ready-reference"; main shelves; and storage.

Four types of work are relevant here:

1. Studies in weeding discarding or relegation to secondary storage are generally based on estimates of the frustration caused by the diminution of the collection by weeding.³¹ Considerable time and ingenuity have been devoted to developing, testing, and predicting the consequences of various quantitative decision rules for weeding. Unfortunately, the inexpensive rules (e.g., those based on date of publication) tend to be low in effectiveness and those that are more effective tend to be uneconomically expensive. Since there is no doubt that the distribution of demand on library collections is highly skewed, that large quantities of books receive very little use, and that the continued expansion of conventional library buildings is expensive, we can confidently expect economic pressures to result in more, not less, research on weeding and associated problems.
2. The design of interlibrary loan arrangements becomes highly relevant because, insofar as the delayed supply of documents and a diminished scope for browsing are acceptable, dependence on interlibrary loan is a temptingly inexpensive alternative to local expenditure on library collections. The problems are basically technical and the literature includes studies of transportation systems,³² the routing of interlibrary loan requests between libraries,³³ and special interlibrary loan facilities (e.g., National Lending Library, described above). However, decision-making is hampered by disagreements concerning the impact on users of increased dependence on remote resources and by uncertainties concerning the financing, control, and dependability of interlibrary loan facilities.
3. Overlap studies have been made to consider the problem that many but not all of the titles held in one library are also held in other nearby libraries. By collaborating in the processing of titles held in common, operational economies might be achieved. By sharing access to uniquely held titles, the range available to each library's users is greatly extended.³⁴ Similar methodological and practical concerns arise in planning and evaluating abstracting and indexing services covering the literature in different areas.
4. The design of hierarchies of collections has also been studied.³⁵ Even the most unitary library is part of a two-stage hierarchy with interlibrary loan resources constituting the second stage. This has taken on a new significance in recent years as some library researchers, drawing heavily on earlier operations research studies, have been propounding a revisionist view of library size. The argument, stated briefly, is that since the distribution of demand over the collection is highly skewed, continued emphasis, even in academic libraries, on maximising library size is likely to continue a decreasingly cost- effective use of resources.³⁶ In several ways, discussions of the controversial question of library size epitomize rather well both the progress and stimulating effects of operations research applied to libraries and also the serious incompletenesses that remain.

Storage methods

For multimillion volume libraries, physical storage is a major problem. Various strategies for economy are possible including sorting and shelving books by size, shelving books on their fore-edges, compact shelving, and remote storage on low-cost sites. However, the marginal gains in economies of space are counterbalanced by reduced accessibility for both staff and users, and increased transportation costs. A whole series of analyses of this problem, dealing with height, physical accessibility, principles of arrangement and cost, has been conducted under the leadership of Leimkuhler at Purdue University.³⁷

Performance of indexing systems

It is important to distinguish clearly between the "information theory" (or "communication theory") associated with Shannon and Weaver and "information storage and retrieval theory." Both are concerned with signaling, but there, is a fundamental difference. "Information theory" is concerned with the direct transmission of signals from A to B regardless of meaning. With information storage and retrieval, the communication is indirect in that the message may have been generated by A but it is not known who, if anyone, would be interested in the signal. In this case, however, the meaning of the signals is of great importance. Each potential B needs to determine which signals generated by each A might be of interest.

The performance of indexing systems is concerned with analyzing what has been retrieved in comparison with what should have been retrieved and also with the costs involved. Traditionally, this has been measured by means of a two-by-two contingency table: Relevant/Not relevant; Retrieved/Not retrieved. For a more detailed discussion see chapter 8 above. In general terms, "precision" (retrieval of relevant items but not nonrelevant items) can be improved only at the expense of "recall" (retrieving all relevant items even though some nonrelevant items are also retrieved) or vice-versa. This is awkward because one ends up with a trade-off rather than a single measure. There are two others problems: (1) the assessment of retrieval performance tends to be a subjective, arbitrary, and inconsistent activity—as is the assignment of descriptors by indexers and catalogers;³⁸ and (2) a retrieved item may be relevant but of no utility to the inquirer since it may be redundant or incomprehensible.

The literature on information retrieval makes extensive use of logic, set theory, probability, and statistics, especially in the work on experimental computer-based retrieval systems³⁹ and on tests of retrieval performance.⁴⁰ It is a relatively self-contained area, characterized by powerful tools and considerable talent. The problem is not in the manipulation of the measurements, or even that the results suggest that there is relatively little to choose between different systems, or that laboratory tests on small-scale experiments may not always yield the best insights. The real problems are at the borders with the rest of the world. The point of departure is the sorting of records between those that are relevant and those that are not. Yet it is not really understood what relevance is, or what it signifies, what the consequences of retrieval are, or when to stop doing it. As with citation analysis, the sophistication of the manipulation of the measurements is far ahead of our understanding of what is being measured.

Underdeveloped areas

Users and potential users

It would be an exaggeration to say that there have been no studies leading to mathematical models of the users and potential users of library services. For example, the phenomena examined in the bibliometric studies reflect patterns of user behavior. Also there have been a very few model-building studies of library use.⁴¹ What are seriously lacking, however, are models of information-gathering behavior. Models of marketing or of user preferences in a library context would seem appropriate.

It is known that, accessibility is a dominant factor in informationgathering behavior. People are likely to choose a source that is convenient rather than one that is particularly likely to provide the information sought but is difficult to obtain. It seems likely that the demand for library services is quite elastic with respect to a "price" in terms of perceived accessibility (see chapter 10). However, our knowledge of what demand is sensitive to—and how elastic it is—remains very incomplete. Improving the physical ambience (as when a new library is opened), reducing travel effort, and increasing the probability of finding what users seek are all known to increase library usage. Financial charges are unusual in libraries. When instituted they decrease demand. There have been endless studies of library use but not of the dynamics of how library services come to be used (or not used). The reasons for this neglect would seem to be that it is a difficult area to tackle, and the traditional research techniques of neither operations researchers nor librarians lend themselves at present to resolving these problems. Unfortunately, serious limitations to the usefulness of quantification in libraries will remain until further progress is made in this aspect.

Analytical cost models

Libraries provide a variety of different services to a variety of different user groups. Typically, the same titles and the same staff serve more than one purpose. Attempts have been made to generate analytical cost models, usually for the purpose of charging for services, for program budgeting, and/or for estimating the library component in overhead charges on research contracts.⁴² Predictably, much depends on the accounting conventions adopted as the basis for attributing costs to cost centers. Particularly in academic libraries, the results are dominated by the attribution of costs of books and serials between research and instruction when both functions are being served simultaneously. The choice here dominates the outcome because it affects not only the books and serials expenses but also a large portion of the labor costs which are directly related to book and serial acquisitions and processing.

Library "goodness"

Older operations research textbooks were apt to imply that one should meet with top management to ascertain the objectives of the organization, identify the options available, then use mathematical techniques to compute the optimal solution. Such a simplistic approach is of little use for library services because the most difficult task is identifying what the problem is and then in structuring it in a form that is both tractable and acceptable. It is here that help is most needed.

Consider the situation. A library serves a variety of different groups with different values, with different behavior patterns, and expressing different needs. A chemist urgently needs to know the thermophysical properties of a compound; a historian is inquiring about an obscure document whose name has been forgotten and which may not, in fact, exist; a bedridden senior citizen may be lonely, bored, and wanting a novel; a disadvantaged citizen wants to know whom to contact about food stamps; a student is sitting in a library carrel with a book. It may not be a library book. The student may be asleep.

Strictly, one cannot determine optimal decisions in library management unless one knows what all these wants are, how effective (and how costly) alternative types of service arrangements are in each case, and what values should be assigned to the generally rather intangible outcomes. It is likely that this will remain impossible to do in any strict manner. Yet, library administrators are continually making decisions based on assumptions, explicit or implicit, on precisely these matters.

Lancaster has provided a very convenient review of progress in the development of measures of library service and in analyses of the often conflicting relationships between them.⁴³ Of the measures discussed in the literature, "immediate availability" and related measures of document delivery are clearly measures of a library's capability. Circulation (borrowing) counts and measures of actual reading ("document exposure") are measures of the utilization of library services. There has been a growing interest in measures of performance, and in the interactions and budgetary relationships between them. We shall return to issues of library "goodness" in chapter 20.

Synthesis

Most studies addressed specific topics. Hamburg and others at the University of Pennsylvania endeavored to provide a coherent and complete approach for a university library and for a large urban public library.⁴⁴ The unifying measure of performance was "document exposure"basically a measure of the number of hours of reading. Considerable ingenuity was applied to transforming all library activities into this one measure of output. However, "document exposure" seems to have found little acceptance in the library community.

A RAND Corporation study entitled An Economic Analysis of Public Library Services examined Beverly Hills Public Library and endeavored to make recommendations that would maximize the net economic benefit to the community of having a free public library service.⁴⁵

A different approach was derived from studies by De Prospo et al.,⁴⁶ extended in Altman et al.,⁴⁷ and further developed in the well-known Output Measures for Public Libraries.⁴⁸ Here a variety of measures of performance are developed without attempting to blend them explicitly into a single objective function, but with systematic attempts to relate them to each library's own planning processes.⁴⁹

Conclusions

The use of measurement and quantification in libraries is probably quite typical of social services. The logistical aspects have proved relatively tractable and some progress has been made. The statistical analysis of observable phenomena of the use of documents (e.g., citations and recorded use of documents) has also progressed—as has analysis of properties of retrieval systems.

The fundamental problem is that the sophistication of the manipulation of what is measured is in great contrast with—and, unfortunately, distracts attention from, the fundamental weakness of our understanding of the significance of what has been measured. Citation analysis provides an excellent example: the mathematics can be done, but the significance of acts of citing is not well understood.⁵⁰ After a period of enthusiasm in the late 1960s and early 1970s, the use of operations research techniques began to lose favor in librarianship. Bommer summarized the criticisms rather well: too much emphasis on mathematics (perfect solutions to hypothetical problems); too little attention to implementation; too little emphasis on the process of investigation and too much on the product (model); and too little attention to the strategic problems of libraries.⁵¹ Yet, in a sense, mathematical approaches went underground in the sense that a steady flow of activity continued, increasingly by librarians and by faculty of schools of librarianship, in quantitative approaches to decisionmaking and planning.

The expansion and diffusion of quantitative approaches bodes well for the future, and the widespread adoption of computers in library service is likely to provide much easier access to data on, for example, the use of catalogs. Nevertheless, some areas, such as those concerned with library objectives and the dynamics of user behavior, are likely to remain difficult to address.

Bibliographic postscript

The intent of this chapter is to discuss briefly the nature and unevenness of measurement and quantification in relation to library services. There are general introductions to quantitative techniques written for librarians⁵² and, more recently, review articles.⁵³ For operations research in libraries there are reviews⁵⁴ and tutorials,⁵⁵ but these are now dated. As quantitative techniques have been absorbed, the literature has become large, diffuse, and less isolated. The references in this chapter, therefore, should, for the most part, be viewed as illustrative examples and not as a guide to the state-of-the- art. To find material on any particular aspect, reference should be made to secondary sources such as the Annual Review of Information Science and Technology, Library and Information Science Abstracts, Library Literature, etc.

Go to Chapter 17

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¹ P. M. Morse, Library Effectiveness (Cambridge, Mass.: MIT Press, 1968).

² A bibliography published in 1976 listed 700 items: M. K. Buckland and D. H. Kraft, "A Bibliography on Operations Research in Libraries," in Reader in Operations Research for Libraries, edited by P. Brophy et at. (Englewood, Colo.: Information Handling Services, 1976), pp. 355-92.

³ Library services are not alone in these characteristics; see Y. Hasenfeld, Human Services Organizations (Englewood Cliffs, N.J.: Prentice Hall, 1983).

⁴ D. H. Hertzel, "Bibliometrics, History of the Development of Ideas," Encyclopedia of Information Science and Technology, vol. 42 (New York: Marcel Dekker, 1987), pp. 144-214; F. Narin and J. K. Moll, "Bibliometrics," Annual Review of Information Science and Technology 12 (1977): 35-58; R. N. Broadus, "Early Approaches to Bibliometrics," Journal of the American Society for Information Science 38, no. 2 (March 1987): 127-9; Collection Management 2 (Fall 1978): 195-261: Special Issue on Bibliometrics.

⁵ M. R. Oliver, "The Effect of Growth on the Obsolescence of Semi- Conductor Physics Literature," Journal of Documentation 27 (1971): 11-17.

⁶ A. Bookstein, "Patterns of Scientific Productivity and Social Change: A Discussion of Lotka's Law and Bibliometric Symmetry," Journal of the American Society for Information Science 28, no. 4 (1977): 206-10; M. L. Pao, "An Empirical Examination of Lotka's Law," Journal of the American Society for Information Science 37, no. I (January 1986): 26-33.

⁷ M.G. Kendall, "The Bibliography of Operational Research," Operational Research Quarterly 11 (1960): 31-6; M. G. Kendall, "Natural Law in the Social Sciences," Journal of the Royal Statistical Society (Series A) 124 (1961): 1-18; E. A. Wilkinson, "The Ambiguity of Bradford's Law," Journal of Documentation 28 (1972): 122-30.

⁸ M. B. Line and A. Sandison, "Obsolescence and Changes in the Use of Literature with Time," Journal of Documentation 30 (1974): 283-350; B. C. Griffith et al., "Aging of Scientific Literature," Journal of Documentation 35, no. 3 (September 1979): 179- 96.

⁹ W. Goffman, "Mathematical Approach to the Spread of Scientific Ideas—The History of Mast Cells," Nature 212, no. 5061 (1966): 449-52.

¹⁰ D. de S. Price, Little Science, Big Science (New York: Colombia University Press, 1963); D. de S. Price, "Networks of Scientific Papers," Science 149 (1965): 510-15; K. W. McCain, "Cocited Author Mapping as a Valid Representation of Intellectual Structure," Journal of the American Society for Information Science 37, no. 3 (May 1986): 111-22.

¹¹ R. A. Fairthorne, "Empirical Hyperbolic Distributions (Brad ford- Zipf-Mandelbrot) for Bibliometric Description and Prediction," Journal of Documentation 25 (1969): 319-43; B. C. Brookes, "Towards Informetrics: Haitun, Laplace, Zipf, Bradford and the Alvey Programme," Journal of Documentation 40, no. 2 (June 1984): 120-43; L. Egghe, "Consequences for Lotka's Law for the Law of Bradford," Journal of Documentation 41, no. 3 (September 1985): 173-89.

¹² D. Crane, Invisible Colleges: Diffusion of Knowledge in Scientific Communities (Chicago, Ill.: University of Chicago Press, 1972).

¹³ T. J. Allen, "Roles in Technical Networks," in Communication Among Scientists and Engineers, edited by C. R. Nelson, and D. K. Pollock (Lexington, Mass.: Heath Lexington Books, 1970), pp. 191- 208.

¹⁴ H. Small and E. Greenlee, "Collagen Research in the 1970s," Scientometrics 10, nos 1-2 (1986): 95-117.

¹⁵ E. Garfield, "Citation Indexing for Studying Science," Nature 227 (1970): 669-71.

¹⁶ P. F. Cole, "Journal Usage Versus Age of Journal," Journal of Documentation 19 (1963): 1-11.

¹⁷ B. C. Brookes, "Optimum p% Library of Scientific Periodicals," Nature 232, no. 5 311 (1971): 458-61; M. K. Buckland, Book Availability and the Library User (New York: Pergamon Press, 1975); B. Houghton, "Cutback on Periodicals," New Library World 73 (1972): 2 10; B. K. Sinha and R. C. Clelland, "Modelling for the Management of Library Collections," Management Science 22, no. 5 (1975): 547-57.

¹⁸ A. Kent et al., Use of Library Materials: The University of Pittsburgh Study (New York: Marcel Dekker, 1979); K. W. R. Brownsley and Q. L. Burrell, "Library Circulation Distributions: Some Observations on the PLR Sample," Journal of Documentation 42, no. 1 (March 1986): 22-45.

¹⁹ R. E. Molyneux, "Patterns, Processes of Growth, and the Projection of Library Size: A Critical Review of the Literature on Academic Library Growth," Library and Information Science Research 8, no. 1 (January-March 1986): 5-28.

²⁰ D. H. Revill, "'Availability' as a Performance Measure for Academic Libraries," Journal of Librarianship 19, no. 1 (January 1987): 15-30; J. Mansbridge, "Availability Studies in Libraries," Library and Information Science Research 8, no. 4 (OctoberDecember 1986): 299-314.

²¹ For a history of this library, see B. Houghton, Out of the Age of Dinosaurs: The Evolution of the National Lending Libraryfor Science and Technology (London: Bingley, 1972). See also D. J. Urquhart, The Principles of Librarianship (Metuchen, N.J.: Scarecrow Press, 1981).

²² D. J. Urquhart, and R. M. Bunn, "A National Loan Policy for Scientific Serials," Journal of Documentation 27 (1959): 21-37. Also reprinted in Reader in Operations Research for Libraries, edited by P. Brophy et al. (Englewood, Colo.: Information Handling Services, 1976).

²³ M. K. Buckland, Book Availability and the Library User (New York: Pergamon Press, 1975); M. K. Buckland, "An Operations Research Study of a Variable Loan and Duplication Policy at the University of Lancaster," Library Quarterly 42, no. 1 (January 1972): 97-106.

²⁴ W. M. Shaw, "Library-User Interface: A Simulation of the Circulation Subsystem," Information Processing Management 12 (1976): 77-91.

²⁵ J. Daly et al., The Use of Gaming in Education for Library Management: Final Report on a Research Project (Lancaster, England: University of Lancaster Library, Occasional Papers, 8, 1976).

²⁶ Morse, Library Effectiveness.

²⁷ C.-C. Chen, Applications of Operations Research Models to Libraries (Cambridge, Mass.: MIT Press, 1976).

²⁸ P. B. Kantor, "Availability Analysis," Journal of the American Society for Information Science 27, no. 5/6 (1976): 311- 19.

²⁹ T. Hu et al., A Benefit-Cost Analysis of Alternative Library Delivery Systems (Westport, Conn.: Greenwood Press, 1975).

³⁰ R. E. Nance et al., "Information Networks: Definitions and Message Transfer Models," Journal of the American Society for Information Science 23, no. 4 (1972): 231-47; W. B. Rouse and S. Rouse, Management of Library Networks: Policy Analysis, Implementation, and Control (New York: Wiley, 1980).

³¹ W. C. Lister, "Least Cost Decision Rules for the Selection of Library Materials for Compact Storage," Ph.D. thesis, Purdue University, Lafayette, Ind., 1967; H. H. Fussler and J. L. Simon, Patterns in the Use of Books in Large Research Libraries (Chicago, IL: University of Chicago Press, 1969); S. J. Slote, Weeding Library Collections (Littleton, Colo.: Libraries Unlimited, 1975); J. C. Urquhart and N. C. Urquhart, Relegation and Stock Control in Libraries (Stocksfield, England: Oriel Press, 1976).

³² A. Reisman et al., "Timeliness of Library Materials Delivery: A Set of Priorities," Socio-Economic Planning Sciences 6, no. 2 (1972): 145-52.

³³ W. B. Rouse and S. H. Rouse, Management of Library Networks: Policy Analysis, Implementation, and Control (New York: Wiley, 1980).

³⁴ W. S. Cooper et al., "The Duplication of Monograph Holdings in the University of California Library System," Library Quarterly 45, no. 3 (1975): 233-75; M. K. Buckland et al., "Methodological Problems in Assessing the Overlap Between Bibliographical Files and Library Holdings," Information Processing and Management 11 (1975): 89-105; W. G. Potter, "Studies of Collection Overlap: A Literature Review," Library Research 4, no. I (September 1982): 3-21.

³⁵ B. C. Brookes, "The Design of Hierarchical Information Systems," Information Storage and Retrieval 6 (1970): 127-36.

³⁶ D. Gore, ed., Farewell to Alexandria: Solutions to Space, Growth and Performance Problems of Libraries (Westport, Conn.: Greenwood Press, 1976). For library size, see footnote 5 of chapter 20.

³⁷ For example, F. F. Leimkuhler and J. G. Cox, "Compact Book Storage for Libraries," Operational Research Quarterly 12 (1964): 419-27; F. F. Leimkuhler, "On Information Storage Models," in Planning Library Services, edited by A. G. Mackenzie and I. M. Stuart (Lancaster, England: University of Lancaster Library Occasional Papers, 3, 1969).

³⁸ T. Saracevic, "The Concept of 'Relevance' in Information Science: A Historical Review," in Introduction to Information Science, edited by T. Saracevic (New York: Bowker, 1970), pp. 111-51.

³⁹ For an introduction see G. Salton and M. J. McGill, Introduction to Modern Information Retrieval (New York: McGraw-Hill, 1983); G. Salton, "Mathematics and Information Retrieval," Journal of Documentation 35, no. 1 (March 1979): 1-29; A. Bookstein, "Probability and Fuzzy-set Applications to Information Retrieval," Annual Review of Information Science and Technology 20 (1985): 117-51.

⁴⁰ See Information Retrieval Experiment, edited by K. Sparck Jones (London: Butterworths, 1981); Information Retrieval Research, edited by R. N. Oddy et al. (London: Butterworths, 1981).

⁴¹ See, for example, B. S. Nozik, "A Stochastic Model to Predict Demand for Library Services," Ph.D. dissertation, University Microfilms no. BCD75-08029 School of Librarianship, University of California, Berkeley, 1974; W. M. Shaw, "Loan Period Distribution in Academic Libraries," Information Processing Management 12 (1976): 157-9.

⁴² F. F. Leimkuhler and M. D. Cooper, "Cost Accounting and Analysis for University Libraries," College and Research Libraries 32, no. 6 (November 1971): 449-64.

⁴³ F. W. Lancaster, The Measurement and Evaluation of Library Services (Washington, D.C.: Information Resources Press, 1977). See also B. C. Vickery and A. Vickery, Information Science in Theory and Practice (London: Butterworths, 1987) and N. A. Van House, "Public Library Effectiveness: Theory, Measures, and Determinants, " Library and Information Science Research 8, no. 3 (July-September 1986): 261-83.

⁴⁴ M. Hamburg et al., Library Planning and Decision-Making Systems (Cambridge, Mass.: MIT Press, 1974).

⁴⁵ J. P. Newhouse and A. J. Alexander, An Economic Analysis of Public Library Services (Lexington, Mass.: Lexington Books, 1972).

⁴⁶ E. R. De Prospo et al., Performance Measures for Public Libraries (Chicago: American Library Association, 1973).

⁴⁷ E. Altman et al., A Data Gathering and Instructional Manual for Performance Measures in Public Libraries (Chicago: Celadon Press, 1976).

⁴⁸ N. A. Van House et al., Output Measures for Public Libraries: A Manual of Standardized Procedures, 2nd ed. (Chicago: American Library Association, 1987); cf. P. B. Kantor, Objective Performance Measures for Academic and Research Libraries (Washington, D.C.: Association of Research Libraries, 1984).

⁴⁹ Specifically C. R. McClure et al., Planning and Role Setting for Public Libraries: A Manual of Options and Procedures (Chicago: American Library Association, 1987).

⁵⁰ See footnote 7 of chapter 8.

⁵¹ M. Bommer, "Operations Research in Libraries: A Critical Assessment," Journal of the American Society for Information Science 25, no. 3 (1975): 137-9; see also M. Elton and B. Vickery, "The Scope for Operational Reseach in the Library and Information Field," Aslib Proceedings 25, no. 3 (1975): 305-19.

⁵² See, for instance, K. F. Stock, Grundlagen und Praxis der Bibliothekssiatistik (Munich, F.R.G.: Verlag Dokumentation, 1974); 1. K. Ravichandra Rao, Quantitative Methods for Library and Information Science (New York: Wiley, 1983).

⁵³ M. T. Kinnucan et al., "Statistical Methods in Information Science Research," Annual Review of Information Science and Technology 22 (1987): 147-78.

⁵⁴ Planning Library Services, edited by A. G. Mackenzie and I. M. Stuart (Occasional Papers, 3) (Lancaster, England: University of Lancaster Library, 1969); A. G. Mackenzie and M. K. Buckland, "Operational Research," in British Library and Information Science 1966-70s, edited by H. A. Whatley (London: Library Association, 1972), pp. 224-31; Operations Research: Implications for Libraries, edited by D. R. Swanson and A. Bookstein (Chicago, Ill.: University of Chicago Press, 1972). Also issued as Library Quarterly 42, no. 1 (1972); Hamburg et al., Library Planning; Reader in Operations Research for Libraries, edited by P. Brophy et al. (Englewood, Colo.: Information Handling Services, 1976); P. B. Kantor, "A Review of Library Operations Research," Library Research 1, no. 4 (Winter 1979): 295-345; P. Oswitch, "Modelling Information System Dynamics: A Perspective," Library and Information Science Research 5, no. 2 (Summer 1983): 129-55.

⁵⁵ Elton and Vickery, "The Scope for Operational Research," Aslib Proceeedings 25, no. 3 (1973): 305-19; D. H. Kraft, "Library Operations Research," in Larc Institute on Library Operations Research, edited by H. W, Axford (Tempe, Ariz.: Larc Association, 1973), pp. 19-62; D. H. Kraft and D. H. McDonald, " Library Operations Research: Its Past and Our Future", in The Information Age: Its Development, Its Impact, edited by D. P. Hammer (Metuchen, N.J.: Scarecrow Press, 1976), pp. 122-44; A. Hindle, M. K. Buckland and P. Brophy, "The Techniques of Operations Research: A Tutorial," in Reader in Operations Research for Libraries, edited by P. Brophy et al. (Englewood, Colo.: Information Handling Services, 1976), pp. 3-27; F. F. Leimkuhler, "Operations Research," Encyclopedia of Library and Information Science vol. 20 (New York: Marcel Dekker, 1968), pp. 412-84; A. Bookstein and K. Kocher, "Operations Research in Libraries," Advances in Librarianship 9 (1979): 143-84.

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