College and Research Libraries LOUISE WOMACK HUGHES South of Explosive Exponentialism in Acade~nic Libraries Being unfamiliar with significance levels, and correction techniques, librarians are overly concerned with lack of absolute precision in li- brary counts. The handling of normal error is normal for modern statis- tics. From the admittedly imperfect statistics collected by university librarians since the 1940s, conclusions that are useful and statistically valid may be drawn. For example, the manifest << (4) 257,631 128,281 150,049 123,311 135,533 165,594 152,822 181,745 109,390 88,896 193,576 137,399 89,880 65,934 88,173 76,023 70,465 68,796 68,439 76,342 69,741 79,763 74,861 51,864 65,798 72,781 58,777 97,660 47,177 54,417 65,490 34,197 52,268 38,345 79,835 51,666 64,367 40,370 70,119 X= 2,075,611.4 books s = 1,194,840.9 books Range= 6,498,637 books $5,760,585 3,029,624 3,418,200 3,173,973 3,552,508 4,588,759 3,281,869 2,626,046 2,110,586 2,160,561 4,132,807 2,551,913 1,824,686 2,423,999 1,597,881 2,019,516 4,838,097 1,417,431 1,438,691 1,584,079 1,005,272 2,452,199 1,513,317 1,741,033 1,275,624 865,983 1,508,467 1,240,910 1,460,133 1,169,192 1,206,368 1,552,434 1,007,934 1,418,317 1,060,677 1,056,789 701,604 1,003,942 800,736 1,451,715 $1,433,351 642,291 1,183,408 997,960 897,109 1,381,015 1,047,226 814,131 692,648 726,999 1,475,737 964,822 580,125 1,051,056 595,666 580,732 3,813,068 560,578 496,735 484,939 306,295 679,417 600,924 701,644 569,131 329,241 610,587 523,793 587,218 339,335 485,975 546,093 313,391 480,646 419,015 343,825 301,116 240,649 289,442 451,212 South of Explosive Exponentialism I 347 ANALYSIS OF SAMPLE The forty largest academic libraries listed in Table 1 are arranged in de- scending ranked order according to total volumes (column 3). The mean of the distribution is 2,075,611.4 volumes; the median is 1,600,000 volumes; the range is 6,498,637 volumes; and the standard deviation is 1,194,840.9 volumes. The analysis of the data was accomplished on a computer, and resulted in forty punched cards, and a Program Sheet. INTERPRETATION OF SAMPLE: GEOGRAPHICAL Consider in Table 1 the forty libraries by geographical area: Northeast, North Central, South, and West. With ten of the largest academic libraries in the South, compared to ten in the Northeast, thirteen in the North Central, and seven in the West, superficially it would ap- pear that the South is very well off. That is far from true. When we see these li- braries plotted on a rna p ( Figure 1 ) , 3 it is obvious immediately that there is .a tremendous difference in density of great libraries by area. And when we compare this outline map with an ordinary road map of the coterminous United States, one is immediately impressed with the vast differences in the human geography of the regions-in communication lines, in population centers, in the whole net- work of inhabitation. The ten libraries in the South cover very poorly their large area of land and their share of the population. CHRONOLOGICAL DEVELOPMENT Table 2 is a graphic presentation of some of the same forty libraries arranged by rank again (number of volumes) and in column 2 of this table is given the age of all the institutions supporting the 3 The area divisions are reproduced from an outline map of the U.S. Department of Commerce, Bureau of the Census, published in the U.S. Book of Facts, Statistics & Information, 88th ed. (New York: Essan- dess Special Edition, 1967) , xiv. largest libraries in the South compared to the ages of all the institutions sup- porting the great libraries above the largest Southern library (the Library of the University of Texas). Here we see that the academic environments sup- porting the largest libraries range in age from Harvard's 332 years to the Univer- sity of Oklahoma's 78 years (excepting the composite age of the Joint Universi- ty Libraries). The University of Texas was only 87 years of age in 1965, but so was the University of California in Los Angeles, which has far outranked it in acquisitions. Why? Surely not wealth. Both areas have long been .affluent. The significant trend here seems to be popu- lation. Libraries grow most where most of the people live; libraries grow most rapidly in the Standard Metropolitan Statistical Areas. Many of the Southern universities in the group are as old or older than academic institutions in the .advantaged group. The University of Virginia was 149 when Stanford was only 83. Age is seemingly not a dominant fac- tor. The density of the largest libraries follows the density of the population, the SMSA's. In the major body of Table 2, it is shown by means of rectangles (hatched and stippled) when each of these select- ed largest academic libraries passed the 1,000,000-volume mark. Texas made it in 1951; Duke at practically the same time. All six of the top largest libraries were already past the 1,000,000-volume mark before 1941. Two of the next ranking group, Chicago and Minnesota, were over the mark in 1941. By 1954 all of the leaders had at least 1,000,000 volumes. Significantly, six of the largest Southern academic libraries passed the point only six years ago. Obviously, there has been considerable delay in library growth in the academic libraries in the South. Returning to Table 1, consider the choice of data. The six columns given in Table E from which these data were chosen present values for: Total vol- SAN FRANCISCO BERKELEY LEGEND LARGEST ACADEMIC LIBRARIES 1964 · 65 . AREA DIVISIONS FROM U.S. BUREAU OF THE CENSUS, 1967. LIBRARY DATA FROM U.S. OFFICE OF EDUCATION, 1968. • LIBRARY LOCATION BOULDER MONT. N . DAK . S. DAK . FIGURE I.-LARGEST ACADEMIC LIBRARIES 1964-65 LEGEND: -SOUTHERN 000Q NORTH CENTRAL - NORTHEASTERN ~ WESTERN TABLE 2.-CHRONOLOGY: MORE THAN 1,000,000 BOOKS 350 I College & Research Libraries • July 1969 umes; Volumes added; Total staff in full- time equivalents ( FTE); Total library operating expenditures; Staff salaries and wages; Expenditures for books and library materials (including binding); and nine of the libraries include micro- form in their counts of total volumes. Much has been written on the choice and potential use of these and other sim- ilar categories. For example, John Weath- erford wisely warned against using the figure for numbers of faculty in an in- stitution to derive the ratio of library ex- penditure per faculty member because a "good" ratio can be obtained by having a small faculty .as well as by having a large library budget. 4 In Radford's excel- lent study of the problems of academic library statistics5 he has made many im- portant observations and contributions (as well as a number of astute, but rath- er mathematically "picayunish" com- ments). Table 1 does not indicate whether or not "Volumes Added" is net. It would be useful to know. It is also progressive when Radford notes that the three major statistical surveys of aca- demic libraries (USOE, ALA, and ARL) have all "concentrated their efforts on the expenditures of libraries, ignoring the income side of library finance." 6 The array of forty libraries in Table 1 shows that Harvard is Number One in every category except expenditures for "Books & other Library Materials." There it is outranked by the library of the Univer- sity of Texas. However, the ALA 1965- 66 report7 placed the University of Tex- as library expenditures at $1,070,083, a more valid figure. Number 40 in the vol- ume-ranked list in Table 1 is the Univer- sity of Colorado, but this institution is 4 John Weatherford, "USUAL: A Visit to the United States University Average Library," Library Journal, XC (December 15, 1965), 5345. G Neil A. Radford, "The Problems of Academic Statistics," Library Quarterly, XXXVIII (July 1968), 231-248. 8 Ibid. , p. 243. 7 American Library Association, Library Statistics of Colleges and Universities, 1965-66. Institutional Data ( Chicago: American Library Association, 1967), p . 154. far from the bottom in the important category of "Volumes Added." Harvard is the giant, and increasing by some 257,000 volumes each year. It is impressive. There are only seven states (excluding Massachusetts), California, Illinois, Michigan, New York, Ohio, Pennsylvania, and Texas, in which the holdings of all the academic libraries, are larger than those of Harvard University alone. Of the top ten academic libraries, Harvard, Yale, Illinois, Columbia, Michi- gan, California at Berkeley, Cornell, Stanford, Chicago, and Minnesota, there is not one in the South. Six of the top ten academic libraries are private institutions. But of the en- tire list, only fourteen of the forty larg- est academic libraries are private. In the past this has been a much larger per- centage. There is a trend toward larger public academic libraries. Two of the largest academic libraries, Harvard and Yale, with more than twelve million of the overall total of some seventy-seven million volumes, are almost exclusively for the education of men. What is the significance of the numer- ical values that were obtained in the analysis? What is the importance of knowing that in this array the mean is 2,075,611.4 volumes, and lies , therefore, just b elow the tenth item, the Univer- sity of Minnesota Library; while the me- dian, which can be ascertained at a glance (inasmuch as the array is in ranked sequence, the median is the mid- dle of the forty items ) , and lies between the nineteenth .and twentieth largest academic libraries-exactly between Northwestern and New York U niversi- ties? If this distribution fitted a normal curve, the mean and median would nearly coincide. Instead, we can ob- serve from the lines drawn on Table 1 representing the mean and the median, that this distribution is definitely "lop- sided," or strongly skewed toward the higher values . In other words, the vari- ates (volumes in this case) plotted South of Explosive Exponentialism I 351. graphically would not make the smooth- ly rising and falling slope, expected in a normal curve. Instead, we have a jagged picture. Most of the volumes, many more than normally expected, are in the few very largest libraries. For example, Har- vard has a variance from the mean of 4,17 4,621 volumes, while Yale's variance is only 555,697 volumes. The University of Texas library looms as an abnormal peak in its position as number 17, with a variance of 843,561 volumes, while the University of Oklahoma library exceeds its expected value by only 100,241 vol- umes. The trend is a centralization move- ment, an exponential "snowball effect." The biggest libraries are getting bigger faster than the others. The total number of volumes in the aggregate United States college and university libraries in 1964 was 227,100,000 volumes, and of these, over 77,000,000 were in 40 out of 2,140 academic libraries. Good students are attracted to good faculties; and good faculties are attract- ed to institutions having the best librar- ies. "And-and this is the whole point- libraries which are good, for the diversi- ty of interests which are represented in a university faculty, necessarily are, or soon become, large libraries."8 Intertwined also (for better or for worse) are large, growing academic li- 8 Verner Clapp, "Graduate Education and Library Resources,'' Journal of the Graduate R esearch Center of Souther-n Methodist University, XXX ( 1962), p. 51. braries, and large, spreading population vortexes. The most reassuring develop- ment in urban affairs in the past several years is the increasing awareness of the importance of the quality of the environ- ment in which man lives. In 1967 the Department of Housing and Urban De- velopment introduced a guide to cities applying for a grant in its Demonstra- tion Cities Program. Applications for grants have been filed from over two hundred cities and counties. These plan- ners must take into consideration the fact that man develops and demands great academic libraries in urban centers. Li- braries exist because of man, and the social organizations he invents. Investi- gations of libraries are part of the com- prehensive attack on human problems, and must include the methodology of modern statistics. While correcting the flaws in our gath- ering of library statistics, it is advisable to remember that a 3 per cent margin of error is allowed in matters of life and death; and organizations risk capital, regularly and successfully, on a 5 per cent chance of error. Even considering the "family joke" of the library that jumped (in published statistics) from 50,000 volumes in 1962 to 100,000 vol- umes in 1964, by adding 5,000 volumes, we still have a sample that is worthy of statistical analysis. The situation could rapidly improve with enforced standards of what should be counted. • •