College and Research Libraries


R. MARVIN MciNNIS 

The Formula Approach to Library Size: 

An Empirical Study of Its Efficacy 

in Evaluating Research Libraries 
Formula approaches to the determination of adequate library size, es-
pecially along lines developed by Clapp and I or dan have in recent 
years become a significant element of the librarians' arsenal. Never-
the less, as has all too often been pointed out by those responsible for 
budgets and funding, the empirical basis of the Clapp-]ordan formula 
is rather vague. In this paper the possibilities of using statistical re-
gression analysis to provide such an empirical analysis are reviewed. 
The results indicate that it is indeed difficult to provide such an em-
pirical foundation but it can be shown that there is not likely any up-
ward bias to the Clapp-Jordan formula. 

THE UNIVERSITY LIBRARIAN is contin-
ually faced with a need to answer the 
question of whether his library collec-
tion is large enough to support the teach-
ing and research activities of the uni-
versity in anything like an adequate 
way. One device that he has at hand, 
and one that he has been turning to 
quite frequently in recent years, is a 
formula which is based on the careful 
judgment of experts in library evalua-
tion, and which is intended to indicate 
a minimum scale of adequacy. Several 
such formulae are available although 
most of these stem from the . one sug-
ges.ted by Clapp and Jordan. 1 Clapp 
and Jordan begin by listing the variables 
that should be relevant to the determi-
nation of the size of collections for aca-
demic libraries. 

1. the size and characteristics of the 
student body 

2. the size and research commitment 
of the faculty 

3. curriculum-numbers of depart-

Mr. Mcinnis is associate professor of 
economics, Queen's University, Kingston, 
Ontario, Canada. 

190 I 

ments, courses, etc. 
4. methods of instruction 
5. the availability of study places on 

campus 
6. proximity to other libraries 
7. the intellectual climate of the uni-

versity. 
In their proposed formula, Clapp and 

Jordan took into account only the first 
three of the above variables. The re-
maining ones are admittedly difficult to 
conceive of in a quantitatively measur-
able fashion. In brief, the formula pro-
posed by Clapp and Jordan states: Be-
gin with a basic library with a num her 
of volumes indicated by one or another 
of the well-known select undergraduate 
libraries. Then add 100 volumes per full-
time faculty member, 12 volumes per 
enrolled student and 12 additional 
volumes per undergraduate honors stu-
dent, 335 volumes per major under-
graduate subject offered, 3,050 volumes 
per MA field offered, and 24,500 vol-
umes for every field in which study for 
the PhD is undertaken at the institu-
tion. What one arrives at is an indica-
tion of the minimum number of volumes 
that the library should have if it is to 



Formula Approach to Library Size I 191 

perform at all adequately as an academ-
ic library. Similar formulae are offered 
for current periodical titles and for gov-
ernment documents. The weights in the 
formulae are judgmental although based 
on a number of indicators of good library 
practice and the magnitude of biblio-
graphic materials relevant to study and 
research at the university level. 

What is rather surprising is that one 
can find so little in the way of reported 
attempts to determine empirically wheth-
er the Clapp-Jordan formula or any 
variant of it generally fits existing aca-
demic libraries. In particular, one would 
like to know whether the weights in 
the formula have a reasonably accurate 
empirical basis. It would seem that this 
problem would be suitable for 1 solution 
by linear regression analysis.2 The 
Clapp-Jordan formula can be written as 
a weighted sum of several variables, all 
of which are quantitatively measurable. 
Let us adopt the following symbols for 
the variables: 

ao = a constant representing a mini-
mum viable undergraduate library 
( Clapp-Jordan say 50,750 vols.) 

F = the number of faculty 
E = total number of students enrolled 
H = number of undergraduate honors 

students 
U = number of major undergraduate 

subjects 
M = master's fields offered 
D = doctoral fields offered 

The Clapp-Jordan formula, for the num-
ber of volumes, V, can then be written: 

[1] V = 50,750 + 100F + 12E + 
12H + 335U + 3050M + 
24,500D 

The issue of concern here is the weights 
applied to the variables in [ 1]. Let us 
take a step back and treat them as un-
knowns. Then with statistics drawn 
from a sample of universities for each 
of the variables in the equation one could 
use regression analysis to estimate the 
values of the terms in equation [2]: 

[2] V = ao + a1F + a2E + a3H + 
a4U + a5M + a6D + e 

The variable e represents a random er-
ror. That is to say, equation [2] will not 
give a precise prediction of V but one 
that will be in error to some degree. The 
estimates are made on the assumption 
that these errors are randomly distrib-
uted.3 A further, and very important as-
sumption for what follows, is that each 
of the variables on the right-hand side 
of the equation exerts an independent 
influence on V. 

An empirically estimated formula is 
such a natural extension of the Clapp-
Jordan approach that it is a bit surpris-
ing that there is so little record of ex-
perimentation along these lines. I have 
found only one report of work of this 
type. Edwin W. Reichard and Thomas 
J. Orsagh used regression analysis to 
account for library expenditures and, 
what is more pertinent here, holdings 
of .the libraries of colleges and univer-
sities.4 They studied random samples of 
about three hundred institutions for the 
two years 1952 and 1962. However, they 
related numbers of volumes only to vari-
ables indicating the size of the institu-
tions and made no attempt to take into 
account breadth and diversity of pro-
grams. In that sense they make only a 
partial study of the formula approach. 
Their size variables relate to faculty and 
students, as do those of the Clapp-Jor-
dan formula, except .that Reichard and 
Orsagh separate graduate from under-
graduate students. Equation [3] restates 
the results they obtained by regressing 
the number of volumes on · the number 
of undergraduate students ( Eu), the 
number of graduate students ( Eg), and 
the number of faculty (F) in 1962.5 

[3] V = 27,100 - 9.6Eu - 59Eg + 
969F + e 
R2 = .75 

At first glance these results would ap-
pear to be a distressing commentary on 
the Clapp-Jordan formula. The coeffi-



192 I College & Research Libraries • May 1972 

cients bear no resemblance at all to those 
proposed by Clapp and Jordan. In equa-
tion [ 3] the preponderant influence upon 
library size is the number of faculty, and 
Reichard and Orsagh emphasize this as 
a particularly striking attribute of their 
findings. Numbers of students, both un-
dergraduate and graduate, appear to be · 
negatively related to library size. More-
over, the constant term is much smaller 
than the basic academic library with 
which Clapp and Jordan claim one 
should start. 

The last of these features of their re-
sults may just reflect the fact that the 
data used by Reichard and Orsagh were 
drawn from a list of academic institu-
tions that must exhibit varying degrees 
of adequacy in their library facilities. If 
the sample is truly random it will con-
tain inadequate as well as adequate li-
braries. More seriously for our present 
purposes, however, is a flaw in their 
analysis which effectively invalidates the 
conclusions they reach. The size vari-
ables Eu, E g, and F are patently not in-
dependent of each other. Indeed, one 
would expect them to be rather highly 
correlated. One would probably get 
quite similar results using either facul-
ty or student enrollment separately but 
the statistical analysis has no way of iso-
lating their true separate influences. The 
fact that in this particular application 
F came out with a positive sign and a 
large coefficient and the E variables did 
not warrants no conclusion at all. The 
technical term given by statisticians to 
this problem is multicollinearity. 

I want now to report on an effort at a 
more valid approximation to the Clapp-
Jordan formula by purely empirical 
means. It differs from the work de-
scribed above in three respects. First, I 
attempt to rid the analysis of multicol-
linearity, although without complete 
success. Second, I incorporate a mea-
sure of the diversity of academic pro-
grams at the universities included in the 
analysis. Third, I focus only on estab-

lished graduate schools. This last marks 
a sharp deviation from either Reichard 
and Orsagh or Clapp and Jordan. The 
rationale is primarily that the present 
study is just a part of a larger one that 
has as its aim the development of an 
alternative approach to evaluating the 
adequacy of library resources for grad-
uate training and research. What I have 
done here could be repeated with ref-
erence to a broader set of institutions 
with only a modest effort. However, the 
present results may have some general 
interest beyond the particular question 
that concerns me-the adequacy of li-
braries for graduate study and research. 
From that point of view I have selected 
as a frame of reference the successful 
graduate schools of the United States. 
Operationally, I define these to be the 
thirty-six leading universities in the 
United States in terms of PhD's grant-
ed during the period 1959- 62. 6 There 
are other graduate schools, of course, 
but those incorporated in the analysis are 
the ones that appear to have been 
clearly successful. There is some pre-
sumption that their library resources meet 
a standard of adequacy (or at least if 
they do not it has not impaired their 
viability as graduate schools to any no-
ticeable degree). 

What I am dealing with is not really 
a sample but the whole population of 
most successful graduate schools ( at 
least on the pragmatic definition of suc-
cess that I have given). Statistically, 
however, this might be thought of as a 
sample of the population of conceptual-
ly successful graduate schools. Looking 
at the evidence in this way it is difficult 
for us to judge how random the sam;. 
pie may be. Since a good number of the 
institutions far exceed the minimum 
levels of adequacy postulated by Clapp 
and Jordan, we might fairly expect the 
predictions of library size given by the 
formula estimated here to overshoot the 
results obtained with the Clapp-Jordan 
formula. 



Formula Approach to Library Size I 193 

Numbers of volumes and periodical 
titles were obtained from statistics pub-
lished by the American Library Associa-
tion. 7 Enrollment, both graduate and 
undergraduate, and numbers of faculty 
were from publications of the U.S. De-
partment of Health, Education and Wel-
fare. 8 These bodies of data are reason-
ably well known and whatever weak-
nesses they may have are not peculiar 
to the present study. The number of 
fields in which institutions offer study 
for the PhD degree, the measure of di-
versity of programs utilized here, was 
developed from listings in American Cal-
leges and Universities. 9 

To get around the problem raised 
by the correlation between numbers of 
students of both sorts and the number 
of faculty members, one of these vari-
ables had to be chosen as the primary 
indicator of size of the institution. With-
out intending to enter into the ideolog-
ical debate on the appropriate locus of 
power on campuses, I adopted the num-
ber of faculty as the primary indicator of 
size. I am dealing with major research 
institutions where it is likely that this 
indicator of the size of the institution 
would have the most bearing on the de-
termination of library size. The number 
of students is then introduced relative 
to the number of faculty and the number 
of graduate students relative to the total 
number of students. The important point 
here is the introduction of the various 
measures of size as a group with some 
effort to capture the independent in-
fluences of each variable. It would have 
been just as suitable to use enrollment 
as the primary measure of size and to 
add variables for the number of faculty 
members per hundred students. 

Numbers of fields is suggested by 
Clapp and Jordan as an indicator of the 
breadth of program offered by an in-
stitution. I make no attempt to handle 
MA fields separately. Mostly they will 
be fields in which the PhD is offered 
and, certainly, for the selection of uni-

versities being studied, the addition of 
fields where the MA but not the PhD is 
offered would not likely add much to the 
analysis. The definition and identifica-
tion of fields of doctoral study is both 
difficult and ambiguous. The lists of 
fields offered by institutions usually has 
an administrative basis and often re-
flects peculiarities of the historical de-
velopment of the institution. Moreover, 
fields appear to be more narrowly de-
fined in the natural sciences than in the 
social sciences. Language fields offer an 
acute example of variations in the desig-
nation of offerings. Some universities 
note very specifically what languages 
they offer (Spanish, Italian, French, Por-
tuguese) whereas others organize them 
into broad groupings (Romance Lan-
guages ) . There is no real alternative to 
grouping specific offerings into those 
broad categories that appear to be fairly 
commonly used, so as to assure a tol-
erable level of uniformity among uni-
versities.10 Area studies proved to be 
much more difficult. Since the univer-
sities generally regard the comprehen-
sive study of a particular area as a dis-
tinct field, I accept this assumption. It is 
really doubtful if the numbers of fields 
can be given any very precise interpreta-
tion, given the possible variations in the 
treatment of field designations. At any 
rate, an attempt has been made here to 
specify a standard list of fields and to 
note which of them are offered at each 
university. However, the ambiguities in 
the basic evidence are such that it 
should not be thought that the data used 
here conform precisely to such a neat 
tabulation. Little more can be said than 
to caution readers about the weakness 
of this variable. 

Science and nonscience fields have 
been tallied separately on the grounds 
that their bibliographic needs may differ, 
especially when summarized in such a 
gross way as ·numbers of volumes or 
periodical titles. The variables used in 
this analysis are listed below. 



194 I College & Research Libraries • May 1972 

V 1 ~ library holdings in volumes (in 
'OOO's) 

V 2 = current periodical titles (in '000' s) 
F = number of faculty11 
S = student enrollment per 100 faculty 

members 
G = graduate students per 1,000 stu-

dents enrolled 
D = total number of doctoral fields 
D s = number of natural science doctoral 

fields 
Dn = number of nonscience doctoral 

fields. 

Several regression equations were esti-
mated, utilizing various combinations of 
the above variables. The specification 
of the relationship which, a priori, ap-
peared to be most promising gave the 
results shown in equations [ 4] and [5]. 
The numbers in parentheses below the 
coefficients of the explanatory variables 
are values of the statistic t that is used 
in evaluating the statistical significance 
of the estimated coefficients. 

[4] 

R2 = .29 

[5] 

-
R2 =.54 

V 1 = -875.30 + .089F + .007S 
( .67) ( .23) (.01) 
+ 2.504G + 23.336Ds + 

( .77) (.50) 
97.980Dn + e 

(2.26) 

F = 3.924 

V2 = -17.450 + .003F + .006S 
( 1.92) ( 1.18) ( 1.34) 

+ .037G + .101Ds + 
( 1.64) ( .31) 

.891Dn + e 
(2.94) 

F = 9.216 

The result for numbers of periodical ti-
tles, equation [5], is much stronger than 
for numbers of volumes of books. The 
main conclusion that can be reached 
from both equations, however, is that the 
explanatory variables that are tested do 
not perform especially well. The ran-
dom element is large, particularly in 
the case of V 1· The proportion of the 

variance of V 1 that is accounted for by 
the indicators of size and diversity is 
only .29.12 For V 2 the regression equa-
tion does a little better and R2 is .54. 
That is to say that the equation is able 
to account for 54 percent of the varia-
tion in numbers of periodical titles. In 
both cases, though, the random element 
is substantial. Cross-section regressions 
that have genuine explanatory content 
not infrequently have a low R2 • How-
ever, we cannot be entirely pleased 
with results that, at best, account for 
only half of the variations in library 
size among institutions. Even more seri-
ous is the failure of most of the explana-
tory variables to show up with a statis-
tically significant influence on library 
size. If we accept an approximate test 
that the value of the t statistic should ex-
ceed two before we conclude, with a 
probability of .95, that any coefficient 
probably exceeds zero, we find that only 
one of the postulated variables has a 
significant influence upon library size. 
That is D n, the number of nonscience 
fields offered. That one variable accounts 
for almost all of the explanatory power 
of the regression equation. For numbers 
of volumes, the coefficients of all other 
variables are small and have such large 
variances that one could not conclude 
that they are really different from zero. 
It is doubtful that it is even worth point-
ing out that the coefficients imply very 
different weights from those of the Clapp-
} ordan formula. Even in the case of the 
one statistically significant variable, the 
regression results imply that a library 
adds about 98,000 volumes per nonsci-
ence field in which it offers the PhD. 
That is several times the figure used by 
Clapp and Jordan. The result would also 
imply that none of the other variables 
-faculty or students or science doctoral 
programs-likely has any significant in-
dependent influence on library size. Such 
a result, although apparently damaging 
to the ·Clapp-Jordan formula, lacks 
credibility. 



I?' 

FormulaApproach to Library Size I 195 

A major difficulty lies in the nasty mat-
ter of multicollinearity which, in spite of 
the care which I tried to exercise, has 
not been excluded. It turns out that the 
number of doctoral programs is rather 
highly correlated with the number of 
members of faculty. The simple corre-
lation coefficient with ·total doctoral pro-
grams is .75. With the number of non-
science doctoral programs it is .66. In 
either case the correlation is far too 
high to provide for separate estimation 
of the influence of numbers of faculty 
and numbers of programs. 

The implication of the statistical anal-
ysis should be clearly put-the Clapp-
Jordan formula, as stated, is not empir-
ically verifiable. The problem is not 
just one of limitations to the statistical 
techniques employed. It is more funda-
mental. Fields of intellectual activity 
and participants in those fields, carrying 
on teaching and research, are intricate-
ly bound together. If it makes little se~se 
to conceive of university programs with 
no students, teachers, or researchers, or 
of participants with no programs, ~t 
makes little sense to postulate that li-
brary size is separately influenced by 
these factors. To account for library 
size in a causative, explanatory way an 
entjrely different .tack must be taken. I 
offer no solution in this paper but en-
courage students of library science to de-
velop one, for in doing so they will nec-
essarily evolve a much sharper and more 
realistic conceptualization of the univer-
sity library. 

A way around the statistical difficulties 
described above, but one that leads us 
away from the Clapp-Jordan formula, is 
to utilize one or the other but not both 
of the variables F and D. Equations 
[6] and [7] present the results of re-
gressions which leave out the number 
of programs. 

'[6] V1 = -1231 + .724F + .617S + 
( .93) ( 3.13) ( 1.05) . 

5.907G + e 
( 1.94) 

-
R2 = .22 
[7] 

-
R2 = .44 

F =4.30 
V2 = -22 + .0085F = .OlliS + 

( 2.2) ( 5.01) ( 2.57) 
.0671G + e 
( 3.02) 

F = 10.28 

Neither of these new equations improves 
the fit of the relationship to account for 
a greater part of the variability of li-
brary size. In that respect there is no 
improvement. However, the relationship 
that appears to exist between library 
size and the size and nature of the uni-
versi.ty can be given a more satisfactory 
interpretation. The number of faculty 
members, taken as a general indicator 
of the size of the university, exerts a 
strong influence on library size. The 
number of volumes rises by 724 for 
every additional faculty member; the 
number of current periodical titles by 
BK The coefficient of •the F variable is 
statistically significant in both cases. The 
additional influence on the number of 
volumes in the university library appears 
to relate more to the research and grad-
uate training function of the university 
rather than the extent to which student 
enrollment differs from proportionality 
with faculty size. However, both influen-
ces are statistically significant in the de-
termination of the numbers of current 
periodical titles. 

The regression equations, either in-
cluding or excluding numbers of doctoral 
fields, give predictions of library size that 
vary widely from the actual figures for 
the universities included in the sam-
ple. These residual deviations warrant 
study to see first if they are truly ran-
dom as has been assumed in the esti-
mati~n of the regression equations, or 
whether they can be associa1ted with any 
readily recognizable characteristics of 
universities. One possibly interesting 
question that comes to mind is wheth~r 
the unexplained or residual part of li-
brary size is related to commonly held 
views of the quality ranking of gr.aduate 



196 I College & Research Libraries • May 1972 

schools. That turns out not to be the 
case. The largest underpredictions, in-
dicating university libraries that are 
much larger than would be expected on 
the basis of average praotice, are for 
Harvard, Yale, Illinois, and Duke. Sub-
stantial overpredictions are made for 
Wisconsin, Pittsburgh, and Pennsylvania. 
The equations that incorporate numbers 
of dootoral programs produce large over-
predictions for Chicago and Johns Hop-
kins as well. These last, especially, 
would hardly be regarded as weak grad-
uate schools . The one characteristic 
which stands out in the residuals from 
the regression equations is that the equa-
tions underpredict for those institutions 
(e.g., Harvard, Yale, Illinois, Duke) 
which are renowned for their special at-
tention to libraries. This result gets some 
corroboration from a positive, although 
not strong, correlation between residuals 
from the equation for volumes and that 
for periodical titles. What this seems to 
point to is that for some academic insti-
tutions the library is more than just a 
resource for teaching and research but 
is something of an end in itself. These 
institutions would presumably jus·tify li-
brary collections much larger than would 
be indicated by their usual research 
needs, on the grounds that they view as 
a valid part of their function the preser-
vation of part of civilization's heritage. 
In that sense, some universities have 
been prepared to develop national or 
regional libraries while others have been 
more content to restrict their ambitions 
to the needs of teaching and research 
on their campuses. I would be hesitant 
to press too far the notion that the posi-
tive residuals from the regression equa-
tions reflect the extrauniversity or, per-
haps more accurately extraresearch, 
goals of universities. They seem to point 
in that direction but the random ele-
ment is too great and the fit of the re-
gression equations too poor to make 
much of such an argument. No other 
systematic element appears to be evi-

dent in the residuals. 
The principal object of this study was 

to evaluate the Clapp-Jordan formula as 
a basis for estimating minimum levels of 
adequacy of academic libraries for grad-
uate studies and research. That is not 
readily done directly. It was necessary 
to modify the formula to be able to esti-
mate the relationship between library 
size and size and diversity of research 
efforts and graduate training programs 
by means of regression analysis. It would 
be inappropriate to attempt to compare 
directly the coefficients of the regression 
equations presented in this paper with 
the weights of the Clapp-Jordan formu-
la. One point that might be made in 
this regard, though, is that the propor-
tion of students who are in graduate pro-
grams-a variable that does not enter 
into the Clapp-Jordan formula-plays an 
important role, especially in the reduced 
version. 13 

A better method of evaluation would 
be to compare the predictions obtained 
with the regression equations with those 
obtained from the Clapp-Jordan for-
mula. This cannot be done with quite as 
much precision as might be desired since 
I have not obtained all of ·the informa-
tion that would go into the Clapp-
J or dan formula. What is missing, though, 
is the number of undergraduates in hon-
ors programs and tfe number of under-
graduate fields of specialization. Where 
we are dealing with libraries of several 
million volumes these variables have lit-
tle influence. For few institutions could 
they account for more than 100,000 vol-
umes. A more serious matter is the de-
gree of arbitrariness that is involved in 
counting numbers of fields of doctoral 
study. I indicated earlier that these 
could be counted at varying levels of 
aggregation. My chief concern in pre-
paring data for the regression analysis 
was to put the listings of fields for all 
universities on as comparable a basis as 
possible. It is not precisely clear how 
Clapp and Jordan handle this problem 

~I 

I 

I 
I 



• 

Formula'i\pproach to Library Size I 197 

but they seem to accept university state-
ments about fields at face value without 
concern for consistency. The weight at-
tached to numbers of doctoral fields is 
so large that this variable plays the 
strongest role of any in the formula. It 
therefore becomes especially important 
that the variable is adequately defined. 
In their original presentation, Clapp and 
Jordan give explicit results for the appli-
cation of their formula to only ·three 
full-fledged universities: Illinois, Michi-
gan, and UCLA. They count twelve 
more fields for Michigan and nine more 
for Illinois than I and five fewer for 
UCLA.14 Since they do not document 
precisely how they ascertain the number 
of fields I have no way of reconciling 
these counts but I strongly suspect that 
they have not determined that fields are 
defined consistently between universi-
ties.15 

Consider first the three schools for 
which Clapp and Jordan provide explic-
it estimates. Using my data rather than 
theirs we get the following formula re-
sults: 

Illinois 
Michigan 
UCLA 

2,163,000 vols. 
2,226,000 vols. 
1,723,000 vols. 

My figure for Illinois is well below that 
shown by Clapp and Jordan and for 
UCLA it is slightly higher. The main 
concern here, however, is how these re-
sults compare with predictions from the 
regression equations. For both UCLA 
and Michigan I get very similar results 
with either Regression II, incorporating 
numbers of fields in line with the Clapp-
J or dan approach, or Regression I, using 
only size variables. And in both cases 
the regression predictions are well above 
those obtained with the Clapp-Jordan 
formula. For Illinois, Regression I agrees 
closely with the predictions from the 
Clapp-Jordan formula, whereas with Re-
gression II the prediction is 350,000 vol-
umes higher and well above that of the 
Clapp-Jordan formula. 

Illinois 
Michigan 
UCLA 

Regression I Regression II 
2,07 4,000 2,423,000 
3,065,000 2,995,000 
2,378,000 2,413,000 

Similar comparisons can be made for 
other universities, using the data gath-
ered for my regression analyses. As a 
general rule the regression equations 
produce a higher figure for the expected 
number of volumes than does the 
Clapp-Jordan formula. This is not sur-
prising since the regression equations en-
deavor to measure the average relation-
ship, whereas the Clapp-Jordan formula 
is intended to indicate a minimum stan-
dard. Whether the Clapp-Jordan formu-
la indeed points to minimum levels of 
adequacy is something that cannot be 
concluded from this analysis. What can 
be said, however, is that there is noth-
ing to indicate that it produces an over-
prediction. Applied to those universities 
that are already heavily engaged in grad-
uate education and research at the doc-
toral level in a serious way, the Clapp-
J ordan formula does not produce results 
that are patently too high. In the light 
of suspicions expressed by government 
officials and budgetary authorities this 
may be an important conclusion. We 
must recall, though, that it is a conclu-
sion reached through comparison with 
the results of regression analysis which 
was subject to a high degree of varia-
bility. It should not, therefore, be un-
duly emphasized. Still, it may be of 
some comfort to those who have used the 
Clapp-Jordan formula in support of 
claims to build collections of a minimal-
ly adequate size that they cannot be ac-
cused of excesses. For university re-
search libraries Clapp and Jordan offer 
a · conservative guide. Viewed in that 
light, the results reported in this paper 
suggest that as a very rough, quickly 
computed guide to minimum levels of 
library size, the Clapp-Jordan formula 
should remain in the librarian's tool kit. 
What I hope that this attempt at em-



198 I College & Research Libraries • May 1972 

pirical verification of the formula has 
shown, however, are the inherent weak-
nesses of the formula and its sensitiv-
ity to definition of fields. More impor-

tantly, I hope that it has shown the 
need for developing predictive formulas 
from causative explanatory 'models of 
the nature of research libraries. 

REFERENCES 

1. Verner W. Clapp and Robert T. Jordan, 
"Quantitative Criteria for Adequacy of Ac-
ademic Library Collections," College & 
Research Libraries 26:371-80 (Sept. 1965). 

2. Readers unfamiliar with statistical tech-
niques will find an explanation of linear 
regression analysis in any introductory text-
book on statistics with application to busi-
ness or the social sciences. 

3. The particular assumption made here is 
the common one that they follow a nor-
mal distribution. 

4. See their "Holdings and Expenditures of 
U.S. Academic Libraries: An Evaluative 
Technique," College & Research Libraries 
27:478--87 (Nov. 1966). 

5. Their results for 1952 are not fundamen-
tally different. 

6. These were drawn from the list presented 
by Allen M. Cartter, An Assessment of 
Quality in Graduate Education ( Washing-
ton, D.C.: American Council on Educa-
tion, 1966). 

7. Library Statistics of Colleges and Univer-
sities 1965-66 (Chicago: American Li-
brary Association, 1967). 

8. Students Enrolled for Advanced Degrees, 
Fall 1966 (Washington: G.P .0., 1968) 
and Opening Fall Enrollment in Higher 
Education, 1966 (Washington: G.P.O., 
1967). 

9. American Colleges and Univetsities (lOth 
ed., Washington: American Council on 
Education, 1968). 

10. It appears that reasonable unifon11ity can 
be obtained with the use of the following 
classes: Classical Languages, Other An-
cient Languages, English, Romance, Ger-
manic including Scandinavian, Slavic, Near 
and Middle Eastern, and Oriental langu-
ages. Since language fields are highly in-
tensive in the use of library resources this 
categorization may be too aggregative. 
These fields would probably use a larger 
body of literature each than many of the 
natural science fields. However, to be more 
specific for some universities would require 

either special information from the uni-
versities or assumptions ·about what sub-
areas are covered. 

11. An attempt has been made to approxi-
mate full-time equivalent faculty num-
bers by weighting part-time faculty one-
half that of full-time. My first thought was 
that, in terms of their demands on bib-
liographic resources for research, part-time 
faculty should be counted the san1e as 
full-time. Indeed, some faculty are re-
garded as part-time because ' they have ap-
pointments in research institutes. The defi-
nition of part-time status seems to vary 
widely from institution to institution so 
that one found curious anomalies in stu-
dent-faculty ratios if part-time faculty were 
not given a lesser weight. 

12. [2, is the coefficient of determination, ad-
justed for the · number of degrees of free-
dom. It is perhaps more directly informa-
tive than the commonly used R-the co-
efficient of correlation-as an indicator of 
the goodness of fit of the regression equa-
tion. I show also the statistic F for the 
estimated equations in order to provide a 
test of the hypothesis that the explanatory 
variables are unrelated in the sense that 
the regression coefficients are really zero. 
That hypothesis would be rejected, at a 
.95 level of confidence, if F exceeds 2.53 
for 5 and 30 degrees of freedom. 

13. Let us call this for brevity, Regression I. 
The version which includes numbers of 
science and nonscience doctoral fields will 
be called Regression II. 

14. Clapp and Jordan, "Quantitative Criteria." 
15. I indicated previously that I considered 

the argument that a doctoral program is 
one that a university sees fit to declare, 
but this approach must be unsatisfactory 
since it leads to results that are difficult 
to interpret. Administrative practices and 
views about tl1e appropriate scope of dis-
ciplines vary widely, especially in the or-
ganization of doctoral programs. 

( 

~ 
I