College and Research Libraries


MARIANNE COOPER and HERBERT W. COOPER 

Interpreting Results of 

Statistical Studies 
Statistical analysis is a tool to be used by librarians only after critical 
decisions have been made about the nature of their libraries' opera-
tions. It is shown that different conclusions might be drawn from 
identical data by presupposing different, but equally plausible, rela-
tionships between the variables. Different conclusions might also re-
sult from analyzing subsets of data rather than the sample as a whole. 
The role of the librarian as a basic decision-maker in statistical studies 
is emphasized by presenting alternative interpretations of a hypo-
thetical set of data. 

LmRARIANS, LIKE OTHER professional 
scholars, are making increased use of 
statistical techniques to analyze data. 
Their purpose is to make comparisons or 
forecasts that are as free as possible from 
subjective factors or preconceived no-
tions. In order to use statistical tech-
niques effectively, however, librarians 
must consider two points very carefully. 
Both are related to the relative positions 
of the librarian and the tool called sta-
tistical analysis. 

The first point is that the librarian 
must decide what relationships can rea-
sonably be expected to exist between the 
variables of interest. After the librarian 
makes this decision, statistical analysis 
can be used to evaluate the most likely 
values of various constants. 

This sequence of events is nicely il-
lustrated in a recent paper by Reichard 
and Orsagh. 1 They collected values of 

1 Edwin W. Reichard and Thomas J. Orsagh, "Hold-
ings and Expenditures of U.S. Academic Libraries," 
College and R esearch Libraries, XXVII (November 
1966), 479-87. 

Dr. Herbert - Cooper is Director of Re-
search for Alcorn Combustion Co: in New 
York. Mrs. Cooper is a DLS student at 
Columbia University. 

266/ 

five variables for each of approximately 
three hundred institutions. The data 
were: expenditures for current acquisi-
tions, holdings, number of undergradu-
ates, number of graduate students, and 
number of faculty members. The investi-
gators then decided, a priori, that they 
would use equations of the following 
form to correlate the data. 2 

E = C1 + C2 U + CsG + C4F ( 1) 

After this decision was made, statistical 
analysis was used to provide the best 
values of the constants C 1, C 2 , C 3 , and 
C4. The point to be emphasized is that 
the investigator provides the basic form 
of the equation, and statistical analysis 
provides the values of the constants. 

Equation 1 is the mathematical equiv-
alent of the following statements. "The 
increases in expenditures are directly 
proportional to the increases in the num-
ber of undergraduates, number of grad-
uate students, and number of faculty 
members. It costs C2 dollars to add one 
undergraduate, C 3 dollars to add one 
graduate student, and c4 dollars to add 
one faculty member, in all schools, at 

2 E, U, G, F refer respectively to expenditures for 
current acquisitions, and number of undergraduates, 
graduates, and faculty. 



Interpreting Results of Statistical Studies I 267 

all enrollment and faculty levels." While 
this is certainly a plausible assumption, 
it leads to the conclusion that the under-

r graduates have, if anything, a somewhat 
negative influence on expenditures and 
that it costs seven times as much to add 
a faculty member as it does to add a 
graduate student. 

Other conclusions, however, might be 
drawn from the same data if a slightly 
different viewpoint were initially taken. 
In a library there must, of course, be a 
bare minimum of equipment and per-
sonnel present to serve even one patron. 

r- Once these minima are present, two, 
~ three, or more can be served with little 

increase in expenditure. This situation 
seems to be analogous to that of a chem-
ical plant where a certain minimum 
amount of equipment and manpower is 
required to produce even a trickle of 
product. Again after these minimum 

~ facilities are present, production can be 
increased, up to a point, by relatively 
slight additional expenditures. In both 
the library and the chemical plant the 
additional expenses are less than pro-
portional to the additional "throughput." 
To pursue this analogy we note that 
costs of chemical plants ( and also many 
other items) are related to their size by 
an equation of the form: 

cost = K ( size ) n ( 2 ) 

where n is typically between 0.4 and 0.8, 
depending on the type of plant and, 
somewhat, on its size range. Equation 2 
implies that the per-cent increase in cost 
is related to the per-cent increase in size. 
If the exponent n is less than 1.0 the 
per-cent cost increase is less than pro-
portional to the per-cent size increases. 
We would therefore expect, in view of 
the above, that equations of the follow-
ing form might be more realistic corre-
lators. 

E = K u A GB F 0 ( 3) 
Since this equation differs fundamental-
ly from the linear ones presented in the 

aforementioned article it is possible 
that different conclusions might result. 
Whether this would, in fact, be the case 
could be established by making simple 
logarithmic transformations and re-ana-
lyzing the data. 

This approach was tried with the hy-
pothetical numbers listed in Table 1 of 
this article, constructed to give results 
similar to those of Reichard and Orsagh. 
Multivariate analysis of the type they 
used led to the following equation. 

E = 5321 - 8. 7U + 116G + 188F 
(4) 

The coefficients indicate that it would 
cost $116 to add a graduate student, 
$188 to add a faculty member, but -$8.70 
(i.e., a credit) to add an undergraduate 
if equation 2 is accepted. If, however, 
the data are analyzed by presupposing 
the percentage type of relationship im-
plied by Equation 3, one obtains the fol-
lowing. 

E = 202 uo.I57 co.aa4 F0.5 ( 5) 

This indicates that expenditures must be 
increased by 1.5 per cent, 3.2 per cent, 
and 4.8 per cent for a 10 per cent in-
crease in the number of undergraduates, 
graduate students, and faculty, respec-
tively, if equation 3 is accepted. 

Which equation should be accepted? 
Unless the "coefficient of multiple de-
termine" is much greater for one of the 
equations the librarian must use his ex-
perience, judgment, and knowledge of 
library procedures, to make this de-
cision. This question always arises in 
empirical studies where causes and 
effects are not investigated. The first 
point, then, is that it is very important 
to examine the nature of the equations 
chosen to represent the data. 

The second point for librarians to con-
sider is that every library situation is, to 
some extent, special and unique. Reich-
ard and Orsagh point out that one must 
use quantifiable variables, while recog-
nizing that many other factors will exert 

. 



268 I College & Research Libraries • July, 1967 

TABLE 1 
HYPOTHETICAL UsER AND ExPENDITURE DATA 

Library u G F E 
1 500 100 50 15,000 
2 1,000 180 90 38,000 
3 1,200 180 150 43,000 
4 1,400 200 120 43 ,000 
5 1,400 220 190 55,000 
6 4,000 BOO 350 125,000 
7 4,400 700 500 145,000 
8 4,500 750 450 150,000 
9 5,500 900 600 165,000 

10 6,000 1,500 800 280,000 

their influences. For example, small col-
lege libraries are likely to have different 
organizational patterns from those of 
large university libraries; while their 
budgets will differ, their service to clien-
tele might be equally effective. 

Consider a hypothetical university 
serving thirteen hundred undergradu-
ates, two hundred graduate students, 
and one hundred and thirty faculty 
members. Its library expenditures would 
be estimated at $41,600 (from Equation 
4) or $41,500 (from Equation 5), if it 
were considered to be an average li-
brary belonging to a population of which 
the ten (hypothetical) samples listed in 
Table 1 are representative. Examination 
of the data, however, suggests two popu-
lations; small libraries (numbers 1 to 5) 
and large libraries (numbers 6 to 10). If 
a multivariate analysis of the first five 
samples, only, is performed one obtains 
the following. 

E = -13294 - 6.62U + 270G + 97F 
(6) 

a nd 

E = 20 u - o.16 GL 431 Fo.26s ( 7) 

These equations lead to predictions of 

$44,700 and $45,800, respectively, for 
the library, considered as a "small" li-
brary. It is noted, parenthetically, that 
the relative influence of undergraduates, 
graduate students, and faculty is differ-
ent in "small" institutions. It is empha-
sized, however, that Table 1 is hypo-
thetical and has been prepared only to 
illustrate the points herein discussed. 
The essence of the second point is that 
by stratifying data one might obtain a 
different but more useful comparison. 
The librarian must furnish the basis of 
comparison. This is a matter requiring 
the librarian's expertise, experience, and 
insights. 

Both of the points discussed above 
can be summarized as follows. 

1. The forms of types of relationships 
assumed to relate the variables are 
chosen before statistical analysis is 
undertaken. These relationships must 
be examined critically in all cases. 

2. Librarians must decide which data 
are to be analyzed, which form useful 
or natural subgroups, etc. These are 
questions relating to libr.arianship and 
are not statistical questions. 

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