08832323.2013.876379
Journal of Education for Business
ISSN: 0883-2323 (Print) 1940-3356 (Online) Journal homepage: http://www.tandfonline.com/loi/vjeb20
An Investigation of U.S. Undergraduate Business
School Rankings Using Data Envelopment Analysis
With Value-Added Performance Indicators
Susan W. Palocsay & William C. Wood
To cite this article: Susan W. Palocsay & William C. Wood (2014) An Investigation of U.S.
Undergraduate Business School Rankings Using Data Envelopment Analysis With ValueAdded Performance Indicators, Journal of Education for Business, 89:6, 277-284, DOI:
10.1080/08832323.2013.876379
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Date: 11 January 2016, At: 20:44
JOURNAL OF EDUCATION FOR BUSINESS, 89: 277–284, 2014
Copyright Ó Taylor & Francis Group, LLC
ISSN: 0883-2323 print / 1940-3356 online
DOI: 10.1080/08832323.2013.876379
An Investigation of U.S. Undergraduate Business
School Rankings Using Data Envelopment Analysis
With Value-Added Performance Indicators
Susan W. Palocsay and William C. Wood
Downloaded by [Universitas Maritim Raja Ali Haji] at 20:44 11 January 2016
James Madison University, Harrisonburg, Virginia, USA
Bloomberg Businessweek ranks U.S. undergraduate business programs annually. These
rankings provide a convenient overall measure of quality, which is important in today’s
environment of concern about higher education costs and employment after graduation. Data
envelopment analysis (DEA) has advantages over previous regression approaches in
characterizing value added. The authors use a DEA approach to estimate relative efficiencies
based on starting salaries and recruiter surveys, identifying some schools as overachievers
relative to their Bloomberg Businessweek rankings. In particular, DEA-based reranking
highlights the ability of some public institutions facing high student–faculty ratios to turn out
well-regarded graduates with high starting salaries.
Keywords: data envelopment analysis, DEA, efficiency, performance, rankings, undergraduate
business schools
Business Week first began ranking undergraduate schools
and colleges of business in 2006 (Lavelle, 2006). Since that
time, the magazine’s successor Bloomberg Businessweek
has refined its methodology, expanded the number of
schools ranked, and provided additional detail on ranking
procedures (Gloeckler, 2013). These rankings, however, do
not account for the efficiency of resource use, so that lower
cost schools achieving the same results as higher cost competitors see no boost in their rankings. Since 2006, college
tuition and fees have increased more than 30% (38.7% for
public institutions and 32.1% for private ones) even as the
national economy has endured its most striking downturn
since the Great Depression (National Center for Education
Statistics, 2013). Meanwhile, student loan debt has
expanded sharply, growing 58% between 2004 and 2012
(Gross, 2013).
Amid public concern about costs and quality, inefficiency in the use of funds by higher education could, over
time, fundamentally erode the support for colleges and
Correspondence should be addressed to Susan W. Palocsay, James
Madison University, Department of Computer Information Systems and
Business Analytics, MSC 0202, 800 S. Main Street, Harrisonburg, VA
22807, USA. E-mail: [email protected]
Color versions of one or more of the figures in the article can be
found online at www.tandfonline.com/vjeb.
universities. A national survey revealed “a chipping away
of public support for higher education and a growing suspicion about how well colleges and universities use the
money they have” (Immerwahr & Johnson, 2009, p. 5). The
survey authors suggested that colleges and universities
address public concerns over high costs proactively, since
governments would likely act with greater regulation and
supervision if the growth of costs remained unchecked. The
combined concerns of students, parents, and government
provide good reasons to investigate the efficiency of higher
education, including undergraduate business education. In
this environment it is important to note that efficiencyadjusted rankings can differ significantly from Bloomberg
Businessweek’s reported rankings (Kreutzer & Wood,
2007).
In this study, we used data envelopment analysis (DEA)
to examine the relative efficiency of U.S. undergraduate
business schools included in the most recent Bloomberg
Businessweek study (Gloeckler, 2013) from an economic,
value-added perspective. DEA was first proposed by
Charnes, Cooper, and Rhodes (1978) to empirically measure how effectively organizational units convert multiple
inputs into multiple outputs in comparison with each other.
DEA calculates a weighted output-over-input ratio for each
unit, which is defined as a relative efficiency score, with 1
indicating efficient status. A piece-wise linear surface is
Downloaded by [Universitas Maritim Raja Ali Haji] at 20:44 11 January 2016
278
S. W. PALOCSAY AND W. C. WOOD
constructed through the efficient units to estimate a frontier,
and efficiency computations are made relative to this frontier (Seiford & Thrall, 1990). Thus, units that lie below the
frontier are assigned scores of less than 1, indicating that
there is a linear combination of efficient units that could
produce as much output using smaller input amounts.
Since its introduction more than 30 years ago, DEA has
gained widespread acceptance as a standard tool for evaluation of economic productivity with successful applications
in numerous nonprofit and for-profit domains (Emrouznejad, Parker, & Tavares, 2008). A brief overview of the
DEA approach in education for business is provided in the
next section. Then we describe the data and DEA model for
estimating relative efficiencies and use these scores to generate a full reranking for comparative purposes. Results are
described in the following section, and we conclude with
suggestions for future research.
DEA APPLICATION TO BUSINESS SCHOOLS
In a 2008 literature review of DEA research, Emrouznejad
et al. identified education as one of the most prevalent areas
of DEA application, finding 44 publications using it as a
keyword. Generally, studies in the higher education sector
have applied DEA at either the academic department level
within one institution or for universities in a particular
country (Sav, 2012). The majority of the latter group focus
on managerial performance in responding to financial
reforms in public university funding (Sav, 2013) and challenges to revenue generation for private institutions (Liu &
Liu, 2010). Commonly used productivity measures were
enrollments, graduation and/or retention rates, and credit
hour production (e.g. Avkiran, 2001; Sexton & Communale, 2010).
Other authors have used different measures of DEA efficiency for U.S. master of business administration (MBA)
programs (Colbert, Levary, & Shaner, 2000; Hirao, 2012)
and for business schools outside the United States in Taiwan (Kong & Fu, 2012) and India (Sreekumar & Mahapatra, 2011). In these studies, the focus was primarily on
postgraduation approval and employment-related outcomes
instead of more traditional administrative standards. As a
group, they demonstrate various DEA modeling approaches
to facilitate comparisons of business schools based on
potential economic benefits being offered.
In Colbert et al. (2000), multiple efficiency scores were
calculated for each of the 24 best Business Week–ranked
MBA programs based on their achievement of either student satisfaction and/or recruiter satisfaction. Input resources were represented by faculty-to-student ratios, average
GMAT scores, and number of elective offerings. In their
experimental trials, the number of efficient programs varied
from 8 to 16 with all of the efficiency scores exceeding 0.9.
In the trial using average salary and average recruiter score
as outputs, the minimum efficiency was 0.9420 and the
DEA model generated an efficiency score of one for 13 of
the 24 schools. This lack of differentiation was attributed to
the similarity of programs in the sample, all prominent topranked MBA programs.
More recently, Hirao (2012) estimated efficiency of U.S.
graduate business schools in terms of translating peer
assessment and average GMAT scores into average starting
salaries and employment rates. The reference data came
from U.S. News & World Report rankings of the top 50
business schools in 2006, of which 27 were private and 23
were public. Peer assessment score (from appraisals by
other department heads) had a stronger positive correlation
with both starting salaries and employment rates than average GMAT scores (0.908 vs. 0.735 for salaries and
0.514 vs. 0.383 for employment). Five of the 50 schools
achieved (relative) efficiency and scores ranged from 0.8087
to 1, with a mean of 0.9356. On average, public institutions
had lower overall efficiencies (0.9155) than private ones
(0.9527). School names were not identified in this study and
no comparative analysis of rankings by DEA was provided.
Kong and Fu (2012) ranked a small group of 21 Taiwanese business colleges using survey data from recent
graduates to construct indicators for job market performance and student satisfaction. With restrictions from
recruiters imposed on indicator weights, only 3 of the colleges had a DEA efficiency score of 1 but all scores were
higher than 0.9. They did, however, find average performance of public schools (0.991) exceeded that of private
ones (0.981).
For the evaluation of 49 business schools in India, Sreekumar and Mahapatra (2011) chose three inputs: faculty/
student ratio, infrastructure, and tuition fees. They developed a broad group of eight outputs that encompassed starting salary and the satisfaction of faculty, students and
recruiters as well as other measures such as international
exchange programs and student awards. DEA showed its
ability to discriminate within this sample by evaluating
only 4 schools as relatively efficient. The minimum score
was 0.356 and mean efficiency was 0.625 with a standard
deviation of 0.175. Further analysis of DEA results was
done to identify peer groups for benchmarking of inefficient
schools to improve performance, although individual
school names were not revealed.
In this study, we extended the application of DEA into
U.S. undergraduate business education with a value-added
purpose. We generally followed the approach in Colbert
et al. (2000) as described previously, augmented by guidance from Kreutzer and Wood (2007) to consider the
impact of tuition costs. Our study benefits from having a
larger sample containing more diverse schools when determining the effect of ranking via DEA scores. We also compared efficiencies of public and private business schools
and investigate the composition of peer groups for additional insights aimed at performance management.
UNDERGRADUATE BUSINESS SCHOOL RANKINGS USING DEA
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DATA AND MEASUREMENT OF EFFICIENCY
SCORES
In the present analysis, data were taken from the Bloomberg
Businessweek 2013 rankings of 124 undergraduate business
schools. The ranking method includes nine variables, all
related in some way to student satisfaction, post-graduation
outcomes or academic quality (Lavelle, 2013). Student satisfaction is measured through a survey sent to graduating
seniors at the ranked schools. Post-graduation outcomes
include employer opinion (from a survey), school-reported
median starting salaries, and admissions to top MBA programs. Academic quality was measured through average
SAT scores, student–faculty ratios, average class size, the
percentage of business majors with internships, and weekly
student hours reported to be spent on schoolwork. In the
final summation, student assessment accounts for 30% of
the ranking, recruiter survey scores account for 20%, starting salaries and MBA admissions contribute 10% each, and
the academic quality items together account for the remaining 30%.
Selection of inputs and outputs for DEA should be
guided by the environment being examined and by organizational objectives (Avkiran, 2001). For our analysis, we
sought a parsimonious set of variables to compare business
programs on the basis of their performance in producing
highly marketable graduates, conditional on resource availability and incoming-student quality. With this perspective
in mind, we chose student/faculty ratio to characterize
school quality and average SAT scores to account for student ability. Annual tuition was included as a third input
measure, consistent with the approach in Kreutzer and
Wood (2007). As DEA permits more than one output, we
were able to incorporate the employer rankings (based on
recruiter opinions) with median starting salaries to reflect
the overall value of graduates from each program.
A statistical summary is given in Table 1. Note that one
institution, Massachusetts-Amherst, was removed from the
data set due to concern about its artificially low reported
tuition. That reported tuition was $1,714, but mandatory
fees were $11,518 (Massachusetts Department of Higher
Education, 2013), making the institution an outlier with no
easy means of correction. The resulting final sample size
was 123. The distribution of private versus public schools
was similar, with 59 private and 64 public institutions.
TABLE 1
Summary Statistics
Measure
M
Median
SD
Minimum
Maximum
Student–faculty ratio
SAT
Tuition ($)
Salary ($)
22.460
20.4
9.537
0.9
65.0
1219.423
1207
103.725
1020
1492
22,712.46
14,985.00
14,666.72
4,710.00
45,735.00
50,626.55
50,000.00
6,823.04
32,500.00
70,000.00
279
TABLE 2
Correlation Coefficients
Student–faculty
ratio
SAT
Item
Student–faculty ratio
SAT
Tuition
Salary
Employer rank
¡.526**
¡.410**
¡.423**
¡.154*
Tuition Salary
Employer
rank
.341**
.738** .321**
.522** ¡.087 .505**
*p D .10. **p D .01.
The correlation coefficients for input and output variables are listed in Table 2, with employer rank inverted for
ease of interpretation. The table shows that students’ average SAT scores had a stronger (positive) correlation with
median starting salaries and employer ranking than student–faculty ratio and tuition costs. These scores were also
associated with student–faculty ratios, indicating that
schools with lower SAT scores also have more students per
faculty member. There was only moderate correlation
between salaries and employer rankings.
DEA is a nonparametric method for deriving an efficient
frontier from empirical data. This frontier is defined by
those schools with the best performance in converting
inputs to outputs, compared to the other schools in the data
set. For an individual school t, efficiency is computed as
the ratio of the weighted sum of outputs to the weighted
sum of inputs, with xt D (x1t, x2t, x3t) and yt D (y1t, y2t) representing the amounts of inputs and outputs, respectively.
Values of the weights for school t were determined by an
optimization model (Ray, 2004) formulated as:
X2
Maximize Xr3D 1
X2
s:t: Xr3D 1
iD1
vrt yrj
vrt yrt
uit xit
1 for each school j in the sample;
u x
i D 1 it ij
where j D 1; 2; :: ; t. . .; 123
vrt ; uit 0 for r D 1; 2; i D 1; 2; 3
where vrt is the weight of output r for r D 1 (salary), and 2
(employer rank) and uit is the weight of input i for i D 1
(student-faculty ratio), 2 (SAT), 3 (tuition). Employer rankings and SAT scores were inverted to meet the model’s
requirements. The constraints prevent selection of weights
that would give any school (including school t) an efficiency that is greater than 1 or 100%.
For implementation purposes, the fractional programming model was mathematically transformed into an equivalent linear program by requiring the sum of the weighted
inputs for school t (the denominator in the objective
280
S. W. PALOCSAY AND W. C. WOOD
The relative DEA efficiencies of the 123 business schools,
with model input and output data, are reported in the
Appendix. These scores ranged from 0.281 to 1, with a
mean of 0.579 and a standard deviation of 0.208, as shown
in Figure 1. Thirteen percent of schools in the sample had a
score above 0.9. Efficiency scores for schools that appeared
in the top 20 Bloomberg Businessweek rankings ranged
from 0.51 to 1, with a mean score of 0.86.
The detailed results show that seven of the programs
were efficient with DEA scores of 1. The average starting
salary at the efficient schools was $60,571, with an average
employer ranking of 28. Four of the efficient programs
were originally ranked in the top 10 by Bloomberg Businessweek: University of Virginia (#2), Washington University at St. Louis (#4), University of Pennsylvania (#5), and
University of North Carolina at Chapel Hill (#10). However, there was more variation in Businessweek placement
for the remainder: Brigham Young University (#12), Massachusetts Institute of Technology (#19), and University of
Florida (#37). Massachusetts Institute of Technology (MIT)
was one of three schools with the maximum starting salary
of $70,000 (the other two were Pennsylvania and Carnegie
Mellon). And while Brigham Young and Florida only had
average salaries of $51,000 (see Table 1), they were both
very highly ranked by employers.
DEA scores that were less than 1 indicate the presence of
inefficiencies relative to schools in this efficient set. These
schools were ranked from highest to lowest efficiency score
in Appendix A. When compared to Businessweek rankings,
there were considerable differences, as shown in Figure 2.
30%
Relave Percentage
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RESULTS OF EVALUATING EFFICIENCY SCORES
25%
20%
15%
10%
5%
0%
0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9
DEA Efficiency Score
FIGURE 1. DEA efficiency scores.
0.9-1
15%
Relave Percentage
function) to equal 1. By constructing and solving a separate
linear program for each of the 123 schools in the sample, a
set of weights was found to maximize that particular
school’s efficiency without allowing this ratio to exceed 1
for any school, including itself (Ragsdale, 2012).
12%
9%
6%
3%
0%
Rank Deviaon
FIGURE 2. Comparison of DEA efficiency and Businessweek rankings.
Positive deviations on the right side of the graph indicate
schools that had a higher ranking based on DEA efficiency,
whereas negative deviations were associated with schools
that were ranked higher by Businessweek. Approximately
9% of schools improved their rank position by 50 or more
under the relative efficiency criterion. A closer inspection
revealed two business programs that were particularly noteworthy in this regard: Binghamton, which moved up from
57th to eighth with a DEA score of 0.984, and California
Polytechnic State, that went from 64th to 13th with a DEA
score of 0.945. Both were public institutions with fairly
high student–faculty ratios (31.6 and 30, respectively), yet
they were still able to place their graduates with better than
average starting salaries.
Using the DEA model solutions, it is possible to identify a
peer group and peer weights for each inefficient school.
Then a composite institution can be constructed that can produce at least as much output (or more) using the same or less
input. The hypothetical composite school has a bundle of
input and output values which is mathematically computed
as a linear combination of the input–output sets for efficient
schools. For example, a reference school for Binghamton,
which had an efficiency score of 0.984, can be created by
combining the inputs and outputs of the University of Virginia and Brigham Young University with weights of 76.4%
and 21.9%, respectively. The composite values for this
hypothetical institution are $57,000 (salary), 24.2 (employer
rank), 1325.5 (SAT), 11.6 (student–faculty ratio), and
$5,479 (tuition). An inefficient school could use the composite values as a discussion starter on ways of improving.
In Appendix A, all of the efficient programs were
assigned a rank of 1. However, further examination of DEA
model results did show substantial differences in the number of times each appeared in a peer group for an inefficient
school (Sreekumar & Mahapatra, 2011). The most frequently referenced program was Virginia (79 times), followed by North Carolina at Chapel Hill (56 times). Both of
these were public schools with high rankings in the original
Businessweek study. Among efficient private schools, Pennsylvania, Brigham Young, and MIT were peers for 39, 31,
UNDERGRADUATE BUSINESS SCHOOL RANKINGS USING DEA
Number of Schools
25
20
15
Public
10
Private
5
0
0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1
DEA Efficiency Score
Downloaded by [Universitas Maritim Raja Ali Haji] at 20:44 11 January 2016
FIGURE 3. Comparison of efficiency scores for public and private
schools.
and 37 inefficient schools, respectively. In contrast, Florida
and Washington-St. Louis showed up far less often as peers
(12 and 11 times, respectively).
Efficiency scores for public and private institutions,
shown in Figure 3, were also reviewed (Hirao, 2012). The
mean efficiency measure for public schools was 0.641 in
comparison to 0.511 for private schools. Statistical testing
showed a significant difference between the means of these
two groups (p < .001). However, the mix of schools with
efficiencies of 0.9 or higher was relatively even, with nine
being public and seven private.
A frequent concern with DEA benchmarking is that a
high proportion of units may be rated as efficient, even with
a large sample size in relation to the total number of inputs
and outputs (Seiford & Thrall, 1990). In this study, our
empirical analysis identified only 5.7% of the 123 business
programs as points on the efficient frontier, showing reasonable discrimination across schools. Thus this frontier is
a boundary of schools with efficient input-output levels
measured by DEA scores corresponding to estimates of relative efficiency, rather than an estimation of average effects
as found in regression analysis. As a result, there is no single functional form for use in directly determining the
effects of changes in inputs or outputs or hypothesis testing
(Thanassoulis, 1993). And while DEA provided a rating of
inefficient programs, it did not allow for ranking of the efficient ones (Andersen & Petersen, 1993). However, by treating the frontier schools as potential best practice
institutions, DEA methodology objectively identified a peer
group subset for each inefficient school with weights to target productivity improvements.
CONCLUDING REMARKS
Our objective was to examine the ability of undergraduate
business schools to achieve strong performance in generating valued employees for entry-level positions using published data. Applying DEA, we constructed a multioutput
281
model that incorporated a measure of recruiter satisfaction
in addition to starting salaries for evaluation of overall relative efficiency. This model gave consideration to institutional variations in student–faculty ratios, average SAT
scores, and annual tuition costs. Results show that the DEA
model is able to identify differences between schools that
are not readily apparent in the Bloomberg Businessweek
rankings, providing an alternative view for prospective
students.
Given the increasing public scrutiny of educational costs
versus benefits, mathematical techniques for analyzing efficiency and performance such as DEA can provide additional insight into how undergraduate business schools
compare with each other. As a recommendation for future
research, DEA can be applied in a longitudinal study to
observe which schools are consistently efficient over time.
Investigations using DEA models with alternative efficiency measures, returns to scale, and/or weight distribution
restrictions that address limitations of the basic technique
may also be useful (Ray, 2004). For more advanced analyses, researchers should explore hybrid methodologies that
combine DEA with regression-based efficiency assessment
(Park, Lee, Park, & Kim, 2009; Tofallis, 2001) or multistage DEA models with adjustments for external environmental factors (Sav, 2013).
REFERENCES
Andersen, P., & Petersen, N. C. (1993). A procedure for ranking efficiency
units in data envelopment analysis. Management Science, 39, 1261–1264.
Avkiran, N. K. (2001). Investigating technical and scale efficiencies of
Australian universities through data envelopment analysis. Socio-Economic Planning Sciences, 35, 57–80.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational
Research, 2, 429–444.
Colbert, A., Levary, R. R., & Shaner, M. C. (2000). Determining the relative efficiency of MBA programs using DEA. European Journal of
Operational Research, 125, 656–669.
Emrouznejad, A., Parker, B. R., & Tavares, G. (2008). Evaluation of
research in efficiency and productivity: A survey and analysis of the first
30 years of scholarly literature in DEA. Socio-Economic Planning Sciences, 42, 151–157.
Gloeckler, G. (2013, March 20). Notre Dame’s Mendoza takes no. 1 ranking, again. Bloomberg Businessweek. Retrieved from http://www.
businessweek.com/articles/2013-03-20/notre-dames-mendoza-takes-nodot-1-ranking-again
Gross, J. (2013). How bad is it? The student loan default crisis in perspective. Coalition of State University Aid Administrators. Retrieved from
http://www.cosuaa.org/conference/2013_Resources/Presentations/How%
20Bad%20Is%20It-Loan%20Default-COSUAA%202013.pdf
Hirao, Y. (2012). Efficiency of the top 50 business schools in the United
States. Applied Economics Letters, 19, 73–78.
Immerwahr, J., & Johnson, J. (2009). Squeeze play 2009: The public’s
views on college costs today. San Jose, CA: National Center for Public
Policy and Higher Education.
Kong, W., & Fu, T. (2012). Assessing the performance of business colleges
in Taiwan using data envelopment analysis and student based valueadded performance indicators. Omega, 40, 541–549.
Downloaded by [Universitas Maritim Raja Ali Haji] at 20:44 11 January 2016
282
S. W. PALOCSAY AND W. C. WOOD
Kreutzer, D., & Wood, W. (2007). Value-added adjustment in undergraduate business school ranking. Journal of Education for Business, 82,
357–362.
Lavelle, L. (2006, May 8). The best undergraduate B-schools. Business
Week, 76–93.
Lavelle, L. (2013, March 20). FAQ: How we ranked the schools. Bloomberg Businessweek. Retrieved from http://www.businessweek.com/
articles/2013–03-20/faq-how-we-ranked-the-schools#rDlr-sr
Liu, C. A., & Liu, W. (2010). Performance evaluation on private higher
education using data envelopment analysis. Proceedings of the IIE
Annual Conference, 1–6.
Massachusetts Department of Higher Education. (2013). Resident mandatory
fee rates. Retrieved from http://www.mass.edu/campuses/res_fees.asp
National Center for Education Statistics. (2013). Digest of education statistics 2012, table 381. Retrieved from http://nces.ed.gov/programs/digest/
d12/tables/dt12_381.asp
Park, K. S., Lee, K. W., Park, M. S., & Kim, D. (2009). Joint use of DEA
and constrained correlation analysis for efficiency valuations involving
categorical variables. The Journal of the Operational Research Society,
60, 1775–1785.
Ragsdale, C. (2012). Spreadsheet modeling & decision analysis (6th ed.).
Mason, OH: South-Western Cengage Learning.
Ray, S. C. (2004). Data envelopment analysis: Theory and techniques
for economics and operations research. New York, NY: Cambridge
University Press.
APPENDIX
Sav, G. T. (2012). Productivity, efficiency, and managerial performance regress and gains in United States universities: A data envelopment analysis. Advances in Management & Applied Economics, 2
(3), 13–32.
Sav, G. T. (2013). Four-stage DEA efficiency evaluations: Financial
reforms in public university funding. International Journal of Economics and Finance, 5, 24–33.
Seiford, L. M., & Thrall, R. M. (1990). Recent developments in DEA: The
mathematical approach to frontier analysis. Journal of Econometrics, 46
(1–2), 7–38.
Sexton, T. R., & Comunale, C. L. (2010). An efficiency analysis of U.S.
business schools. Journal of Case Studies in Accreditation and
Assessment, 1. Retrieved from http://www.aabri.com/manuscripts/
09256.pdf
Sreekumar, S., & Mahapatra, S. S. (2011). Performance modeling of Indian
business schools: A DEA-neural network approach. Benchmarking: An
International Journal, 18, 221–239.
Thanassoulis, E. (1993). A comparison of regression analysis and data
envelopment analysis as alternative methods for performance assessments. The Journal of the Operational Research Society, 44,
1129–1144.
Tofallis, C. (2001). Combining two approaches to efficiency assessment. The Journal of the Operational Research Society, 52, 1225–
1231.
DATA AND SCHOOL RANKINGS BY DEA EFFICIENCY
Efficiency
rank
College/university
1
1
1
1
1
1
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Virginia (McIntire)
Washington U.-St. Louis (Olin)
Pennsylvania (Wharton)
North Carolina-Chapel Hill (Kenan Flagler)
Brigham Young (Marriott)
MIT (Sloan)
Florida (Warrington)
Binghamton
Michigan-Ann Arbor (Ross)
Texas-Austin (McCombs)
UC-Berkeley (Haas)
Indiana (Kelley)
California Polytechnic State (Orfalea)
Notre Dame (Mendoza)
Emory (Goizueta)
Cornell (Dyson)
NYU (Stern)
Ohio State (Fisher)
Illinois-Urbana-Champaign
William & Mary (Mason)
Carnegie Mellon (Tepper)
USC (Marshall)
Texas A & M (Mays)
Louisiana State (Ourso)
Boston College (Carroll)
Florida International (Landon)
North Carolina State (Poole)
Student–faculty
SAT
score
Tuition ($)
Starting
salary ($)
Employer
rank
BW
rank
Efficiency
score
9.9
10
9.7
10.9
15
0.9
18.9
31.6
12.5
24
17.3
20.4
30
15
9.7
15.8
12.2
19
17.6
12.1
11
24.4
25
28
22.5
35
32
1390
1492
1461
1350
1219
1457
1286
1321
1377
1362
1396
1299
1234
1414
1377
1416
1444
1305
1345
1343
1415
1384
1230
1152
1355
1052
1185
9,622
44,100
39,088
5,823
4,710
41,770
6,170
5,570
13,040
10,738
14,985
8,750
5,472
42,464
42,400
27,045
41,358
9,168
16,556
8,677
44,880
43,722
9,330
5,193
43,140
5,217
5,748
60,000
62,000
70,000
60,000
51,000
70,000
51,000
57,000
65,000
55,000
60,000
55,000
55,000
57,000
60,000
58,922
63,250
50,000
55,000
55,000
70,000
54,000
52,000
43,000
60,000
41,748
44,472
15
34
26
28
3
80
8
36
14
4
17
1
74
5
16
21
25
13
6
98
69
11
7
91
9
95
57
2
4
5
10
12
19
37
57
8
9
11
13
64
1
7
3
14
34
21
27
24
31
33
118
6
113
95
1
1
1
1
1
1
1
0.9837
0.9800
0.9782
0.9659
0.9647
0.9451
0.9428
0.9240
0.9224
0.8945
0.8655
0.8632
0.8192
0.8131
0.7978
0.7879
0.7647
0.7417
0.7390
0.7225
(Continued on next page)
Downloaded by [Universitas Maritim Raja Ali Haji] at 20:44 11 January 2016
UNDERGRADUATE BUSINESS SCHOOL RANKINGS USING DEA
Efficiency
rank
College/university
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
Northeastern (D’Amore-McKim)
West Virginia
Arizona (Eller)
Houston (Bauer)
Georgetown (McDonough)
Rutgers-New Brunswick
Arkansas-Fayetteville (Walton)
Wisconsin-Madison
Georgia Tech (Scheller)
Buffalo
Connecticut
Georgia (Terry)
Purdue (Krannert)
James Madison
South Florida
Virginia Tech (Pamplin)
Penn State-University Park (Smeal)
Texas-Dallas (Jindal)
Minnesota (Carlson)
U. of Washington (Foster)
Case Western (Weatherhead)
Alabama-Tuscaloosa (Culverhouse)
Boston U.
Colorado State
Kansas State
Oklahoma (Price)
Delaware (Lerner)
New Jersey
Villanova
Miami U. (Farmer)
Wake Forest
Michigan State (Broad)
Bentley
Tulane (Freeman)
Tennessee-Chattanooga
Iowa (Tippie)
Kansas-Lawrence
Arizona State (Carey)
Richmond (Robins)
South Carolina (Moore)
Missouri-Columbia (Trulaske)
Bowling Green State
Lehigh
Pittsburgh (Katz)
Utah (Eccles)
Oregon (Lundquist)
Southern Methodist (Cox)
Rutgers-Newark
Ohio
Worcester Polytechnic Institute
Clemson
Cincinnati (Lindner)
Santa Clara (Leavey)
Akron
Fordham (Gabelli)
Northern Illinois
U. of Miami
283
Student–faculty
SAT
score
Tuition ($)
Starting
salary ($)
Employer
rank
BW
rank
Efficiency
score
21.1
22
14
18
22
29
62
23
15
20
15
17.6
33.4
26.8
49
27
31
12
27
17.7
8.5
21
16
24
41.3
30
19.5
21
14.8
18.6
13.3
26.2
19
15.5
39.4
36
27
27
13.4
19
20.1
17.7
16.4
32
27.7
15
24
44
29
31
28.7
18.9
16
23
18.1
44.7
16.7
1367
1059
1135
1158
1372
1290
1111
1270
1291
1125
1226
1255
1179
1156
1226
1180
1226
1267
1305
1290
1267
1150
1296
1163
1105
1170
1218
1231
1322
1240
1333
1127
1207
1327
1065
1140
1155
1182
1301
1217
1185
1068
1279
1262
1120
1143
1283
1060
1100
1190
1220
1142
1275
1103
1230
1040
1284
39,320
5,794
9,114
6,796
42,360
10,688
6,141
10,273
7,718
5,570
8,712
7,646
9,900
8,808
6,330
9,187
17,824
10,566
12,560
12,383
40,120
9,200
42,400
6,874
6,829
8,700
10,150
10,102
42,150
13,067
42,700
13,800
38,130
41,500
5,722
7,678
8,790
9,208
44,210
10,088
9,272
10,393
41,920
17,568
8,921
9,310
37,050
10,356
10,216
40,790
11,870
9,124
40,572
9,553
41,000
9,488
39,980
55,000
45,000
50,000
50,771
63,000
55,000
46,000
52,000
50,000
40,000
55,000
47,750
52,000
58,000
42,000
50,000
56,000
45,000
51,000
52,000
47,500
58,000
52,000
43,390
43,000
53,000
55,000
53,400
55,000
55,000
57,000
52,000
50,000
55,000
32,500
42,000
47,250
49,000
56,764
47,499
47,500
49,000
57,000
48,000
45,000
40,000
52,000
50,000
49,000
63,000
44,195
43,000
52,500
45,000
57,500
45,000
50,000
19
111
30
75
22
27
81
29
48
62
44
39
18
45
124
24
2
110
38
49
51
82
20
87
53
33
65
92
31
32
40
12
10
78
118
42
59
46
106
63
77
99
55
41
121
79
70
105
89
86
58
66
90
72
68
43
113
25
111
50
103
16
81
105
32
41
112
54
44
58
29
121
52
26
75
39
48
69
73
23
89
114
88
76
59
15
22
18
43
20
49
120
100
110
77
17
87
78
90
35
82
117
107
30
119
86
51
94
84
38
108
40
106
70
0.7199
0.7173
0.7066
0.7042
0.6983
0.6932
0.6929
0.6656
0.6647
0.6632
0.6573
0.6500
0.6452
0.6327
0.6303
0.6265
0.6259
0.6198
0.6193
0.6127
0.6080
0.6070
0.5990
0.5961
0.5878
0.5861
0.5837
0.5829
0.5802
0.5735
0.5656
0.5587
0.5405
0.5249
0.5245
0.5198
0.5164
0.5147
0.5054
0.5038
0.4960
0.4954
0.4897
0.4873
0.4825
0.4727
0.4667
0.4629
0.4618
0.4581
0.4541
0.4539
0.4528
0.4517
0.4515
0.4506
0.4400
(Continued on next page)
284
S. W. PALOCSAY AND W. C. WOOD
Downloaded by [Universitas Maritim Raja Ali Haji] at 20:44 11 January 2016
Efficiency
rank
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
College/university
Toledo
Colorado-Boulder (Leeds)
Tulsa (Collins)
John Carroll (Boler)
Illinois State
Bradley (Foster)
Elon (Love)
Babson
Denver (Daniels)
Baylor (Hankamer)
DePaul (Driehaus)
George Washington
Vermont
Texas Christian (Neeley)
Seton Hall (Stillman)
American (Kogod)
San Diego
Kentucky (Gatton)
Syracuse (Whitman)
Marquette
Duquesne (Palumbo)
Fairfield (Dolan)
Bryant
Ohio Northern University (Dicke)
Seattle (Albers)
Butler
Loyola-Chicago (Quinlan)
St. Louis (Cook)
Loyola-Maryland (Sellinger)
Quinnipiac
Loyola Marymount
California-Riverside
Hofstra (Zarb)
Providence College
Rochester Institute of Technology
(Saunders)
St. Joseph’s (Haub)
St. Thomas (Opus)
Xavier (Williams)
Belmont
Student–faculty
SAT
score
Tuition ($)
Starting
salary ($)
Employer
rank
BW
rank
Efficiency
score
35
33.3
19
10
32
13.5
26
21
18
24.4
18
20
29.4
24
19
18.9
15.7
28.1
25
24.3
19.5
25
25.8
15
18
18.3
20
21
18
22.5
22
65
22
25
18
1020
1169
1207
1083
1105
1224
1218
1267
1300
1211
1129
1270
1130
1196
1175
1220
1216
1090
1182
1184
1112
1150
1125
1105
1149
1143
1165
1185
1180
1089
1192
1070
1147
1152
1131
9,774
12,646
32,410
32,130
10,050
27,920
28,633
41,888
38,232
30,586
31,650
45,735
13,344
36,500
32,700
37,554
39,486
9,676
37,610
32,810
27,668
41,090
35,591
35,678
34,200
32,280
33,810
34,740
41,026
38,000
38,012
12,192
34,900
41,350
32,784
45,000
46,700
53,500
41,500
43,500
45,000
47,000
50,000
45,000
51,000
55,000
50,000
47,321
53,000
52,500
50,000
50,000
38,250
51,500
48,000
48,000
52,522
52,000
44,000
47,500
47,000
47,500
46,000
47,000
53,000
44,000
41,000
45,500
47,000
41,917
123
54
67
115
47
120
37
60
56
97
52
88
108
84
94
114
102
96
50
71
76
107
35
101
100
104
83
109
103
61
117
112
116
93
73
116
101
55
79
99
98
42
36
68
66
60
71
123
28
85
56
46
122
72
74
96
83
63
62
67
47
104
91
53
61
65
124
115
109
93
0.4372
0.4295
0.4271
0.4268
0.4256
0.4208
0.4193
0.4174
0.4152
0.4148
0.4121
0.4078
0.4022
0.4013
0.3953
0.3941
0.3897
0.3787
0.3773
0.3648
0.3581
0.3560
0.3501
0.3488
0.3486
0.3484
0.3481
0.3456
0.3389
0.3346
0.3273
0.3261
0.3199
0.3191
0.3104
23.5
19
25
18.9
1115
1180
1107
1147
37,670
33,040
32,140
24,900
47,300
39,644
44,000
35,500
64
122
85
119
92
80
102
97
0.3101
0.3004
0.2939
0.2811
ISSN: 0883-2323 (Print) 1940-3356 (Online) Journal homepage: http://www.tandfonline.com/loi/vjeb20
An Investigation of U.S. Undergraduate Business
School Rankings Using Data Envelopment Analysis
With Value-Added Performance Indicators
Susan W. Palocsay & William C. Wood
To cite this article: Susan W. Palocsay & William C. Wood (2014) An Investigation of U.S.
Undergraduate Business School Rankings Using Data Envelopment Analysis With ValueAdded Performance Indicators, Journal of Education for Business, 89:6, 277-284, DOI:
10.1080/08832323.2013.876379
To link to this article: http://dx.doi.org/10.1080/08832323.2013.876379
Published online: 03 Sep 2014.
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Download by: [Universitas Maritim Raja Ali Haji]
Date: 11 January 2016, At: 20:44
JOURNAL OF EDUCATION FOR BUSINESS, 89: 277–284, 2014
Copyright Ó Taylor & Francis Group, LLC
ISSN: 0883-2323 print / 1940-3356 online
DOI: 10.1080/08832323.2013.876379
An Investigation of U.S. Undergraduate Business
School Rankings Using Data Envelopment Analysis
With Value-Added Performance Indicators
Susan W. Palocsay and William C. Wood
Downloaded by [Universitas Maritim Raja Ali Haji] at 20:44 11 January 2016
James Madison University, Harrisonburg, Virginia, USA
Bloomberg Businessweek ranks U.S. undergraduate business programs annually. These
rankings provide a convenient overall measure of quality, which is important in today’s
environment of concern about higher education costs and employment after graduation. Data
envelopment analysis (DEA) has advantages over previous regression approaches in
characterizing value added. The authors use a DEA approach to estimate relative efficiencies
based on starting salaries and recruiter surveys, identifying some schools as overachievers
relative to their Bloomberg Businessweek rankings. In particular, DEA-based reranking
highlights the ability of some public institutions facing high student–faculty ratios to turn out
well-regarded graduates with high starting salaries.
Keywords: data envelopment analysis, DEA, efficiency, performance, rankings, undergraduate
business schools
Business Week first began ranking undergraduate schools
and colleges of business in 2006 (Lavelle, 2006). Since that
time, the magazine’s successor Bloomberg Businessweek
has refined its methodology, expanded the number of
schools ranked, and provided additional detail on ranking
procedures (Gloeckler, 2013). These rankings, however, do
not account for the efficiency of resource use, so that lower
cost schools achieving the same results as higher cost competitors see no boost in their rankings. Since 2006, college
tuition and fees have increased more than 30% (38.7% for
public institutions and 32.1% for private ones) even as the
national economy has endured its most striking downturn
since the Great Depression (National Center for Education
Statistics, 2013). Meanwhile, student loan debt has
expanded sharply, growing 58% between 2004 and 2012
(Gross, 2013).
Amid public concern about costs and quality, inefficiency in the use of funds by higher education could, over
time, fundamentally erode the support for colleges and
Correspondence should be addressed to Susan W. Palocsay, James
Madison University, Department of Computer Information Systems and
Business Analytics, MSC 0202, 800 S. Main Street, Harrisonburg, VA
22807, USA. E-mail: [email protected]
Color versions of one or more of the figures in the article can be
found online at www.tandfonline.com/vjeb.
universities. A national survey revealed “a chipping away
of public support for higher education and a growing suspicion about how well colleges and universities use the
money they have” (Immerwahr & Johnson, 2009, p. 5). The
survey authors suggested that colleges and universities
address public concerns over high costs proactively, since
governments would likely act with greater regulation and
supervision if the growth of costs remained unchecked. The
combined concerns of students, parents, and government
provide good reasons to investigate the efficiency of higher
education, including undergraduate business education. In
this environment it is important to note that efficiencyadjusted rankings can differ significantly from Bloomberg
Businessweek’s reported rankings (Kreutzer & Wood,
2007).
In this study, we used data envelopment analysis (DEA)
to examine the relative efficiency of U.S. undergraduate
business schools included in the most recent Bloomberg
Businessweek study (Gloeckler, 2013) from an economic,
value-added perspective. DEA was first proposed by
Charnes, Cooper, and Rhodes (1978) to empirically measure how effectively organizational units convert multiple
inputs into multiple outputs in comparison with each other.
DEA calculates a weighted output-over-input ratio for each
unit, which is defined as a relative efficiency score, with 1
indicating efficient status. A piece-wise linear surface is
Downloaded by [Universitas Maritim Raja Ali Haji] at 20:44 11 January 2016
278
S. W. PALOCSAY AND W. C. WOOD
constructed through the efficient units to estimate a frontier,
and efficiency computations are made relative to this frontier (Seiford & Thrall, 1990). Thus, units that lie below the
frontier are assigned scores of less than 1, indicating that
there is a linear combination of efficient units that could
produce as much output using smaller input amounts.
Since its introduction more than 30 years ago, DEA has
gained widespread acceptance as a standard tool for evaluation of economic productivity with successful applications
in numerous nonprofit and for-profit domains (Emrouznejad, Parker, & Tavares, 2008). A brief overview of the
DEA approach in education for business is provided in the
next section. Then we describe the data and DEA model for
estimating relative efficiencies and use these scores to generate a full reranking for comparative purposes. Results are
described in the following section, and we conclude with
suggestions for future research.
DEA APPLICATION TO BUSINESS SCHOOLS
In a 2008 literature review of DEA research, Emrouznejad
et al. identified education as one of the most prevalent areas
of DEA application, finding 44 publications using it as a
keyword. Generally, studies in the higher education sector
have applied DEA at either the academic department level
within one institution or for universities in a particular
country (Sav, 2012). The majority of the latter group focus
on managerial performance in responding to financial
reforms in public university funding (Sav, 2013) and challenges to revenue generation for private institutions (Liu &
Liu, 2010). Commonly used productivity measures were
enrollments, graduation and/or retention rates, and credit
hour production (e.g. Avkiran, 2001; Sexton & Communale, 2010).
Other authors have used different measures of DEA efficiency for U.S. master of business administration (MBA)
programs (Colbert, Levary, & Shaner, 2000; Hirao, 2012)
and for business schools outside the United States in Taiwan (Kong & Fu, 2012) and India (Sreekumar & Mahapatra, 2011). In these studies, the focus was primarily on
postgraduation approval and employment-related outcomes
instead of more traditional administrative standards. As a
group, they demonstrate various DEA modeling approaches
to facilitate comparisons of business schools based on
potential economic benefits being offered.
In Colbert et al. (2000), multiple efficiency scores were
calculated for each of the 24 best Business Week–ranked
MBA programs based on their achievement of either student satisfaction and/or recruiter satisfaction. Input resources were represented by faculty-to-student ratios, average
GMAT scores, and number of elective offerings. In their
experimental trials, the number of efficient programs varied
from 8 to 16 with all of the efficiency scores exceeding 0.9.
In the trial using average salary and average recruiter score
as outputs, the minimum efficiency was 0.9420 and the
DEA model generated an efficiency score of one for 13 of
the 24 schools. This lack of differentiation was attributed to
the similarity of programs in the sample, all prominent topranked MBA programs.
More recently, Hirao (2012) estimated efficiency of U.S.
graduate business schools in terms of translating peer
assessment and average GMAT scores into average starting
salaries and employment rates. The reference data came
from U.S. News & World Report rankings of the top 50
business schools in 2006, of which 27 were private and 23
were public. Peer assessment score (from appraisals by
other department heads) had a stronger positive correlation
with both starting salaries and employment rates than average GMAT scores (0.908 vs. 0.735 for salaries and
0.514 vs. 0.383 for employment). Five of the 50 schools
achieved (relative) efficiency and scores ranged from 0.8087
to 1, with a mean of 0.9356. On average, public institutions
had lower overall efficiencies (0.9155) than private ones
(0.9527). School names were not identified in this study and
no comparative analysis of rankings by DEA was provided.
Kong and Fu (2012) ranked a small group of 21 Taiwanese business colleges using survey data from recent
graduates to construct indicators for job market performance and student satisfaction. With restrictions from
recruiters imposed on indicator weights, only 3 of the colleges had a DEA efficiency score of 1 but all scores were
higher than 0.9. They did, however, find average performance of public schools (0.991) exceeded that of private
ones (0.981).
For the evaluation of 49 business schools in India, Sreekumar and Mahapatra (2011) chose three inputs: faculty/
student ratio, infrastructure, and tuition fees. They developed a broad group of eight outputs that encompassed starting salary and the satisfaction of faculty, students and
recruiters as well as other measures such as international
exchange programs and student awards. DEA showed its
ability to discriminate within this sample by evaluating
only 4 schools as relatively efficient. The minimum score
was 0.356 and mean efficiency was 0.625 with a standard
deviation of 0.175. Further analysis of DEA results was
done to identify peer groups for benchmarking of inefficient
schools to improve performance, although individual
school names were not revealed.
In this study, we extended the application of DEA into
U.S. undergraduate business education with a value-added
purpose. We generally followed the approach in Colbert
et al. (2000) as described previously, augmented by guidance from Kreutzer and Wood (2007) to consider the
impact of tuition costs. Our study benefits from having a
larger sample containing more diverse schools when determining the effect of ranking via DEA scores. We also compared efficiencies of public and private business schools
and investigate the composition of peer groups for additional insights aimed at performance management.
UNDERGRADUATE BUSINESS SCHOOL RANKINGS USING DEA
Downloaded by [Universitas Maritim Raja Ali Haji] at 20:44 11 January 2016
DATA AND MEASUREMENT OF EFFICIENCY
SCORES
In the present analysis, data were taken from the Bloomberg
Businessweek 2013 rankings of 124 undergraduate business
schools. The ranking method includes nine variables, all
related in some way to student satisfaction, post-graduation
outcomes or academic quality (Lavelle, 2013). Student satisfaction is measured through a survey sent to graduating
seniors at the ranked schools. Post-graduation outcomes
include employer opinion (from a survey), school-reported
median starting salaries, and admissions to top MBA programs. Academic quality was measured through average
SAT scores, student–faculty ratios, average class size, the
percentage of business majors with internships, and weekly
student hours reported to be spent on schoolwork. In the
final summation, student assessment accounts for 30% of
the ranking, recruiter survey scores account for 20%, starting salaries and MBA admissions contribute 10% each, and
the academic quality items together account for the remaining 30%.
Selection of inputs and outputs for DEA should be
guided by the environment being examined and by organizational objectives (Avkiran, 2001). For our analysis, we
sought a parsimonious set of variables to compare business
programs on the basis of their performance in producing
highly marketable graduates, conditional on resource availability and incoming-student quality. With this perspective
in mind, we chose student/faculty ratio to characterize
school quality and average SAT scores to account for student ability. Annual tuition was included as a third input
measure, consistent with the approach in Kreutzer and
Wood (2007). As DEA permits more than one output, we
were able to incorporate the employer rankings (based on
recruiter opinions) with median starting salaries to reflect
the overall value of graduates from each program.
A statistical summary is given in Table 1. Note that one
institution, Massachusetts-Amherst, was removed from the
data set due to concern about its artificially low reported
tuition. That reported tuition was $1,714, but mandatory
fees were $11,518 (Massachusetts Department of Higher
Education, 2013), making the institution an outlier with no
easy means of correction. The resulting final sample size
was 123. The distribution of private versus public schools
was similar, with 59 private and 64 public institutions.
TABLE 1
Summary Statistics
Measure
M
Median
SD
Minimum
Maximum
Student–faculty ratio
SAT
Tuition ($)
Salary ($)
22.460
20.4
9.537
0.9
65.0
1219.423
1207
103.725
1020
1492
22,712.46
14,985.00
14,666.72
4,710.00
45,735.00
50,626.55
50,000.00
6,823.04
32,500.00
70,000.00
279
TABLE 2
Correlation Coefficients
Student–faculty
ratio
SAT
Item
Student–faculty ratio
SAT
Tuition
Salary
Employer rank
¡.526**
¡.410**
¡.423**
¡.154*
Tuition Salary
Employer
rank
.341**
.738** .321**
.522** ¡.087 .505**
*p D .10. **p D .01.
The correlation coefficients for input and output variables are listed in Table 2, with employer rank inverted for
ease of interpretation. The table shows that students’ average SAT scores had a stronger (positive) correlation with
median starting salaries and employer ranking than student–faculty ratio and tuition costs. These scores were also
associated with student–faculty ratios, indicating that
schools with lower SAT scores also have more students per
faculty member. There was only moderate correlation
between salaries and employer rankings.
DEA is a nonparametric method for deriving an efficient
frontier from empirical data. This frontier is defined by
those schools with the best performance in converting
inputs to outputs, compared to the other schools in the data
set. For an individual school t, efficiency is computed as
the ratio of the weighted sum of outputs to the weighted
sum of inputs, with xt D (x1t, x2t, x3t) and yt D (y1t, y2t) representing the amounts of inputs and outputs, respectively.
Values of the weights for school t were determined by an
optimization model (Ray, 2004) formulated as:
X2
Maximize Xr3D 1
X2
s:t: Xr3D 1
iD1
vrt yrj
vrt yrt
uit xit
1 for each school j in the sample;
u x
i D 1 it ij
where j D 1; 2; :: ; t. . .; 123
vrt ; uit 0 for r D 1; 2; i D 1; 2; 3
where vrt is the weight of output r for r D 1 (salary), and 2
(employer rank) and uit is the weight of input i for i D 1
(student-faculty ratio), 2 (SAT), 3 (tuition). Employer rankings and SAT scores were inverted to meet the model’s
requirements. The constraints prevent selection of weights
that would give any school (including school t) an efficiency that is greater than 1 or 100%.
For implementation purposes, the fractional programming model was mathematically transformed into an equivalent linear program by requiring the sum of the weighted
inputs for school t (the denominator in the objective
280
S. W. PALOCSAY AND W. C. WOOD
The relative DEA efficiencies of the 123 business schools,
with model input and output data, are reported in the
Appendix. These scores ranged from 0.281 to 1, with a
mean of 0.579 and a standard deviation of 0.208, as shown
in Figure 1. Thirteen percent of schools in the sample had a
score above 0.9. Efficiency scores for schools that appeared
in the top 20 Bloomberg Businessweek rankings ranged
from 0.51 to 1, with a mean score of 0.86.
The detailed results show that seven of the programs
were efficient with DEA scores of 1. The average starting
salary at the efficient schools was $60,571, with an average
employer ranking of 28. Four of the efficient programs
were originally ranked in the top 10 by Bloomberg Businessweek: University of Virginia (#2), Washington University at St. Louis (#4), University of Pennsylvania (#5), and
University of North Carolina at Chapel Hill (#10). However, there was more variation in Businessweek placement
for the remainder: Brigham Young University (#12), Massachusetts Institute of Technology (#19), and University of
Florida (#37). Massachusetts Institute of Technology (MIT)
was one of three schools with the maximum starting salary
of $70,000 (the other two were Pennsylvania and Carnegie
Mellon). And while Brigham Young and Florida only had
average salaries of $51,000 (see Table 1), they were both
very highly ranked by employers.
DEA scores that were less than 1 indicate the presence of
inefficiencies relative to schools in this efficient set. These
schools were ranked from highest to lowest efficiency score
in Appendix A. When compared to Businessweek rankings,
there were considerable differences, as shown in Figure 2.
30%
Relave Percentage
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RESULTS OF EVALUATING EFFICIENCY SCORES
25%
20%
15%
10%
5%
0%
0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9
DEA Efficiency Score
FIGURE 1. DEA efficiency scores.
0.9-1
15%
Relave Percentage
function) to equal 1. By constructing and solving a separate
linear program for each of the 123 schools in the sample, a
set of weights was found to maximize that particular
school’s efficiency without allowing this ratio to exceed 1
for any school, including itself (Ragsdale, 2012).
12%
9%
6%
3%
0%
Rank Deviaon
FIGURE 2. Comparison of DEA efficiency and Businessweek rankings.
Positive deviations on the right side of the graph indicate
schools that had a higher ranking based on DEA efficiency,
whereas negative deviations were associated with schools
that were ranked higher by Businessweek. Approximately
9% of schools improved their rank position by 50 or more
under the relative efficiency criterion. A closer inspection
revealed two business programs that were particularly noteworthy in this regard: Binghamton, which moved up from
57th to eighth with a DEA score of 0.984, and California
Polytechnic State, that went from 64th to 13th with a DEA
score of 0.945. Both were public institutions with fairly
high student–faculty ratios (31.6 and 30, respectively), yet
they were still able to place their graduates with better than
average starting salaries.
Using the DEA model solutions, it is possible to identify a
peer group and peer weights for each inefficient school.
Then a composite institution can be constructed that can produce at least as much output (or more) using the same or less
input. The hypothetical composite school has a bundle of
input and output values which is mathematically computed
as a linear combination of the input–output sets for efficient
schools. For example, a reference school for Binghamton,
which had an efficiency score of 0.984, can be created by
combining the inputs and outputs of the University of Virginia and Brigham Young University with weights of 76.4%
and 21.9%, respectively. The composite values for this
hypothetical institution are $57,000 (salary), 24.2 (employer
rank), 1325.5 (SAT), 11.6 (student–faculty ratio), and
$5,479 (tuition). An inefficient school could use the composite values as a discussion starter on ways of improving.
In Appendix A, all of the efficient programs were
assigned a rank of 1. However, further examination of DEA
model results did show substantial differences in the number of times each appeared in a peer group for an inefficient
school (Sreekumar & Mahapatra, 2011). The most frequently referenced program was Virginia (79 times), followed by North Carolina at Chapel Hill (56 times). Both of
these were public schools with high rankings in the original
Businessweek study. Among efficient private schools, Pennsylvania, Brigham Young, and MIT were peers for 39, 31,
UNDERGRADUATE BUSINESS SCHOOL RANKINGS USING DEA
Number of Schools
25
20
15
Public
10
Private
5
0
0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1
DEA Efficiency Score
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FIGURE 3. Comparison of efficiency scores for public and private
schools.
and 37 inefficient schools, respectively. In contrast, Florida
and Washington-St. Louis showed up far less often as peers
(12 and 11 times, respectively).
Efficiency scores for public and private institutions,
shown in Figure 3, were also reviewed (Hirao, 2012). The
mean efficiency measure for public schools was 0.641 in
comparison to 0.511 for private schools. Statistical testing
showed a significant difference between the means of these
two groups (p < .001). However, the mix of schools with
efficiencies of 0.9 or higher was relatively even, with nine
being public and seven private.
A frequent concern with DEA benchmarking is that a
high proportion of units may be rated as efficient, even with
a large sample size in relation to the total number of inputs
and outputs (Seiford & Thrall, 1990). In this study, our
empirical analysis identified only 5.7% of the 123 business
programs as points on the efficient frontier, showing reasonable discrimination across schools. Thus this frontier is
a boundary of schools with efficient input-output levels
measured by DEA scores corresponding to estimates of relative efficiency, rather than an estimation of average effects
as found in regression analysis. As a result, there is no single functional form for use in directly determining the
effects of changes in inputs or outputs or hypothesis testing
(Thanassoulis, 1993). And while DEA provided a rating of
inefficient programs, it did not allow for ranking of the efficient ones (Andersen & Petersen, 1993). However, by treating the frontier schools as potential best practice
institutions, DEA methodology objectively identified a peer
group subset for each inefficient school with weights to target productivity improvements.
CONCLUDING REMARKS
Our objective was to examine the ability of undergraduate
business schools to achieve strong performance in generating valued employees for entry-level positions using published data. Applying DEA, we constructed a multioutput
281
model that incorporated a measure of recruiter satisfaction
in addition to starting salaries for evaluation of overall relative efficiency. This model gave consideration to institutional variations in student–faculty ratios, average SAT
scores, and annual tuition costs. Results show that the DEA
model is able to identify differences between schools that
are not readily apparent in the Bloomberg Businessweek
rankings, providing an alternative view for prospective
students.
Given the increasing public scrutiny of educational costs
versus benefits, mathematical techniques for analyzing efficiency and performance such as DEA can provide additional insight into how undergraduate business schools
compare with each other. As a recommendation for future
research, DEA can be applied in a longitudinal study to
observe which schools are consistently efficient over time.
Investigations using DEA models with alternative efficiency measures, returns to scale, and/or weight distribution
restrictions that address limitations of the basic technique
may also be useful (Ray, 2004). For more advanced analyses, researchers should explore hybrid methodologies that
combine DEA with regression-based efficiency assessment
(Park, Lee, Park, & Kim, 2009; Tofallis, 2001) or multistage DEA models with adjustments for external environmental factors (Sav, 2013).
REFERENCES
Andersen, P., & Petersen, N. C. (1993). A procedure for ranking efficiency
units in data envelopment analysis. Management Science, 39, 1261–1264.
Avkiran, N. K. (2001). Investigating technical and scale efficiencies of
Australian universities through data envelopment analysis. Socio-Economic Planning Sciences, 35, 57–80.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational
Research, 2, 429–444.
Colbert, A., Levary, R. R., & Shaner, M. C. (2000). Determining the relative efficiency of MBA programs using DEA. European Journal of
Operational Research, 125, 656–669.
Emrouznejad, A., Parker, B. R., & Tavares, G. (2008). Evaluation of
research in efficiency and productivity: A survey and analysis of the first
30 years of scholarly literature in DEA. Socio-Economic Planning Sciences, 42, 151–157.
Gloeckler, G. (2013, March 20). Notre Dame’s Mendoza takes no. 1 ranking, again. Bloomberg Businessweek. Retrieved from http://www.
businessweek.com/articles/2013-03-20/notre-dames-mendoza-takes-nodot-1-ranking-again
Gross, J. (2013). How bad is it? The student loan default crisis in perspective. Coalition of State University Aid Administrators. Retrieved from
http://www.cosuaa.org/conference/2013_Resources/Presentations/How%
20Bad%20Is%20It-Loan%20Default-COSUAA%202013.pdf
Hirao, Y. (2012). Efficiency of the top 50 business schools in the United
States. Applied Economics Letters, 19, 73–78.
Immerwahr, J., & Johnson, J. (2009). Squeeze play 2009: The public’s
views on college costs today. San Jose, CA: National Center for Public
Policy and Higher Education.
Kong, W., & Fu, T. (2012). Assessing the performance of business colleges
in Taiwan using data envelopment analysis and student based valueadded performance indicators. Omega, 40, 541–549.
Downloaded by [Universitas Maritim Raja Ali Haji] at 20:44 11 January 2016
282
S. W. PALOCSAY AND W. C. WOOD
Kreutzer, D., & Wood, W. (2007). Value-added adjustment in undergraduate business school ranking. Journal of Education for Business, 82,
357–362.
Lavelle, L. (2006, May 8). The best undergraduate B-schools. Business
Week, 76–93.
Lavelle, L. (2013, March 20). FAQ: How we ranked the schools. Bloomberg Businessweek. Retrieved from http://www.businessweek.com/
articles/2013–03-20/faq-how-we-ranked-the-schools#rDlr-sr
Liu, C. A., & Liu, W. (2010). Performance evaluation on private higher
education using data envelopment analysis. Proceedings of the IIE
Annual Conference, 1–6.
Massachusetts Department of Higher Education. (2013). Resident mandatory
fee rates. Retrieved from http://www.mass.edu/campuses/res_fees.asp
National Center for Education Statistics. (2013). Digest of education statistics 2012, table 381. Retrieved from http://nces.ed.gov/programs/digest/
d12/tables/dt12_381.asp
Park, K. S., Lee, K. W., Park, M. S., & Kim, D. (2009). Joint use of DEA
and constrained correlation analysis for efficiency valuations involving
categorical variables. The Journal of the Operational Research Society,
60, 1775–1785.
Ragsdale, C. (2012). Spreadsheet modeling & decision analysis (6th ed.).
Mason, OH: South-Western Cengage Learning.
Ray, S. C. (2004). Data envelopment analysis: Theory and techniques
for economics and operations research. New York, NY: Cambridge
University Press.
APPENDIX
Sav, G. T. (2012). Productivity, efficiency, and managerial performance regress and gains in United States universities: A data envelopment analysis. Advances in Management & Applied Economics, 2
(3), 13–32.
Sav, G. T. (2013). Four-stage DEA efficiency evaluations: Financial
reforms in public university funding. International Journal of Economics and Finance, 5, 24–33.
Seiford, L. M., & Thrall, R. M. (1990). Recent developments in DEA: The
mathematical approach to frontier analysis. Journal of Econometrics, 46
(1–2), 7–38.
Sexton, T. R., & Comunale, C. L. (2010). An efficiency analysis of U.S.
business schools. Journal of Case Studies in Accreditation and
Assessment, 1. Retrieved from http://www.aabri.com/manuscripts/
09256.pdf
Sreekumar, S., & Mahapatra, S. S. (2011). Performance modeling of Indian
business schools: A DEA-neural network approach. Benchmarking: An
International Journal, 18, 221–239.
Thanassoulis, E. (1993). A comparison of regression analysis and data
envelopment analysis as alternative methods for performance assessments. The Journal of the Operational Research Society, 44,
1129–1144.
Tofallis, C. (2001). Combining two approaches to efficiency assessment. The Journal of the Operational Research Society, 52, 1225–
1231.
DATA AND SCHOOL RANKINGS BY DEA EFFICIENCY
Efficiency
rank
College/university
1
1
1
1
1
1
1
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Virginia (McIntire)
Washington U.-St. Louis (Olin)
Pennsylvania (Wharton)
North Carolina-Chapel Hill (Kenan Flagler)
Brigham Young (Marriott)
MIT (Sloan)
Florida (Warrington)
Binghamton
Michigan-Ann Arbor (Ross)
Texas-Austin (McCombs)
UC-Berkeley (Haas)
Indiana (Kelley)
California Polytechnic State (Orfalea)
Notre Dame (Mendoza)
Emory (Goizueta)
Cornell (Dyson)
NYU (Stern)
Ohio State (Fisher)
Illinois-Urbana-Champaign
William & Mary (Mason)
Carnegie Mellon (Tepper)
USC (Marshall)
Texas A & M (Mays)
Louisiana State (Ourso)
Boston College (Carroll)
Florida International (Landon)
North Carolina State (Poole)
Student–faculty
SAT
score
Tuition ($)
Starting
salary ($)
Employer
rank
BW
rank
Efficiency
score
9.9
10
9.7
10.9
15
0.9
18.9
31.6
12.5
24
17.3
20.4
30
15
9.7
15.8
12.2
19
17.6
12.1
11
24.4
25
28
22.5
35
32
1390
1492
1461
1350
1219
1457
1286
1321
1377
1362
1396
1299
1234
1414
1377
1416
1444
1305
1345
1343
1415
1384
1230
1152
1355
1052
1185
9,622
44,100
39,088
5,823
4,710
41,770
6,170
5,570
13,040
10,738
14,985
8,750
5,472
42,464
42,400
27,045
41,358
9,168
16,556
8,677
44,880
43,722
9,330
5,193
43,140
5,217
5,748
60,000
62,000
70,000
60,000
51,000
70,000
51,000
57,000
65,000
55,000
60,000
55,000
55,000
57,000
60,000
58,922
63,250
50,000
55,000
55,000
70,000
54,000
52,000
43,000
60,000
41,748
44,472
15
34
26
28
3
80
8
36
14
4
17
1
74
5
16
21
25
13
6
98
69
11
7
91
9
95
57
2
4
5
10
12
19
37
57
8
9
11
13
64
1
7
3
14
34
21
27
24
31
33
118
6
113
95
1
1
1
1
1
1
1
0.9837
0.9800
0.9782
0.9659
0.9647
0.9451
0.9428
0.9240
0.9224
0.8945
0.8655
0.8632
0.8192
0.8131
0.7978
0.7879
0.7647
0.7417
0.7390
0.7225
(Continued on next page)
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UNDERGRADUATE BUSINESS SCHOOL RANKINGS USING DEA
Efficiency
rank
College/university
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
Northeastern (D’Amore-McKim)
West Virginia
Arizona (Eller)
Houston (Bauer)
Georgetown (McDonough)
Rutgers-New Brunswick
Arkansas-Fayetteville (Walton)
Wisconsin-Madison
Georgia Tech (Scheller)
Buffalo
Connecticut
Georgia (Terry)
Purdue (Krannert)
James Madison
South Florida
Virginia Tech (Pamplin)
Penn State-University Park (Smeal)
Texas-Dallas (Jindal)
Minnesota (Carlson)
U. of Washington (Foster)
Case Western (Weatherhead)
Alabama-Tuscaloosa (Culverhouse)
Boston U.
Colorado State
Kansas State
Oklahoma (Price)
Delaware (Lerner)
New Jersey
Villanova
Miami U. (Farmer)
Wake Forest
Michigan State (Broad)
Bentley
Tulane (Freeman)
Tennessee-Chattanooga
Iowa (Tippie)
Kansas-Lawrence
Arizona State (Carey)
Richmond (Robins)
South Carolina (Moore)
Missouri-Columbia (Trulaske)
Bowling Green State
Lehigh
Pittsburgh (Katz)
Utah (Eccles)
Oregon (Lundquist)
Southern Methodist (Cox)
Rutgers-Newark
Ohio
Worcester Polytechnic Institute
Clemson
Cincinnati (Lindner)
Santa Clara (Leavey)
Akron
Fordham (Gabelli)
Northern Illinois
U. of Miami
283
Student–faculty
SAT
score
Tuition ($)
Starting
salary ($)
Employer
rank
BW
rank
Efficiency
score
21.1
22
14
18
22
29
62
23
15
20
15
17.6
33.4
26.8
49
27
31
12
27
17.7
8.5
21
16
24
41.3
30
19.5
21
14.8
18.6
13.3
26.2
19
15.5
39.4
36
27
27
13.4
19
20.1
17.7
16.4
32
27.7
15
24
44
29
31
28.7
18.9
16
23
18.1
44.7
16.7
1367
1059
1135
1158
1372
1290
1111
1270
1291
1125
1226
1255
1179
1156
1226
1180
1226
1267
1305
1290
1267
1150
1296
1163
1105
1170
1218
1231
1322
1240
1333
1127
1207
1327
1065
1140
1155
1182
1301
1217
1185
1068
1279
1262
1120
1143
1283
1060
1100
1190
1220
1142
1275
1103
1230
1040
1284
39,320
5,794
9,114
6,796
42,360
10,688
6,141
10,273
7,718
5,570
8,712
7,646
9,900
8,808
6,330
9,187
17,824
10,566
12,560
12,383
40,120
9,200
42,400
6,874
6,829
8,700
10,150
10,102
42,150
13,067
42,700
13,800
38,130
41,500
5,722
7,678
8,790
9,208
44,210
10,088
9,272
10,393
41,920
17,568
8,921
9,310
37,050
10,356
10,216
40,790
11,870
9,124
40,572
9,553
41,000
9,488
39,980
55,000
45,000
50,000
50,771
63,000
55,000
46,000
52,000
50,000
40,000
55,000
47,750
52,000
58,000
42,000
50,000
56,000
45,000
51,000
52,000
47,500
58,000
52,000
43,390
43,000
53,000
55,000
53,400
55,000
55,000
57,000
52,000
50,000
55,000
32,500
42,000
47,250
49,000
56,764
47,499
47,500
49,000
57,000
48,000
45,000
40,000
52,000
50,000
49,000
63,000
44,195
43,000
52,500
45,000
57,500
45,000
50,000
19
111
30
75
22
27
81
29
48
62
44
39
18
45
124
24
2
110
38
49
51
82
20
87
53
33
65
92
31
32
40
12
10
78
118
42
59
46
106
63
77
99
55
41
121
79
70
105
89
86
58
66
90
72
68
43
113
25
111
50
103
16
81
105
32
41
112
54
44
58
29
121
52
26
75
39
48
69
73
23
89
114
88
76
59
15
22
18
43
20
49
120
100
110
77
17
87
78
90
35
82
117
107
30
119
86
51
94
84
38
108
40
106
70
0.7199
0.7173
0.7066
0.7042
0.6983
0.6932
0.6929
0.6656
0.6647
0.6632
0.6573
0.6500
0.6452
0.6327
0.6303
0.6265
0.6259
0.6198
0.6193
0.6127
0.6080
0.6070
0.5990
0.5961
0.5878
0.5861
0.5837
0.5829
0.5802
0.5735
0.5656
0.5587
0.5405
0.5249
0.5245
0.5198
0.5164
0.5147
0.5054
0.5038
0.4960
0.4954
0.4897
0.4873
0.4825
0.4727
0.4667
0.4629
0.4618
0.4581
0.4541
0.4539
0.4528
0.4517
0.4515
0.4506
0.4400
(Continued on next page)
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S. W. PALOCSAY AND W. C. WOOD
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Efficiency
rank
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
College/university
Toledo
Colorado-Boulder (Leeds)
Tulsa (Collins)
John Carroll (Boler)
Illinois State
Bradley (Foster)
Elon (Love)
Babson
Denver (Daniels)
Baylor (Hankamer)
DePaul (Driehaus)
George Washington
Vermont
Texas Christian (Neeley)
Seton Hall (Stillman)
American (Kogod)
San Diego
Kentucky (Gatton)
Syracuse (Whitman)
Marquette
Duquesne (Palumbo)
Fairfield (Dolan)
Bryant
Ohio Northern University (Dicke)
Seattle (Albers)
Butler
Loyola-Chicago (Quinlan)
St. Louis (Cook)
Loyola-Maryland (Sellinger)
Quinnipiac
Loyola Marymount
California-Riverside
Hofstra (Zarb)
Providence College
Rochester Institute of Technology
(Saunders)
St. Joseph’s (Haub)
St. Thomas (Opus)
Xavier (Williams)
Belmont
Student–faculty
SAT
score
Tuition ($)
Starting
salary ($)
Employer
rank
BW
rank
Efficiency
score
35
33.3
19
10
32
13.5
26
21
18
24.4
18
20
29.4
24
19
18.9
15.7
28.1
25
24.3
19.5
25
25.8
15
18
18.3
20
21
18
22.5
22
65
22
25
18
1020
1169
1207
1083
1105
1224
1218
1267
1300
1211
1129
1270
1130
1196
1175
1220
1216
1090
1182
1184
1112
1150
1125
1105
1149
1143
1165
1185
1180
1089
1192
1070
1147
1152
1131
9,774
12,646
32,410
32,130
10,050
27,920
28,633
41,888
38,232
30,586
31,650
45,735
13,344
36,500
32,700
37,554
39,486
9,676
37,610
32,810
27,668
41,090
35,591
35,678
34,200
32,280
33,810
34,740
41,026
38,000
38,012
12,192
34,900
41,350
32,784
45,000
46,700
53,500
41,500
43,500
45,000
47,000
50,000
45,000
51,000
55,000
50,000
47,321
53,000
52,500
50,000
50,000
38,250
51,500
48,000
48,000
52,522
52,000
44,000
47,500
47,000
47,500
46,000
47,000
53,000
44,000
41,000
45,500
47,000
41,917
123
54
67
115
47
120
37
60
56
97
52
88
108
84
94
114
102
96
50
71
76
107
35
101
100
104
83
109
103
61
117
112
116
93
73
116
101
55
79
99
98
42
36
68
66
60
71
123
28
85
56
46
122
72
74
96
83
63
62
67
47
104
91
53
61
65
124
115
109
93
0.4372
0.4295
0.4271
0.4268
0.4256
0.4208
0.4193
0.4174
0.4152
0.4148
0.4121
0.4078
0.4022
0.4013
0.3953
0.3941
0.3897
0.3787
0.3773
0.3648
0.3581
0.3560
0.3501
0.3488
0.3486
0.3484
0.3481
0.3456
0.3389
0.3346
0.3273
0.3261
0.3199
0.3191
0.3104
23.5
19
25
18.9
1115
1180
1107
1147
37,670
33,040
32,140
24,900
47,300
39,644
44,000
35,500
64
122
85
119
92
80
102
97
0.3101
0.3004
0.2939
0.2811