The Effect of Class Size on Student
Performance and Retention at
Binghamton University
Jack Keil
Peter J. Partell
Motivation for Study



Preliminary Audit by NYS Comptroller’s
Office recommended SUNY Campuses
increase class sizes (“faculty productivity”)
Majority of research on subject conducted
at elementary & secondary levels
Gauge effect of auditor’s recommendation
at Binghamton University
Hypothesis 1: Student Performance

There is an inverse relationship
between class size and student
performance.
Binghamton University - Institutional Setting





9,300 Undergraduates
2,700 Graduate Students
Highly Selective
Outstanding retention and
graduation rates
Often cited among top universities
in the U.S.
Colleges Within the University





Decker School of Nursing
Harpur College of Arts & Sciences
Management
Watson School of Engineering
Education & Human Development
(no freshmen)
Data Sample: Performance

Freshmen entering Fall 1996:
•  First-time
•  Full-time
•  Degree-Seeking


Fall 1996 & Spring 1997 Semester
Courses
One record per student per course
Dependent Variable: Grade in Course


End-of-Semester Course Grade
Collapse +’s and -’s
•  Convenience
•  No difference

Assign Numeric Values (0-4)
Distribution of Grades in Sample





A’s = 33%
B’s = 39%
C’s = 20%
D’s = 4%
F’s = 4%
(n=9345)
Explanatory Variable: Class Size




End-of-Semester Enrollments
Cross-listed Courses
Average = 142
Linear versus Non-Linear Specification
Possible Form of Relationship
Between Class Size and Grades
+
Negative Linear
Grade
-
-
Class Size
+
Possible Form of Relationship
Between Class Size and Grades
+
Negative Log
Grade
-
-
Class Size
+
Characteristics of Negative Log
Grade
Negative Log
90
80
70
69
10
20
60 70
Class Size
Ordered Logit Regression

Categorical Dependent
Variable
 More than 2 categories
 Categories are ordered
n
Chi-Squared
Significance
Variable
Constant
Class Size
EOP Student
Management Student
Nursing Student
Engineering/Computer Science Student
Age of Student
Female Student
Unknown Ethnicity
Black
Hispanic
Asian
Non-Resident Alien
TOEFL Test
High School Rank
SAT Verbal
SAT Math
Science or Math Course
Subsection
Subsection*Class Size
Subsection (Science/Math)
Sci./Math Subsection*Class Size
Model II (Linear)
Model IV (Log)
9,345
2,030
.0000
9,345
2,129
.0000
Coefficient
-2.9800***
-.0019***
.0887
-.0452
-.1414
-.5369***
.1296***
.1890***
-.1412
-.3686***
-.3057***
-.3048***
-.4084
1.1593***
.0206***
.0022***
.0037***
-1.1525***
-.7556***
.0004
-.1224
-.0014***
Std. Error
.7311
.0002
.0982
.0675
.1249
.0693
.0371
.0436
.1058
.1004
.0914
.0577
.2758
.1415
.0019
.0003
.0003
.0576
.0905
.0006
.1428
.0005
Coefficient
-1.8019**
-.3221***
.0168
-.0411
-.1539
-.5249***
.1232***
.1792***
-.1431
-.3882***
-.3164***
-.3115***
-.4071
1.1770***
.0207***
.0022***
.0037***
-1.0771***
-1.3707***
.1842***
1.2803**
-.3058***
Std. Error
.7401
.0246
.0988
.0679
.1258
.0689
.0372
.0437
.1061
.1006
.0917
.0577
.2770
.1416
.0019
.0003
.0003
.0570
.2997
.0634
.5097
.0950
Effect of Class Size on Freshman Grades
0.6
Predicted Probability
0.5
0.4
0.3
0.2
0.1
0
5
20
35
50
65
80
95 110 125 140 155 170 185 200 215 230 245 260 275 290
Class Size
F
D
C
B
A
Additional Variables of Interest
Variable
Significant?
EOP Students
SAT Verbal
SAT Math
High School Rank
Science and Math
n
y
y
y
y
Direction
+
+
+
-
Additional Variables (cont’d)
Variable
Significant?
Direction
Subsection
Subsection*Class Size
y
y
+
Subsection (Sci./Math)
Sub. (Sci./Math)*
Class Size
y
+
y
-
Hypothesis 2: Student Retention

Students with high average class
sizes are less likely to be
retained.
Data Sample: Retention

Freshmen entering Fall 1996:
•  First-time
•  Full-time
•  Degree-Seeking

Fall 1996 & Spring 1997 Semesters
Dependent Variable: Retention

Check Fall 1997 Enrollment
• If yes, Retained = 1
• If no, Retained = 0

Distribution:
• Not Retained = 9%
• Retained
= 91%
Explanatory Variable:
Average Class Size



Student’s Average Class Size Across
Fall 1996 & Spring 1997 Semesters
Average = 99
Linear versus Non-Linear Specification
Linear Model
Log Model
N
Chi-Squared
Significance
Variable
Coefficient
1221
87.94
.0001
n
Chi-Squared
Significance
Prob.
Level
Variable
Constant
Average Class Size (Natural
Log)
EOP Student
Management Student
Nursing Student
Engineering/Computer Science
Student
Age of Student
Female Student
Unknown Ethnicity
Black
Hispanic
Asian
Non-Resident Alien
First-Year GPA (Natural Log)
High School Rank
SAT Verbal
SAT Math
% Science and Math Credits
Constant
Average Class Size
2.8268
-.0093
.5102
.0153
EOP Student
Management Student
Nursing Student
Engineering/Computer Science
Student
Age of Student
Female Student
Unknown Ethnicity
Black
Hispanic
Asian
Non-Resident Alien
First-Year GPA (Natural Log)
High School Rank
SAT Verbal
SAT Math
% Science and Math Credits
-.0053
.6430
1.1079
-.2090
.9935
.1634
.2916
.5976
.1053
-.3736
.2817
.9981
-.5455
.0035
-.7111
2.8506
-.0150
-.0018
-.0031
.8580
.6226
.1271
.6361
.2289
.2388
.9911
.5278
.0001
.2431
.2713
.1186
.2060
1221
87.10
.0001
Coefficient
Prob.
Level
5.6162
-.8214
.2380
.0271
-.0342
.6546
1.1767
-.1674
.9580
.1559
.2613
.6706
.1102
-.3866
.2700
.9738
-.5554
-.0050
-.7029
2.8609
-.0151
-.0019
-.0031
.7248
.6057
.1139
.6474
.2351
.2299
.9869
.5321
.0001
.2393
.2609
.1190
.2727
Effect of Class Size on Freshman Retention
1
Predicted Probability
0.9
0.8
0.7
0.6
0.5
5
20
35
50
65
80
95 110 125 140 155 170 185 200 215 230 245 260 275 290
Class Size
Additional Variables of Interest
Variable
Significant?
EOP Students
SAT Verbal
SAT Math
High School Rank
% Sci./Math
First-Year GPA
n
n
n
n
n
y
Direction
+
Summary of Findings on
Performance

Negative relationship between
class size and student performance
(grades)
 Probability of getting an A
decreases at a decreasing rate
Summary of Findings on Retention

Negative relationship between
average class size and freshman
retention
 Probability of being retained
decreases at an increasing rate
Contributions of Study

Analyzes effects of class size at
a post-secondary institution
 Tests the effect of class size on
variable other than student
performance: retention
 Large n analysis
Future Research

Add data from multiple institutions
•  Current results apply to
• Binghamton University only

Add faculty variables, e.g., Rank
 Test sensitivity of results by using
mid-semester enrollments