Indicators of College Success of Freshman and Transfer Undergraduate Students

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INDICATORS OF COLLEGE SUCCESS OF FRESHMAN AND TRANSFERUNDERGRADUATE STUDENTS

BY

ESHA SINHA

BA, Banasthali University, India, 2002MA, Gokhale Institute of Politics and Economics, India, 2004

DISSERTATION

Submitted in partial fulfillment of the requirements forthe degree of Doctor of Philosophy in Economics

in the Graduate School ofBinghamton University

State University of New York2010



UMI Number: 3419222

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iii

Accepted in partial fulfillment of the requirements forthe degree of Doctor of Philosophy in Economics

in the Graduate School ofBinghamton University

State University of New York2010

April 12, 2010

Edward Charles Kokkelenberg, Co-Chair and AdvisorDepartment of Economics, Binghamton University

Solomon Polachek, Co-ChairDepartment of Economics, Binghamton University

Daniel Henderson, MemberDepartment of Economics, Binghamton University

Ronald Ehrenberg, Outside ExaminerDirector, Cornell Higher Education Research Institute (CHERI)



iv

ABSTRACT

My dissertation analyzed the determinants of college success of freshman and transfer

undergraduate students. I looked at correlation of Scholastic Aptitude Test scores and

Advanced Placement credits with semester grade point average, probability of graduation,

transfer and attrition. I also analyzed time to degree, transfer and attrition. I also took a more

focused approach and investigated correlation of Advanced Placement grades with college

course grades in five subject areas. Until now I had only looked at the performance of

freshman students. I turned my attention to transfer students in my third chapter. I

investigated time to degree of vertical, horizontal and reverse transfer students. I used two

longitudinal datasets for my data analysis. One is based on enrollment files covering a period

of 20 semesters of a 4-year research intensive public university and the other is a longitudinal

survey dataset spanning 10 years. For modeling purposes I used Ordinary Least Squares,

Tobit Regression, Multinomial Logit, Fixed Effects Logistic Regression and Cox

Proportional Hazard model. The choices of models are made keeping in mind the nature of

dependent variable and the research question being addressed. In my first chapter I conclude

that for freshman students who report Advanced Placement grades, AP credits are a better

predictor of their college success. For freshman students who do not report AP grades, SAT

prove to be a good predictor of their college performance. I found similar results when I

looked at course grades in Biology, Chemistry, English, Mathematics and Physics in my

second chapter. An Advanced Placement grade in the respective subject is a more significant

predictor of securing grade A in that particular subject’s college course. My analysis of

transfer students showed that students who attend more than institution take longer time to

graduate relative to students who start and end their baccalaureate in the same institution. I

also found the result that presence of articulation agreements across institutions can help

reduce time to degree for transfer students.



v

ACKNOWLEDGEMENTS

It is a pleasure to thank those who have made this dissertation possible. I’m greatly indebted

to my advisor Professor Edward C.Kokkelenberg, who guided me throughout in this process

of finding answers to my research questions. I’m extremely grateful to my parents who

encouraged me since childhood to pursue my dreams. I’m thankful to my sisters for keeping

my spirits up in the five long years that I stayed away from them. I would like to specially

mention my husband Dipankar who saw me through my confidence slumps.



vi

TABLE OF CONTENTS

List of Tables vii

List of Figures ix

Chapter One: Is Advanced Placement better than Scholastic Aptitude Test? 1

Chapter Two: Predictors of Course Grades 51

Chapter Three: Time to Degree of Various Kinds of Transfer Students 91

Appendices 127

Bibliography 135



vii

LIST OF TABLES

Table 1.2.1: Research on Scholastic Aptitude Test 10

Table 1.2.2: Research on Advanced Placement Program 14

Table 1.4.1: Number of freshman students who took only SAT test and/ortook at least one AP exam 27

Table 1.5.1: Explanation of Dummy Variables 34

Table 1.6.1: Tobit Regression, LHS Variable: Semester GPA (SAT Students) 37

Table 1.6.2: Tobit Regression, LHS Variable: Semester GPA (AP Students) 38

Table 1.6.3: Multinomial Logit Regression for Graduation (Outcome One),Transferring Out (Outcome Two) and Dropping Out (Outcome Three) 39

Table 1.6.4: Time to Degree, Transfer Out and Drop Out (SAT Students) 40

Table 1.6.5: Time to Degree, Transfer Out and Drop Out (AP Students) 41

Table 1.7.1: Marginal Effects (Mean) from Tobit Regression for SAT Students 42

Table 1.7.2: Marginal Effects (Mean) from Tobit Regression for AP Students 43

Table 1.7.3: Relative Risk Ratio from Multinomial Logit Regression 45

Table 2.2.1: Determinants of College Grades 57

Table 2.4.1: Number of freshman students who took only SAT test and/or 63took at least one AP exam

Table 2.4.2: Biology Courses 64

Table 2.4.3: Chemistry Courses 64

Table 2.4.4: English Courses 64

Table 2.4.5: Physics Courses 65

Table 2.4.6: Mathematics Courses 65

Table 2.6.1: Biology Courses: SAT Students: Grade A 72

Table 2.6.2: Biology Courses: AP Students: Grade A 73

Table 2.6.3: Chemistry Courses: SAT Students: Grade A 74

Table 2.6.4: Chemistry Courses: AP Students: Grade A 75



viii

Table 2.6.5: English Courses: SAT Students: Grade A 76

Table 2.6.6: English Courses: AP Students: Grade A 77

Table 2.6.7: Mathematics Courses: SAT Students: Grade A 78

Table 2.6.8: Mathematics Courses: AP Students: Grade A 79

Table 2.6.9: Physics Courses: SAT Students: Grade A 80

Table 2.6.10: Physics Courses: AP Students: Grade A 81

Table 3.2.1: Literature Review on Performance of Transfer Students 96

Table 3.4.1: Origin Institution of Transfer Students (University Data) 105

Table 3.4.2: Educational Pipeline based on NLSY 1997 106

Table 3.6.1: Time to Degree, Attrition and Persistence (University Data) 121

Table 3.6.2: OLS Regression for Transfer Students (NLSY 1997 Data) 122

Table 3.6.3: OLS Regression for Non-Transfer Students (NLSY 1997 Data) 122

Table 1.A.1: Out of Sample Prediction (AP Students) 127

Table 2.A.1: Percent Female Model: Biology Courses: SAT Students: Grade A 130

Table 2.A.2: Percent Female Model: Biology Courses: AP Students: Grade A 131

Table 2.A.3: Percent Female Model: Mathematics Courses: SAT Students: Grade A 132

Table 2.A.4: Percent Female Model: Mathematics Courses: AP Students: Grade A 133

Table 3.A.1: Time to Degree by Enrollment Status of Students (University Data) 134



ix

LIST OF FIGURES

Figure 1.4.1: Mean SAT Verbal Score with One SD bounds for SAT and AP students 28

Figure 1.4.2: Mean SAT Math Score with One SD bounds for and AP students 29

Figure 1.4.3: Mean High School GPA with One SD bounds for SAT and AP students 30

Figure 1.7.1: Survival Plot for SAT Students 47

Figure 1.7.2: Survival Plot for AP Students 48

Figure 3.4.1: Histogram of Time to Degree of Bachelor Degree Holder Students who havetransferred from 2-year College (System) with an Associate degree 108

Figure 3.4.2: Histogram of Time to Degree of Bachelor Degree Holder Students who havetransferred from 2-year College (System) without an Associate degree 108

Figure 3.4.3: Histogram of Time to Degree of Bachelor Degree Holder Students who havetransferred from 4-year College (System) with a degree 109

Figure 3.4.4: Histogram of Time to Degree of Bachelor Degree Holder Students who havetransferred from 4-year College (System) without a degree 109

Figure 3.4.5: Histogram of Time to Degree of Bachelor Degree Holder Students who havetransferred from 2-year Instate(New York) College (Outside System) 110

Figure 3.4.6: Histogram of Time to Degree of Bachelor Degree Holder Students who havetransferred from 4-year Instate (New York) College (Outside System) 110

Figure 3.4.7: Histogram of Time to Degree of Bachelor Degree Holder Students who havetransferred from 2-year Out of state College (Outside System) 111

Figure 3.4.8: Histogram of Time to Degree of Bachelor Degree Holder Students who havetransferred from 4-year Out of state College(Outside System) 111

Figure 3.4.9: Boxplot of Time to Degree of Bachelor Degree Holder Students by PreviousDegree (University Data) 112

Figure 3.4.10: Boxplot of Time to Degree of Bachelor Degree Holder Students by Type ofCollege (University Data) 113

Figure 3.4.11: Boxplot of Time to Degree of Bachelor Degree Holder Students by UniversitySystem (University Data) 114

Figure 3.4.12: Boxplot of Time to Degree of Bachelor Degree Holder Students (NLSY) 115

Figure 1.A.1: Indifference Curve for Predicted Semester GPA (SAT Students) 128

Figure 1.A.2: Indifference Curve for Predicted Semester GPA (AP Students) 129



1

Is Advanced Placement Better Than Scholastic Aptitude Test?

Esha Sinha

AbstractThere are two indicators that may predict college success; Test results of Advanced Placement (AP) courses and SAT scores. Which of these is more strongly correlated with college GPA, actual graduation, and shorter time todegree? Are these two indicators compliments, substitutes, or are they indeedcontradictory in their predictions? I divided freshman cohorts at a publicuniversity into two groups; those that offered only SAT scores in their collegeapplications, and those that offered both SAT scores and report their Advanced

Placement data. When I consider the performance of students who report only

SATs and did not take any AP exams, I find that SAT score is correlated with their post-freshman GPA. However, for students who took both an AP exam and reportSATs, post-freshman GPA is higher than for those with SATs only. Other factorscorrelated with whether a student graduates, transfers or drops out areinvestigated using multinomial logit. Time taken to degree, transfer or droppingout from college is analyzed using a competing risk approach. For SAT only

students, the SAT scores are not correlated with time to transfer or dropout, buthigher SAT math scores are associated with reduced time to degree. Also higherSAT Verbal scores are associated with higher chances of transferring as opposedto staying on to get a degree or even dropping out. In the case of students whoreport AP results, the presence of AP credits reduces the risk of dropping outrelative to transferring. On the other hand, students who only have reported SAT

scores have higher chances of transferring out relative to staying on and graduating. The existence of AP credits lessened both the time to degree andtransfer but increased time to dropout. Higher SAT scores did reduce time todegree (but not as much as AP credits), though it did not influence time totransfer and time to dropout.



2

1.INTRODUCTION

The Scholastic Aptitude Tests (SAT) and the Advanced Placement Courses and Exams

(AP) are commonly used indicators of a student’s college readiness and potential ability. Theseindicators ostensibly predict success in higher education: But there are nuances. In fact, they

signal two different things. The presence of high SAT scores indicates an aptitude for college and

that a student can understand college studies, whereas the presence of successful AP work

indicates readiness for college and that the student has a high probability of excelling in college

courses.

SATs provide a measure of ability in mathematics and spoken and written English

language; but they are not directly related to any high school coursework. Students take a SAT

test over a period of one or a few days. On the other hand, AP course work is closely related to

high school studies and taking AP courses is a year-long commitment. Hence, by nature SAT and

AP are significantly different from each other. I note that both indicators are used by

administrators in evaluating college admission applications. The College Board, high schools,

teachers, students, and parents devote their time and resources towards both or either of these two

tests. Across the nation, 48% of high school graduates took SAT in 2006-2007 1. In 2008-2009

1,691,905 students (140% increase from 1999) from 17,374 high schools (35% increase from

1999) took a total of 2,929,929 Advanced Placement exams (155% increase from 1999) 2.

Students applying to colleges want to signal that they are capable of being a successful

student, and it would help the applicant to know which (SAT or AP) is a better signal of that.

Colleges take into account a host of factors including SAT and AP when considering applications

1 2007 Digest of Education Statistics. Table 134: SAT score averages of college-bound seniors, byrace/ethnicity: Selected years, 1986-87 through 2006-072 AP Data 2009 (2009). 2009 Annual AP Program Participation. College Board, New York



3

for undergraduate degrees, and they too would find it useful to know if successful AP work is

better than high SAT scores in predicting a student’s subsequent college performance. SAT and

AP programs are administered by College Board and they are trying to fill an information gap

which lies between high school and colleges. As per McCauley (2007), there is disparity between

K-12 system and post-secondary system which results in many students feeling unprepared for

college education. Kobrin (2007) too raised this concern that even though high school students

are increasingly earning high school diplomas but are ill-prepared for college. National Center for

Education Statistics calculated a college qualification index. “It is a composite index of college

readiness or qualification based on five possible measures of academic performance: cumulative

academic coursework GPAs, senior class rank, the NELS 1992 test scores, the SAT and ACT

college entrance examination scores” (NCES, 2005). Greene and Winters (2005) developed their

own measure of college readiness for public high school students so as to be eligible for entry

into four least selective colleges. Their index included three criteria reflecting three hurdles a

student need to cross to be ready for college: namely, graduate with a regular high school

diploma, complete a minimum set of course requirements (four years of English, three years of

Math and two years each of natural science, social science and foreign language); and read at

basic level (score above basic level on NAEP reading assessment).

Due to the different formulae on which NCES qualification index and Green and Winters

readiness index are based, they give a different picture of how qualified or prepared high school

students are for college. According to college qualification index, among all 1992 high school

graduates, nearly two-thirds (65%) appeared to have been at least minimally qualified for

admission to a four-year college or university. Greene and Winters estimated in 2002 that only

34% of high school graduates in the nation had the skills and qualifications necessary to attend

college. Even though the two indices produced different results, the issue that comes across is that

high school performance by itself is not a sufficient signal and it needs to be complemented by



4

aptitude tests and rigorous coursework. Aptitude tests like SAT and rigorous college coursework

under Advanced Placement Program are trying to fill this signaling gap. The current study is a

small attempt to understand how successful they are in this process by looking at three parameters

of college success (semester GPA, graduation, and time to degree).

There are some aspects which the study does not address. First, the student must commit

time and energy in either taking SAT tests or in undertaking the year-long AP curriculum and

then taking the AP test. These costs are undertaken with the idea of admission to a better college

or an easier course load when in college. The question of the benefits offsetting these costs can

only be answered indirectly and I do not attempt do so here. I do not have evidence of the

colleges applied to by any student nor do I know how the progress through a college curriculum

is eased by such AP test results.

Second, families incur costs with the college application process. These include not only

the direct costs of applications and campus visits but also psychic costs of year-long effort to

analyze material and make decisions. These latter psychic costs are indeed alternative costs

because it takes the focus of the family away from other endeavors or decisions. Unfortunately, I

do not have any data on this aspect. So I cannot answer the question of the efficacy of SATs or

APs in minimizing these costs or increasing the benefits to families.

Third, there are significant opportunity costs to both the individual and the society in any

college choice or even the choice of not going to college. I do not address these issues here.

Fourth, college admission officers must select from an increasingly diverse and growing pool of

applicants. Methods to enhance the prediction of who will most benefit from admission is crucial

as the demand for higher education is increasing and the resources to deliver it are constrained.



5

The total number of high school graduates have increased by 27% from 1993-94 to 2005-

06 and college enrollment has also increased by 28% from Fall 1993 to Fall 2007. The total

number of high school graduates is projected to increase by 9% between 2005-06 and 2018-19.

Similarly between 2007 and 2018, total enrollment is projected to increase between 9% and

13% 3. 12 th graders have increased their expectations for postsecondary education. The percentage

of 12 th graders expecting to gain a bachelor’s degree as their highest degree increased from 19%

in 1981–82 to 34% in 2003–04 4. Around 3,328,000 high school students were expected to

graduate in 2008–09 school year and college enrollment is projected to increase to around 18.2

million in the Fall 2008 5. As more and more high school students decide to get a college degree,

the parameters used by educational institutions to choose among their pool of applicants garner

attention and debate in press, colleges, among students, parents, teachers and researchers 6. An

application packet submitted by a student would include his or her educational and extra-

curricular achievements in school, test scores or/and exam grades (e.g. Scholastic Aptitude Test,

Advanced Placement).

Yet it is well known that resources devoted to higher education are constrained7. One

way to meet this increased demand with limited resources is to increase efficiency and assuring

colleges have students who best fit a specific college’s attributes. This avoids student failures,

drop-outs and transfers. Hence, the use of signaling methods to ascertain future performance is

important. It is here where this paper tries to make a contribution.

3 National Centre for Education Statistics (2009). Projections of Education Statistics to 2018. Figure C andFigure G.4 National Centre for Education Statistics (2006). The Condition of Education. Table 23-1.5 National Centre for Education Statistics (2008). Digest of Education Statistics. Table 104 and Table 2 .6 Yong Tang (2006).”Will American Top Universities Admit students like Pan Lliqun?” People’s Daily.

Available Online at http://english.peopledaily.com.cn/200607/31/eng20060731_288417.html Michael Penn (Fall 2007). “Getting In: The not-so-secret admission process”. On Wisconsin , the UW-Madison Alumni Magazine.Yahoo! Answers on Higher Education. Available Online athttp://answers.yahoo.com/dir/;_ylt=Ao2HYBZCuC7LQd5rCE.osnnHxQt.;_ylv=3?link=list&sid=39654539

7 See Ehrenberg,(2000, 2006)



6

My results suggest that for students who take only SAT, the test scores are correlated

with their future college performance. While for those students who have declared an AP

grade(s), the number of college credits granted to them (on basis of their AP exam grade(s)) is a

better indicator of their college performance relative to SAT scores. The marginal effects from

Tobit regression point out that the college GPA of AP students are more responsive to AP credits.

In case of SAT students, college GPA is responsive to SAT scores but relatively more responsive

to high school GPA. For SAT students, test scores did not affect time to transfer or dropout, but

SAT math score reduced time to degree. Also SAT Verbal score increased the chances of

transferring out relative to staying on to get a degree (or dropping out). In case of AP students,

AP credits reduced the risk of dropping out relative to transferring out, more so when compared

to SAT scores. It also increased the chances of transferring out relative to staying on and

graduating. Increase in AP credits lessened both the time to degree and transfer but increased time

to dropout. Increase in SAT scores reduced time to degree but did not influence time to transfer

and time to dropout. For AP students, the marginal effect of AP credits was more relative to SAT

scores on time to degree. I used a longitudinal student dataset of a public 4-year University for

my data analysis. University students are a selected bunch from an applicant pool. Therefore the

results from my analysis cannot be generalized. If the characteristics of freshman classes across

the nation are similar to the characteristics of the freshman class of the university under study,

then the results will have general implications.



7

2.LITERATURE REVIEW

Scholastic Aptitude Test: SAT Reasoning Test (SAT I) is taken by high school students with an

aim to go to a college of their choice. SAT I is a psychometric test, testing a student's basic ability

in language, mathematics and writing. SAT I was introduced to complement a student's

application package which would include his or her high school performance indicators (high

school GPA, involvement in extra-curricular activities). Why was SAT necessary in the first

place? High school performance of a student is very much dependent on the individuals' family

social and financial background 8. To do away with such differences and also to take care of

differing grading standards across high schools, SAT was introduced to help students with certain

disadvantages to realize their college dreams. James Conant, President of Harvard University

wanted to have a more democratic higher education system in United States, in terms of

accessibility. His thought that degree-granting institutions should not be restricted to students

from elite private schools and rich families, led to the development of SAT. 9 The pattern of the

test does not follow any school’s coursework and is standardized by nature, so that different

schooling backgrounds do not affect a student’s chances of pursuing higher education. SAT has

been scrutinized by researchers to understand how strongly it can predict college success and

Table 1.2.1 is a concise summary of the literature and its main results.

Advanced Placement Program: Advanced Placement program was conceptualized by group of

educators from Harvard, Yale and Princeton Universities and three elite preparatory schools in

1955. The purpose was to provide a stronger academic link between high schools and colleges.

Schools would provide their faculty to teach college courses and encourage students to pursue

8 Persell, C.H.,Catsambis, S. and Cookson, Jr.,P.W. (1992). Family Background, School Type, and College Attendance: A Conjoint System of Cultural Capital Transmission. Journal of Research on Adolescence.2(1), pp1-23. 9 Lemann, N. (2004): A History of Admission Testing. In R. Zwick (Eds.), Rethinking the SAT (pp. 5-14).RoutledgeFalmer: New York and London



8

college education. The program is a result of two projects funded by Fund for the Advancement

of Education of the Ford Foundation. The first project under John Kemper, headmaster of

Andover Academy addressed the problem of academically able high school students repeating

their high school courses in college. The second project Kenyon Plan brought together high

school teachers, university professors and Educational Testing Service representatives. This

group was responsible for preparing course outlines, syllabus and tests. College Board set the

uniform standards for the academic subjects covered by various tests under AP program

(McCaulay, 2007; Preston, 2009). Advanced Placement courses cover 22 academic subjects and

the program offers a total of 37 exams based on AP courses. They are aimed at preparing students

for college-level work (in the process gain college credits while still in school) and an exam is a

culmination of year-long study of specific courses. High schools devote their instructional

facilities and efforts towards AP students. Taking an AP course (exam) is an indicator of how

serious a student is in pursuit for college. One of the reasons that students take AP courses in high

school so that they can get a head start in college and perform better than their peers in college

courses. Students achieving good AP grades receive credits and are exempted from introductory

courses in college, because it is believed that AP courses prepare high school students for college.

To know if the AP Program is doing its job, researchers have investigated the college success of

students taking AP exams/courses. Table 1.2.2 gives a brief overview of the research done on AP

Program.

SAT Subject Test and ACT: SAT Reasoning test and Advanced Placement exams are not the

only aptitude and subject specific tests available to high school students. ACT exams are offered

in English, mathematics, reading and science. SAT II are subject tests in mathematics, science,

english, languages and history. There have been studies on SAT Subject Tests and ACT.

Noble(2004) studied the effects of using ACT composite score on future college performance and



9

racial composition of entering class. Either the ACT score or high school GPA could predict

success in college relative to ACT score and GPA together 10. Noble(2004) also pointed out that as

African-American students scored low on ACT and high school GPA, admission decisions based

on these two parameters would reduce college participation from black students.

College Board Report No. 2001-3 concluded that substituting SAT II scores in place of SAT I

would not change college freshman performance but would lead to change in racial composition

of freshman class. Incremental validity of SAT II was not found any different from SAT I by

Ramist, Lewis and McCamley-Jenkins (2001). Similar results were found by Geiser and Studley

(2001). On the other hand Kobrin, Camara and Milewski (2002) concluded that SAT II score

marginally over SAT I in predicting first-year college performance of particular ethnic groups.

10 Noble, J. (2004). The Effects of Using ACT Composite Scores. In R. Zwick (Eds.), Rethinking the SAT (pp. 303-320). RoutledgeFalmer: New York and London



1 0

Table 1.2.1: Research on Scholastic Aptitude Test

Author(s), Year,

Publication/WP/Book

Main Research

Question

Sample Left Hand Side

Variables

Right Hand SideVariables Ec

Brown and Lightsey

(1970), Educational

and Psychological

Measurement

Differential

Predictive Validity of

SAT scores

1004 fall 1969

freshman students of

Georgia Southern

College

Freshman grades in

English courses.

SAT Verbal, SAT Math

and SAT Composite

Score

Larson and Scrontino

(1976), Educational

and Psychological

Measurement


High School GPA

and SAT scores as

predictors of college

performance over an

eight year period.

University of

Washington fourth

year students for the

period 1966-73

Four Year

Cumulative GPA

High School GPA, SAT

scores

McDonald and

Gowaski (1979),

Educational and

Psychological

Measurement


High School GPA

and SAT scores in

receiving an Honors

degree

Students enrolled in

honors courses in

Marquette University

for the period 1963-

72.

Receiving an Honors

degree

SAT score, High School

GPA, Gender

Crouse, J. andTrusheim,D. (1988),

The Case Against the

SAT

Investigation of thevalidity of the claims

made by ETS and

College Board that

SAT helps students

NLS 1972,HSB 1980

Freshman GPA SAT score, High SchoolGPA, High School Rank,

Parent’s Education



1 1

Morgan, Rick.

(1989),

College Board Report

No. 1989-7.


SAT scores

Validity Service Data

of College Board

Analyzed the correlation of SAT scores with

freshman GPA of classes enrolling in colleges

during the period of 1976 to 1985.

Ramist and Weiss

(1990),

Predicting college

grades: An analysis

of institutional trends

over two decades


SAT scores

Analyzed the

predictive validity

studies of 253 colleges

participating in

College Board

Validity Study Service

from 1964-1988.

Freshman GPA High School GPA,

SAT Verbal,

SAT Math.

Stricker, Rock and

Burton (1993),

Educational and

Psychological

Measurement

Differential


SAT.

4351 full time

students entering

Rutgers University in

Fall 1988

First Semester GPA,

Adjusted (for grading

standards in courses)

GPA

High School GPA,

SAT Verbal,

SAT Math,

Gender, Ethnicity,

Parental Education,

High school type and

location, remedial

courses in English and

Mathematics.

Young and Koplow

(1997), Journal of

General Education

Differential


SAT

214 (survey

respondents) fourth

year Rutgers

Four year cumulative

GPA

SAT score, High

School Rank, Non-

academic constructs



1 2

University students

who entered in Fall

90.

measured by Student

Adaptation to College

Questionnaire(SACQ),

and the Non-Cognitive

Questionnaire, Revised

(NCQR).

Bridgeman, B.,

McCamley-Jenkins,

L. and Ervin, N.

(2000), College

Board Research

Report No. 2000-1.


Recentered SAT

Incoming class of

1994 and 1995 from

23 colleges

Compared the multiple correlation coefficient

between freshman GPA and original SAT scores

with the coefficient between Freshman GPA and

recentered SAT scores. High School GPA was the

only other predictor variable

Burton and

Ramist(2001),

College Board

Research Report No.

2001-2

Review of Predictive Validity studies on SAT

till 1980

Freshman GPA,

College Graduation

SAT score, High

School GPA, High

School Rank

Hezlett et al.(2001),

Annual Meeting of

the National Council

on Measurement in

Education

Meta-analysis of 3000 validity studies on SAT. First Year GPA SAT scores

Cohn, Balch and

Bradley (2004),

Economics of

Education Review

Predicting College

GPA using SAT

scores.

571 Principles of

Economics students at

University of South

Carolina in 2000 and

College GPA SAT score, High

School

GPA, Rank in High

School



1 3

2001.

Kobrin and Michel

(2007), College

Board Research Note

31

Predicting College

GPA using SAT

scores.

Data from SAT

Validity Study on

34,000 students who

entered various 30

colleges in Fall 1995.

Different levels of

success determined by

the range of Freshman

GPA

(e.g.FGPA greater than

or equal to 2.0, 2.5,

…..)

HSGPA, SAT scores Lo

Mattern, Shaw and

Williams (2008),

College Board

Research Note 36.

Correlation of SES

with SAT scores and

HSGPA.

Sample of 424,241

individuals from 2007

College Bound Senior

Database

Correlation among SAT scores, High School GPA

and Rank; and Socioeconomic status-educational

level of parents and household income for all

observations in the sample and also separately for

ethnic groups and females.

Kobrin, J.L.

,Patterson, B.F. ,


Revised SAT

Fall 2006 first-time

first-year students

Comparison of single and multiple correlations of

Revised SAT scores and High School GPA with





1 5

Non-AP exam

students in the kind

of economic

background they

came from,

educational goals,

career goals,

academic success in

college and the

overall in-college

experience.

Morgan and Crone

(1993), ETS

Statistical Report 93-

210.

Same as above 3000 University of

California students

who took AP exams

in Biology, Calculus

AB and Chemistry

Made comparisons between AP students who took

AP exams and the non- AP students by looking at

the differences in the mean course grades of

freshman courses between the two groups of

students.

M

Morgan and Ramist

(1998), ETS

Statistical Report 98-

13.

Same as above Looked at students

who gave AP exams

and students who

did not take AP

exams across

twenty one

Universities

Made comparisons between AP students who scored

3 or above in AP exams and did not take

introductory college courses (due to exemption) and

the non-AP students who took the introductory

courses by looking at the differences in the mean

course grades of non-introductory courses between

the two groups of students across the subjects

covered by Advanced Placement Program.

M



1 6

Dodd, Fitzpatrick, DeAyala, and Jennings

(2002), College

Board Report

No.2002-09

Same as above Looked atUniversity of Texas,

Austin’s students

who gave AP exams

and those who did

not take AP exam.

Same as above M

Geiser and

Santelices (2004),

Expanding

opportunity in higher

education:

leveraging promise

Importance of AP

grades and Honors

Courses in

predicting college

success.

University of

California’s

Fall 1998 to Fall

2001 Freshman

Cohorts

Cumulative Freshman

GPA, Cumulative

Sophomore GPA and

Persistence from

freshman year to

sophomore year

High School GPA,

High School API

quintile 11, SAT score,

SAT subject

score, AP exam grades,

Number of AP or

Honors courses taken

and Parental Education.

O

R

Dougherty, Mellor Comparison among Followed 1994 Probability of Graduating AP course Logistic R

11 API refers to Academic Performance Index which is calculated for California state’s public schools. The quantile in which a high school’s A

the API quintile .



1 7

and Jian (2006),

National Center for

Educational

Accountability AP

Study Series

AP Program

participating

students and non-

AP Program

students. Within AP

Program

participating

students, looked at

students who took

AP course only and

no AP exams and

those who took both

AP course and

exam.

Texas 8 th graders

who graduated from

high school and

enrolled in the

state’s public

college or

university.

in Five Years participation, AP

examination success or

failure, High School’s

demographic and

economic

characteristics.

Morgan & Klaric

(2007), College

Board Research

Report 2007-4

Comparison of

academic careers of

students who took

AP exams and who

did not.

Incoming class of

1994 in 27 collegiate

institutions

Comparison of academic careers of students who

took AP exams and who did not by looking at

graduation rate and choice of college major

L

Xiong, Mattern and

Shaw (2008), North

Eastern Education

Research Association

Annual Conference

Relationship

between

performance on AP

English and college

outcomes.

First-time, first-year

students in the

entering class of

2006 at 1100

colleges and

universities from

SAT Validity Study

Database who had

SAT scores and/or

AP grades in

English Language.

First Year GPA,

Retention to Second

Year,

Institutional Selectivity

AP English Language

scores, SAT composite

score (reading, math

and writing), race,

gender, best language

spoken

O

L



1 8

Keng and Dodd

(2008)

Comparison of

performance of AP

and non-AP

students in college

courses.

Groups of AP and

non-AP students

(took AP exams and

received college

credit, took AP

exams and did not

receive college

credit, took AP

exam and qualify for

college credit but

opt for entry-level

course, concurrently

enrolled AP

students, non-AP

students whose SAT

score and HS rank

match with AP

students) across ten

subject areas from

four entering cohorts

(98-2001) of

University of Texas.

Comparison of means of

First Year GPA, Overall GPA,

Subject GPA,

First Year Credit Hours,

Overall Credit Hours,

Subject Credit Hours,

Grades in Two 300 level Biology courses,

Two 400 level math courses and one 300 level

English course,

across five groups of students in 10 AP subject areas

namely Biology, Calculus AB, Calculus BC,

Chemistry, Macroeconomics, English Language and

Composition, English Literature and composition,

Government and Politics of United States, United

States History and Spanish.

M

Hargrove, Godin and

Dodd (2008), College

Board Research

Report 2008-3.

Comparison of

performance of AP

and non-AP

students in college

outcomes.

Performance in the

first year of college

of five cohorts of

98-2002 and all four

years of college of

four cohorts of 98-

2001 of Texas

First Year GPA,

Fourth Year GPA,

First Year credits,

Fourth Year credits

(OLS).

Four-year graduation rate

(Logistic Regression).

SAT score, Free and

Reduced Lunch

Participation in HS,

Gender,

Ethnicity.

A

a

R





20

3. MY STUDY

The debate between SAT and AP streams from the question, what should be the

admission criteria of colleges? As pointed out by Atkinson (2004), college admission criteria

should be to include students who are prepared for college 12. Lemann and Atkinson proposed a

more curriculum based test 13, 14 (as admission criteria). This can be directly gauged from AP

grades and not from SAT scores because AP courses are subject specific, related to high school

courses and has the level of introductory classes in college. They also inform a student about the

kind of interests he or she has. The purpose of my study is to know whether SAT scores or AP

grades is a better indicator of post-freshman success. Which one is correlated with college

success more? It is important to look beyond freshman level as the first year of any student is

spent experimenting in college. A good freshman GPA indicates that the student has the potential

to survive college. In sophomore, junior and senior levels, the students are considered to be more

serious and focused on what kind of career they would like to pursue even though they don't stop

experimenting (Geiser and Santelices, 2004). Helping a student gain confidence so that he or she

can graduate and can go out in the world and make something out of life is one of the objectives

of college education. A good GPA in post-freshman levels shows confidence of a student and a

probable graduation. The analysis also looks into factors correlated with graduation, transfer,

dropout and time to degree because post-freshman success is not only restricted in good college

grades, but also in graduating from college within four years or transferring to another

educational institution where the students finds a better match for his or her career interests

12 Atkinson, R.C. (2004). Achievement versus Aptitude in College Admissions. In R. Zwick (Eds.),Rethinking the SAT (pp. 15-23). RoutledgeFalmer: New York and London 13 Lemann, N. (2004): A History of Admission Testing. In R. Zwick (Eds.), Rethinking the SAT (pp. 5-14).RoutledgeFalmer: New York and London 14 Atkinson, R.C. (2001). “Standardized tests and access to American universities,” 2001 Robert AtwellDistinguished Lecture, 83 rd Annual Meeting of the American Council on Education, Washington, D.C.,February 18, 2001. Atkinson, R.C. (2004). Achievement versus Aptitude in College Admissions. In R. Zwick (Eds.), Rethinkingthe SAT (pp. 15-23). RoutledgeFalmer: New York and London



21

(Adelman(1999) concluded that taking AP courses in high school is correlated with bachelor

degree completion).

Table 1.2.1 shows that studies investigated predictive validity of SAT scores by looking

at the correlation of College GPA or grades or probability of graduation with SAT scores and

high school GPA. The sample sizes ranged from students in certain courses to freshman cohorts

across universities. Most of the studies concluded that SAT score predicts college success. If high

school GPA entered the regression model, then it was found to be more significant predictor

variable relative to SAT scores. Table 1.2.2 documents previous studies investigating the

correlation of AP grades with college performance. Many of those studies compared AP and non-

AP students. The variable depicting college performance were freshman gpa, gpa at graduation,

persistence to second year and probability of graduation. The main conclusions of the papers

were that AP students were more successful in college than non-AP students. They also exhibited

interest in the field in which they took the AP exam. Students who did not clear AP exam(s) but

experienced the benefits of taking AP course(s) outperformed those students who never enrolled

in AP Program(Dougherty, Mellor and Jian; 2006). Klopfestein and Thomas (2009) had an

opposing result that AP credits are not significant predictor of GPA and persistence. They

controlled for enrollment status, high school quality, SAT scores and socio-economic

characteristics. Getting an opposing result can be attributed to the fact that they controlled for lot

of factors which influence a student’s college performance. My analysis is based on seven

incoming freshman students who had taken only SAT and/or AP exams. Not all students take the

AP exams. For them SAT can still be a good predictor of college success. It is important to

analyze these two populations (people taking only SAT, people taking both SAT and AP)

separately. Most of the papers evaluating SAT’s predictive power pointed out the increment in R-

square after including SAT score with high school GPA as the explanatory variable in the

regression. Change in sample size as SAT is included in the model and the resulting fallacy of



22

comparing Rsquares between regressions run on two different populations is well-pointed out by

Rothstein(2004). Similarly, including AP and SAT in one single model can be problematic.

Geiser and Santelices (2004) and Klopfestein and Thomas (2009) have SAT scores and AP

grades or AP credits in their model. For non-AP students, AP grades or credits would be missing.

Both the papers do not mention anything about “only SAT” students or how they deal with

missing AP grades or AP credits. Comparison between AP and SAT should be based on the same

population or equivalent population. The author decided to run regression models separately by

stratifying the dataset into “ONLY SAT” students and “AP and SAT” students. This approach

makes the results more justified and intuitive.

Most of the econometric analysis in the papers documented in Literature Review has

looked at the issue using Ordinary Least Squares estimation technique. I start of with OLS to

understand the factors that are highly correlated with post-freshman semester GPA and then move

to Tobit regression. The variable of interest here is semester GPA starting from the first semester

of freshman year until the last semester of senior year. Grade point average is a weighted average

of all the course grades and is therefore a continuous variable in the range of zero and four. Hence

it is a continuous variable truncated from both the left and right side. Therefore using Tobit

Regression is a better econometric technique than Ordinary Least Squares as it takes into

consideration the double-side truncated left hand side variable. OLS would provide similar

parameter estimates and the same sign, but they would be inconsistent estimates compared to the

ones produced by Tobit Regression and will eventually influence the significance of explanatory

variables and thus the conclusions of this study.

The variables indicating, graduation or transfer or dropout are investigated using

Multinomial Logistic Regression (Probability of graduation, transfer and dropout were

investigated separately in the beginning as independent events using Logistic Regression). The

approach taken was that an individual student faces the following choices-

1) To continue and graduate from an institution they enrolled in.



23

2) To transfer to another institution where he or she can find a better match in terms of

courses, campus life etc.

3) To take time off from higher education.

Graduation and transferring out are positive events (from the perspective of college

success). While dropping out is a negative event. In the process of exploring the direction in

which AP and SAT (controlling for a host of factors) influence a student’s higher education

choice, the paper makes a valuable contribution in treating the three events as interdependent

unlike previous research. Previous validity studies on Advanced Placement and Scholastic

Aptitude Test have investigated the event of four-year or five-year graduation using only the

econometric methodology of Logistic Regression. The current study has the advantage of access

to a dataset which spans twenty semesters (ten years) and hence could explore delayed (beyond

four and five years) graduation for various students.

Time taken to graduate is analyzed through the model of competing risks using

techniques of event history analysis. As mentioned above, graduation, transfer and drop-out are

interdependent events; therefore a competing risk approach (which takes into consideration

interdependent events) is taken to investigate time to degree. Event-history analysis (EHA) is the

longitudinal analysis of individuals or organizations experiencing events of interest (Allison,

1984). It takes into account the fact that explanatory variables can change over time, which can

influence the occurrence or non-occurrence of an event or events. The EHA technique is

borrowed from other fields-demography, biology and engineering. In demography, scientists look

at events such as births, deaths, marriages etc. In biology, scientists look at the impact of a drug

administered to a subject. The events can be single or multiple. Multiple events can be competing,

which is the case when I look at student exits in the longitudinal dataset. The student can exit the

University by either graduating or transferring to another institution or dropping out. EHA

techniques had been used for competing risk models to study student departure by Ronco(1995),

Denson and Schumacker (1996) and DesJardins et al.(2006). Ronco(1996) looked into different



24

types of student departure (graduation, transfer or dropout). She based her analysis on 1635 first-

time fall 1987 college students who were followed until spring 1994 and found that the risk of

transfer to a two-year college was almost as high as the risk of dropout throughout the enrollment

period and that provisionally-admitted students and those with low GPA’s were at greater risk of

dropping out. Denson and Schumacker (1996) used database from Dallas Public Schools to study

the different modes of departure from school of students who were starting ninth grade for the

first time. They found that the students are at risk of withdrawing or dropping out from school

until the end of their senior year, when graduation is the most likely outcome. They also found

that males relative to females were more likely to withdraw or dropout and females are more

likely to graduate by the second semester of eleventh grade compared to males. DesJardins et

al,(2006) investigated the issue of multiple withdrawals from college and the periods of multiple

enrollment in college on probability of graduation. They followed first-time freshman students of

University of Minnesota-Twin Cities entering in fall 1984, 1986 and 1991 for six years. Students

who withdrew from college once had much lesser probability of graduation. Longer enrollment

spells increased the risk of graduation. Higher ACT scores and college GPAs coming from

middle- or high-income family increased chances of reenrollment.

It is important to point out that it should not come as a surprise that AP grades will be a

better indicator of post-freshman success for students who have taken AP exams. Anybody taking

an AP exam is invariably more serious and focused on his or her career. The AP takers are also

highly motivated people who took the option of challenging themselves. Compared to non-AP

exam or course takers, this group would do better at college because they want to. Hence AP

course grade would be a better indicator of college success than SAT scores for them. Taking an

AP exam is considered as a sign of serious student who is prepared for college relative to non-AP

exam taker. Being a serious student would also bias the grades upward across all students and

also in those courses in which the student has taken the exam.



25

Even though AP can predict success far better than SAT, the issues haunting SAT such as

its predictive power for ethnic minorities and being known as 'wealth test' , plagues AP too. For

certain ethnic groups (African-American, Native American, Hispanics, combined ethnic groups),

SAT overpredicted college grades, and for Asian-Americans, some studies overpredicted,

underpredicted or did not mispredict college grades 15. Camara and Schmidt (1999, 2004) do point

out that racial group differences in mean SAT score doesn’t make it biased as these differences do

exist in other measures of academic achievement 16. Similarly, SAT favors affluent students as

other tests do, a conclusion derived by Zwick (2004) 17. Hence, the criticisms hurled against SAT

holds water for other tests too. Klopfenstein (2004) addressed the issue of low participation of

Black and Hispanic Texas high school students in Advanced Placement programs. He found that

presence of AP programs in high schools did not motivate students from various ethnicities to

participate in them in equal rates. The factor that greatly hindered Black and Hispanic students

AP Program participation is family income after controlling for high school and household

characteristics. Hence, both SAT and AP do have problems in terms of accessibility to different

ethnic minorities and low-income groups.

It is a well known fact that not all high schools in America offer AP courses and even if

they do so, not in all subjects 18. NCES data shows that 66% of US schools (both public and

private schools) offer AP courses. The question of equity and access naturally arise, as not all

high school students receive the same opportunity. Students, who are deprived of AP courses in

school, may lag behind students (who had the chance to go to a school offering AP courses) in

college for no fault of theirs. This does not make the AP program biased towards particular

15 Young, J.W. (2001). Differential validity, differential prediction, and college admission testing: Acomprehensive review and analysis . (College Board Research Report No. 2001-6). New York: The CollegeBoard.16 Camara, W.J., and Schmidt, A.E.(1999), Group differences in standardized testing and socialstratification . College Board Report No. 2001-2. New York: College Board.Camara, W.J., and Schmidt, A.E.(2004), Group Differences in Standardized Test Scores. In R. Zwick

(Eds.), Rethinking the SAT (pp. 189-201). RoutledgeFalmer: New York and London17 Zwick, R,(2004), Is the SAT a “Wealth Test”? In R. Zwick (Eds.), Rethinking the SAT (pp. 203-216).RoutledgeFalmer: New York and London18 Hebel,Sara. “AP Courses Are New Target in Struggle Over Access to College in California”



26

students. Having AP program in school is very much dependent on the school authorities,

teachers and parents 19. This particular issue had been dealt by some previous research studies by

considering socio-economic characteristics (parental education and family income) and high

school rank and location as explanatory variables. My study takes into consideration the socio-

economic variables (race, gender, aid) and high school factors by using “student-teacher-ratio” of

high school. Also variables which can describe the in-college experience of students are also

included in the regression model as college success or failure is an outcome of intermingling of

student ability, socio-economic factors, high school quality and experiences in college campus.

There is a problem of self-selectivity in the current analysis, because it is investigating

freshman students of a particular university and not an applicant pool or students across

universities. A freshman cohort of a University is a selected group of students from the pool of

applicants. They are supposedly better (in terms of academic ability) than the applicants who

could not get in. Therefore their SAT scores, AP grades and subsequent college performance

would be on average higher than the “applicant only” group. Also, the amount of variability in

academic variables will be much lesser. This can influence the precision of estimates on SAT

scores and AP grades. The econometric analysis is not based on a random sample of students, but

a much selected group of individuals. Hence, the results of the analysis cannot be generalized. If

the characteristics of freshman classes across the nation are similar to the characteristics of the

freshman class of the university under study, then the results will have general implications.

19 Gamoran, A.(1992). The variable effects of high school tracking. Sociology of Education , 57(4), 812-828Oakes, J. (1990). Multiplying inequalities: Race, social class, and tracking students’ opportunities to learnmathematics and science. Santa Monica. RAND.



27

4. DATA DESCRIPTION

The data used for analysis is a panel data of students of a public university. Freshman

cohorts from Fall 1997 to Fall 2003 are followed until Spring 2007. Students are followed from

the point they enter the University until they graduate, transfer or drop out 20. It is a person-period

dataset, with each student “i” having a certain number of observations depending on the mode of

exit (graduation, dropout, transfer) from the dataset. A student is observed each semester and the

dataset has end of semester information on a student. The data reveals the following statistics

concerning the SAT exam and AP exam taking patterns of freshman cohorts. As seen from Table

1.4.1, that around 45% to 50% of incoming students do not take AP exams. A very small number

of AP students (ranging from 2 to 7 in each cohort), do not take the SAT test. Of the incoming

freshman class of Fall 1997, 860 students reported only SAT scores and 1118 students reported

SAT scores and AP grade(s). In Fall 2003, 1173 of incoming freshman class reported only SAT

scores and 1269 had both SAT scores and AP grade(s).

Table 1.4.1: Number of freshman students who took only SAT test and/or took at least one AP exam

Freshman Cohort Number of students Only SAT Took SAT and AP exam

1997 2042 860 1118

1998 2198 996 1104

1999 2262 1034 1124

2000 2180 981 1104

2001 2462 1079 1291

2002 2296 1119 1110

2003 2542 1173 1269

The following graphs shows the mean SAT math score, mean SAT verbal score and

mean High School GPA of Only SAT students and those of SAT and AP exam students from the

seven freshman cohorts. As the graphs suggest, students who have taken an AP exam and also

gave the SAT, performed better than students who took only SAT, not only in SAT test but also

20 Adelman(1999) suggested that as students complete degrees not Universities or colleges, it is importantto follow a student, during the time he or she is in college.



28

in high school. The graphs point out that AP students are better performers in college and it is due

to the kind of schooling they experienced and the motivation they have and therefore be evaluated

separately from “only SAT” students during admission process 21.

Figure 1.4.1: Mean SAT Verbal Score With One SD bounds for SAT and AP students

Mean SAT Verbal Score

0

100

200

300

400

500

600

700

800

Fall 97 Fall 98 Fall 99 Fall 00 Fall 01 Fall 02 Fall 03

Cohort

M

e a n

Mean + One SD (AP studeMean (AP Students)Mean - One SD (AP StudeMean + One SD (SAT studMean (SAT Students)

Mean - One SD (SAT Stud

21 Even though the graphs provide a comparison between the two groups of students, econometric analysisis done on them separately.



29

Figure 1.4.2: Mean SAT Math Score With One SD bounds for and AP students

Mean SAT Math Score

0

100

200

300

400

500

600

700

800


Cohort

M

e a n

Mean + One SD (AP Students)

Mean (AP students)Mean - One SD (AP Students)Mean + One SD (SAT Students)Mean (SAT Students)Mean - One SD (SAT Students)



30

Figure 1.4.3: Mean High School GPA With One SD bounds for SAT and AP students

Mean High School GPA

0

20

40

60

80

100

120


Cohort

M

e a n

Mean + One SD (AP Students)Mean (AP Students)Mean - One SD (AP Students)Mean + One SD (SAT StudentsMean (SAT Students)Mean - One SD (SAT Students

I talked about selectivity issue in the previous section. I’m splitting up my seven fall

freshman cohorts into two parts: SAT students and AP students. A second level of selectivity

enters here. I’m sorting among students. As the graphs point out that average performance of AP

students is better than SAT students. I can safely assume that the AP group is relatively better



31

than SAT group; hence significance of ability variables in regression models will be more for the

AP group.

The dataset contains information about gender, ethnicity, kind of courses taken, course

grades, enrollment status, residency status, major declared in each semester and degree major of

the students as long as they are enrolled in the university. There is information about the number

of AP exams and their respective grades reported by the student to the university. Also the

number of AP credits they received. They AP courses and the grades attained in the AP exams are

specific to a field of study. In this paper the first criteria of college success studied is semester

GPA which is a weighted average of various courses in different subjects taken in a semester.

Therefore AP grades in Calculus are more likely to be correlated with college math course grades

than semester GPA. The author decided to use AP credits as the explanatory variable in place of

AP grades as it proved to be more significant and correlated with semester GPA. The advantage

of using AP credits is that it converts all the various AP grades of a student into one single

variable (of measurement of academic ability of the student). Plus it helps in understanding the

efficacy of AP program as the main purpose of program is to train high school students in

college-level courses so that they are placed out of introductory courses in college.

As mentioned in Section Three, socio-economic characteristics which include

demographics such as gender, ethnicity and the total aid offered to students are included in the

model. The dataset had scanty information on family income (as it is a self-reported variable) and

no information on parental educational qualifications. Hence as a proxy for economic background

of student, “financial aid offered” variable is used (Bailey and Weininger, 2002; Calcagno,

Crosta, Bailey and Jenkins, 2007). The number of observations under this variable is not scanty

and more accurately reported. It also varies from semester to semester as the financial condition

of the student changes. The story behind using this variable is that a poor student is more likely to



32

apply for aid and get it too. Therefore the sign on the aid offer variable is hypothesized to be

negative in the regression model on semester GPA keeping other factors constant.

The variables denoting in-college experience (showing involvement in courses and

campus life) are college enrollment status-fulltime/part-time and residency status-staying on-

campus/off-campus (Bailey and Weininger, 2002; Calcagno, Crosta, Bailey and Jenkins, 2007).

Being a fulltime student and/or staying on campus is an indicator of deep involvement with

college life and are an important influencing factor of a student’s performance in college. The aid

offer, enrollment and residency variables are borrowed from community college research studies

which have analyzed graduation and transfer prospects of community college students using both

cross-section and panel data and faced similar problems as us in terms of missing observations

and paucity of data.

Section Three put across the point that high school experience is an important factor

influencing SAT and AP performance. The dataset used in the study, contained information on

only the “name of the high school” the student attended. To control for high school quality in the

regression model, the student-teacher ratio of the concerned high school was used. Student-

teacher-ratio of a high school is the “number of students per teacher in the high school”. The

information was gathered from Common Core of Dataset publicly available on National Center

for Education Statistics. Previous SAT studies have mostly used High School Rank. High School

Rank is available for public schools while the information is not so readily available for private

schools. The students in the dataset came almost in equal numbers from both public and private

schools hence gathering information on them was necessary. Information on private schools was

available from NCES and the variable depicting school quality across both kinds of institutions

was student-teacher-ratio. The variable enters the regression till the third power as they were

found to be significant and to test for diminishing returns.



33

5. MODEL AND METHODOLOGY

As semester GPA lies within the interval of [0,4], Tobit estimation was used, which takes into

account a left and right-censored left hand side variable 22. The model is thus

y * = x’β + ξ

y = 0 if y * < 0

y =y * if 0< y * < 4

y=4 if y *> 4 Eq(1)

where y* is semester GPA, x is the matrix of right hand side variables. The right hand side

variables are academic background variables (High School GPA, SAT Verbal score, SAT Math

score, AP credits given to students upon declaration of AP exam scores), demographic

characteristics (gender, ethnicity), college experience variables (fulltime or part-time status,

staying on-campus or off-campus) and high school characteristics (student teacher ratio of the

high school, the kind of high school-public or private) of the student are considered. Following

table provides a detailed explanation of the dummy variables used in the regressions. Gender,

fulltime status, residency status and ethnicity of student are dummy variables. The data has many

observations where the individual reported “unknown/do not know” under ethnicity. Hence they

were also accounted for in the regressions by assigning them a dummy variable. Dummy

variables were assigned for different cohorts to account for any kind of year-to-year variations.

22 Semester GPA is a weighted average of course grades. Course grades lie in the interval of [0,4] and is discrete. The weightedaverage of the discrete course grades would be continuous.



34

Table 1.5.1: Explanation of Dummy Variables

Gender Dummy Ethnicity DummyMale 0 White Non-Hispanic 0Female 1 Black Non-Hispanic 1 or else 0

Hispanic 1 or else 0

Residency Dummy Asian or Pacific Islander 1 or else 0Offcampus 1 American Indian or Alaskan Native 1 or else 0Oncampus 0 Non-Resident Alien 1 or else 0

Unknown 1 or else 0

Status Dummy Cohort DummyFulltime 1 1997 cohort 1 or else 0Part-Time 0 1998 cohort 1 or else 0

1999 cohort 1 or else 0HS Control Dummy 2000 cohort 1 or else 0Public 1 2001 cohort 1 or else 0Private 0 2002 cohort 1 or else 0

2003 cohort 0

The following Tobit models were run separately for AP and non-AP students from j=1 to j=8

levels. Level = 1 refers to first semester of freshman year and level = 2 refers to second semester

of freshman year. Continuing in this fashion, level = 8 refers to second semester of senior year.

Semester GPA i,j,k =

α + β 1 HSGPA i + β 2 SAT Verbal i + β 3 SAT Math i + β 4AP Credits i + β 5Gender i +

β6 Black i + β 7 Hispanic i + β 8 Asian i + β 9 AmIndian i + β 10 Nonresident i + β 11Unknown i +

β12 Fulltime Status i + β 13 Residency i,j + β 14High School Student-teacher-ratio i,h + β 15High School Student-

teacher-ratio-square ih + β 16High School Student-teacher-ratio-cubed ih + β 17 High School Control i,h + β 18

97Cohort i,k + β 19 98Cohort i,k + β 20 99Cohort i,k + β 21 00Cohort i,k + β 2201Cohort i,k + β 23 02Cohort i,k + Є i,j

Eq(2)

i= student , j=level, k=cohort, h=high school





36

λ(ti) / λ(tk) = exp(- X i’µ ) / exp(- X k ’µ ). Eq(5)

Λ0(t) cancels out, hence Cox model doesn’t have to assume anything about the distribution of

hazard function. It does assume that a student exits the dataset only once and doesn’t show up

again and encounters only one kind of exit. In the data used in this paper, each student has distinct

kind of exit from the dataset. A student can exit the dataset by graduating or dropping out or

transferring. Graduation and Transfer are positive exits, that a student finishes his education or

pursues it somewhere else. Dropout is a negative exit as a student decides to take time off from

pursuing a degree.

Looking only at the probability of graduation can be misleading because dropout, graduation and

transfer are competing outcomes and should be analyzed using a competing risk model. Such a

model helps in calculating the probability of graduation, dropout and transfer in each semester

starting from the semester the student enters the University and takes into account the

interdependence which (may) exist among these three outcomes and indicates the variables which

are important in a students decision to choose among the above three outcomes. Therefore, timeto graduation, transfer and dropout has been investigated, using a competing risk framework.

Separate hazard functions are calculated for the events of graduation, transfer and dropout.









40

Table 1.6.4: Time to Degree, Transfer Out and Drop Out SAT Students

Time to Degree Time to Transfer Out Time to Dropout

Variable Beta SE Hazard Beta SE Hazard Beta SE Hazard

Cumulative GPA 0.464 0.064 1.590 -0.133 0.054 0.876 -1.684 0.141 0.186

High School GPA 0.000 0.001 1.000 0.002 0.001 1.002 0.000 0.003 1.000SAT Verbal Score -0.002 0.000 0.998 0.001 0.000 1.001 0.000 0.001 1.000SAT Math Score 0.001 0.000 1.001 0.000 0.000 1.000 0.000 0.001 1.000

Fulltime 0.738 0.185 2.093 0.467 0.175 1.596 -0.095 0.271 0.909Offcampus -0.259 0.057 0.772 -0.767 0.045 0.464 -0.368 0.139 0.692

Female -0.027 0.050 0.974 0.307 0.045 1.359 -0.042 0.116 0.959Ethnicity Dummy

Other 0.084 0.067 1.088 0.082 0.058 1.086 -0.172 0.160 0.842Black -0.311 0.111 0.733 -0.221 0.088 0.801 0.079 0.208 1.083

Hispanic -0.130 0.101 0.878 -0.106 0.085 0.899 0.283 0.183 1.326Asian 0.008 0.071 1.008 -0.416 0.068 0.659 -0.041 0.184 0.960

American Indian -0.546 0.711 0.580 -0.081 0.451 0.922 -11.561 263.691 0.000Non-resident -0.274 0.226 0.760 -1.027 0.325 0.358 1.003 0.317 2.727

Student TeacherRatio of High

School 0.052 0.171 1.054 0.092 0.149 1.096 0.279 0.390 1.322Student Teacher

Ratio Squared -0.003 0.011 0.997 -0.009 0.010 0.991 -0.018 0.026 0.982Student Teacher

Ratio Cubed 0.000 0.000 1.000 0.000 0.000 1.000 0.000 0.001 1.000High School

Control 0.030 0.073 1.031 0.043 0.062 1.044 0.028 0.146 1.028Cohort Dummy

1997 cohort -0.559 0.092 0.572 0.744 0.085 2.104 -2.118 0.251 0.1201998 cohort -0.570 0.087 0.566 0.676 0.083 1.967 -2.289 0.233 0.101

1999 cohort -0.468 0.086 0.626 0.623 0.084 1.864 -1.599 0.191 0.2022000 cohort -0.526 0.087 0.591 0.658 0.085 1.931 -1.664 0.199 0.1892001 cohort -0.273 0.081 0.761 0.571 0.085 1.771 -1.579 0.199 0.2062002 cohort -0.250 0.076 0.779 0.264 0.086 1.302 -1.147 0.164 0.318

Number ofObservations 4502 4502 4502

Model Fit Statistics

Without With Without With Without WithCriterion

Covariates Covariates Covariates Covariates Covariates Covariates

-2 LOG L 27675.4 27424.64 37253.53 36767.35 4981.729 4591.345AIC 27675.4 27470.64 37253.53 36813.35 4981.729 4637.345SBC 27675.4 27597.28 37253.53 36945.72 4981.729 4726.077



41

Table 1.6.5: Time to Degree, Transfer Out and Drop Out

AP Students

Time to Degree Time to Transfer Out Time to Dropout

Variable Beta SE Hazard Beta SE Hazard Beta SE Hazard

Cumulative GPA 0.308 0.057 1.361 0.073 0.051 1.076 -1.497 0.165 0.224High School GPA -0.001 0.001 0.999 0.000 0.001 1.000 -0.004 0.003 0.996SAT Verbal Score -0.002 0.000 0.999 0.000 0.000 1.000 0.000 0.001 1.000SAT Math Score 0.001 0.000 1.001 0.000 0.000 1.000 -0.001 0.001 0.999

AP Credit Hrs 0.003 0.003 1.003 0.013 0.003 1.013 -0.008 0.010 0.992Fulltime 0.277 0.145 1.319 0.443 0.169 1.558 -0.048 0.318 0.953

Offcampus -0.142 0.047 0.867 -0.516 0.039 0.597 -0.431 0.144 0.650Female -0.033 0.044 0.968 0.245 0.039 1.278 -0.330 0.145 0.719

Ethnicity Dummy

Other -0.058 0.201 0.944 0.149 0.205 1.160 -0.036 0.623 0.965Black 0.004 0.013 1.004 -0.010 0.013 0.990 0.001 0.041 1.001

Hispanic 0.000 0.000 1.000 0.000 0.000 1.000 0.000 0.001 1.000

Asian 0.042 0.073 1.043 0.017 0.063 1.017 0.156 0.199 1.169American Indian 0.333 0.058 1.396 0.079 0.051 1.082 0.145 0.174 1.156

Non-resident-0.234 0.143 0.791 -0.183 0.112 0.833 -0.209 0.382 0.811

Student Teacher Ratioof High School 0.012 0.106 1.012 -0.217 0.095 0.805 0.195 0.260 1.215

Student Teacher RatioSquared 0.062 0.057 1.064 -0.389 0.055 0.677 0.181 0.185 1.198

Student Teacher RatioCubed -9.929 87.580 0.000 0.536 0.412 1.709 -10.261 328.226 0.000

High School Control 0.366 0.176 1.442 -0.462 0.239 0.630 0.946 0.431 2.575Cohort Dummy

1997 cohort -0.503 0.078 0.605 0.809 0.073 2.246 -2.358 0.301 0.095

1998 cohort -0.555 0.077 0.574 0.712 0.074 2.038 -1.984 0.234 0.1381999 cohort -0.422 0.076 0.656 0.723 0.075 2.060 -2.436 0.309 0.0872000 cohort -0.281 0.074 0.755 0.724 0.077 2.063 -1.673 0.221 0.1882001 cohort -0.279 0.069 0.757 0.588 0.075 1.801 -1.794 0.228 0.1662002 cohort -0.100 0.068 0.905 0.427 0.078 1.532 -1.548 0.212 0.213

Number ofObservations 5702 5702 5702

Model Fit Statistics

Without With Without With Without WithCriterion

Covariates Covariates Covariates Covariates Covariates Covariates

-2 LOG L 37661.34 37401.44 50660.32 50140.92 3784.931 3439.517AIC 37661.34 37449.44 50660.32 50188.92 3784.931 3487.517SBC 37661.34 37587.99 50660.32 50333.63 3784.931 3572.508



42

7. DISCUSSION OF RESULTS

Tobit regression result in Table 1.6.2 show that the coefficient on AP credits is larger

than the coefficient on the SAT scores and High School GPA. Female and fulltime students

perform better and staying off campus can lower a students GPA. Non-linear terms of high school

student teacher ratio are significant. The coefficient values on the non-linear terms of student

teacher ratio are very small, but the signs indicate that higher the high school student teacher

ratio, lower is the college semester GPA. The cubic term is positive but its coefficient is small

relative to the coefficients on the linear term and the squared term. Hence even if the impact of

very high student-teacher-ratio is not as negative as a medium value of student-teacher-ratio, but

it is still negative. The coefficients in Tobit regression indicate whether the covariates are

negatively or positively correlated with the right hand side variable. The exact increment in

semester GPA due to a unit change in the covariates is given by the marginal effects or the slope

(look at Tables 1.7.1 and 1.7.2 23).

Table 1.7.1: Marginal Effects (Mean) from Tobit Regression for SAT Students

Sophomore Year Junior Year Senior Year

First Semester SecondSemester First Semester Second

Semester First Semester SecondSemester

MarginalEffect of Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD

HSGPA onSEM GPA 0.0010 4.E-05 0.0015 0.0001 0.0010 0.0001 0.0008 4.E-05 0.0005 4.E-05 0.0007 0.0001

SAT Verbalon SEM

GPA 0.0004 2.E-05 0.0004 2.E-05 0.0004 2.E-05 0.0005 2.E-05 0.0007 0.0001 0.0007 0.0001SAT Mathon SEM

GPA 0.0005 2.E-05 0.0005 3.E-05 0.0004 2.E-05 0.0001 7.E-06-

0.0001 4.E-06-

0.0001 8.E-06

23 Marginal effects are calculated for each observation and the mean of it is reported in the tables



43

Table 1.7.2: Marginal Effects (Mean) from Tobit Regression for AP Students

Sophomore Year Junior Year Senior Year

First Semester SecondSemester First Semester Second

Semester First Semester SecondSemester

MarginalEffect of Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD

HSGPAon SEM

GPA 0.0012 7.E-05 0.0005 3.E-05 0.0013 0.0001 5.E-04 4.E-05 0.0003 3.E-05 0.0004 4.E-05SAT

Verbal onSEMGPA 8.E-06 5.E-07 4.E-05 3.E-06 2.E-04 2.E-05 1.E-04 1.E-05 0.0003 3.E-05 0.0002 2.E-05SAT

Math onSEMGPA 0.0004 2.E-05 0.0003 3.E-05 2.E-04 1.E-05 3.E-04 2.E-05 5.E-05 5.E-06 -4.E-06 4.E-07AP

CreditHrson SEM

GPA 0.0166 0.0010 0.0149 0.0011 0.0141 0.0012 0.0122 0.0010 0.0103 0.0009 0.0085 0.0009

For SAT students (Table 1.7.1), the marginal effect of pre-college variables diminishes

and for SAT Math it turns negative. In junior year, a unit change in SAT Math and Verbal scores

brings about the same change in semester GPA. The marginal effect of SAT Verbal increases in

the later years. For AP students (Table 1.7.2), the marginal effects of SAT scores are very small

relative to AP credits, but the trend as a student goes from sophomore to senior level is similar to

what is experienced by SAT students. If there is a 100 point increase in SAT Math score and 2.4

credit increase in AP credits, it improves semester GPA (first semester, sophomore year) by .04.

A 100 SAT Math score is equivalent to 2.4 AP credits for AP students. Similar conclusions can

be derived for other levels from looking at Table 1.7.3 and 1.7.4.

A student has the choice to graduate, dropout or transfer. Using multinomial logit

modeling technique, one can see the effect of one unit increase in the covariate on the kind of

choices made by the student. Table 1.6.3 reports the multinomial logit regression results. The

choice of transfer is the base category. The coefficients in multinomial logit regression, shows the

direction of effect of covariates on probability of one choice relative to probability of second

choice. For SAT students, higher cumulative GPA (other covariates remaining unchanged),

makes them go for graduation relative to transfer and reduces his incentive to dropout relative to



44

transfer. A student prefers to transfer relative to graduation (dropping out) if he has high (low)

SAT verbal score and low (high) SAT math score. Being fulltime or female, one is going to

choose transfer relative to both graduation and dropping out. The result is opposite if one is

staying off campus or is a non-white student. For AP students, higher cumulative GPA, high

school GPA and AP credits would make them go for transfer relative to graduation and dropping

out. Same results hold if you are a fulltime student or a female. Non-white students (except

Blacks and American Indians) or public school AP students are going to prefer graduating

(transferring out) relative to transfer (dropping) 24.

The concept of relative risk ratios (RRR) of the multinomial logistic regression (given in

Table 1.7.3) is very similar to odds ratio calculated from logistic regression. If “RRR” is greater

than one for a covariate, the risk of the student choosing comparison outcome(graduation or

dropout) relative to the risk of the student choosing referent outcome(transfer) increases as the

covariate increases, given that other covariates remain constant . If Cumulative GPA increases by

one unit, the probability for graduation relative to transfer increases by a factor of 1.298 (SAT

students). Looking at Table 1.7.3, one can see that for both AP students and SAT students, SAT

scores have the same amount and direction of influence on their choices. For AP credits, a unit

increment result in decrease of relative risk of graduation and dropout relative to transfer. The

overall impact of student teacher ratio and its non-linear terms is positive for graduation

(dropping out) relative to transfer.

24 These conclusions are based on the assumption that other covariates in the modelremain unchanged.



45

Table 1.7.3 : Relative Risk Ratio from Multinomial Logit Regression 25 SAT Students AP Students

Outcome One Outcome Three Outcome One Outcome Three

Variable RRR Std. Err. RRR Std. Err. RRR Std. Err. RRR Std. Err.Cumulative

GPA 1.298 0.102 0.200 0.027 0.963 0.072 0.156 0.025

High SchoolGPA 0.997 0.002 0.997 0.003 0.999 0.002 0.996 0.004

SAT VerbalScore 0.998 4.E-04 1.000 0.001 0.999 4.E-04 1.001 0.001

SAT MathScore 1.001 5.E-04 0.999 0.001 1.001 4.E-04 0.999 0.001

AP Credits 0.987 0.004 0.973 0.011Fulltime 0.928 0.240 0.277 0.093 0.664 0.152 0.338 0.134

Offcampus 1.847 0.136 2.620 0.401 1.585 0.099 1.524 0.236Female 0.672 0.046 0.532 0.070 0.697 0.042 0.444 0.069

EthnicityDummy

Other 1.052 0.094 1.517 0.263 1.309 0.103 1.935 0.359Black 1.010 0.145 1.792 0.426 0.965 0.181 0.983 0.417

Hispanic 1.030 0.139 1.953 0.421 1.318 0.194 1.997 0.583Asian 1.636 0.163 1.826 0.372 1.688 0.136 2.356 0.471

AmericanIndian 0.586 0.513 6.E-20 0.000 3.E-13 3.E-07 7.E-13 2.E-06

Non-resident 2.881 1.160 20.213 10.126 2.603 0.797 7.808 4.139StudentTeacher

Ratio of HighSchool 0.875 0.213 0.677 0.317 0.766 0.231 1.066 0.779StudentTeacher

RatioSquared 1.013 0.016 1.032 0.033 1.018 0.020 0.994 0.047StudentTeacher

Ratio Cubed 1.000 0.000 0.999 0.001 1.000 0.000 1.000 0.001High School

Control 0.995 0.099 1.001 0.176 1.028 0.103 0.906 0.199CohortDummy

1997 cohort 0.295 0.038 0.066 0.018 0.256 0.028 0.043 0.0141998 cohort 0.322 0.039 0.069 0.017 0.286 0.031 0.086 0.0211999 cohort 0.362 0.044 0.105 0.023 0.314 0.034 0.045 0.0142000 cohort 0.351 0.043 0.121 0.027 0.392 0.042 0.124 0.0292001 cohort 0.460 0.055 0.114 0.026 0.430 0.045 0.091 0.0232002 cohort 0.641 0.075 0.281 0.054 0.580 0.061 0.154 0.036

Number ofObservations 4503 5705

LogLikelihood -3676 -4319

25 Outcome One is Graduation, Outcome Three is Dropping Out and Transferring Out is Outcome Twowhich is the Base Outcome



46

A student is in the university for a substantial time period and the previous model looked

at the final choice made by him. The student is susceptible to the risks of the three events when he

is in the university and the probability of falling for the risk or surviving it, changes as the time

spent in the university increases. Cox proportional hazard model can provide us the survival

function for the three events or outcomes as well the factors which helps a student to graduate

faster. Tables 1.6.4 and 1.6.5 provide the results for the duration models. The columns of interest

are that of hazard ratio. Hazard Ratio greater than one indicate that a unit increase in the covariate

results in increase of the probability of the outcome (person’s chance of surviving the risk goes

down). The results are very similar to what was concluded in the multinomial logit model. For

SAT and AP students, good college GPA and other academic variables reduces time to degree

(doesn’t survive graduation), except SAT Verbal score. AP credits decrease the time to transfer

and increase the time to dropout (the person survives dropping out). A female (fulltime, off

campus) student, would take more (less, more) time to graduate and transfer and more (less,

more) time to dropout. But, a Black or American Indian/Pacific Islander or Hispanic or Non-

resident who has taken only SAT test, will take longer time to complete a degree. For low (high)

values of student-teacher-ratio, the overall impact is that it reduces (increases) the time to any of

the three events 26. Coming from public high school reduces time to all the three events for SAT

students, while for AP students it reduces time to graduation and drop out. If you enter the

University in fall semester, you take longer to finish your degree or dropout and lesser time to

transfer out.

To understand the different risks faced by the student during the time he is in the university,

survival curves (deduced from survival functions) are plotted across years. Following graphs

points out the survival curves of three outcomes (1-graduation, 2-transfer, 3-dropout). TTE or

Time to Event is in year units (zero years to ten years). The graphs are very similar in case of

26 The results holds for both SAT and AP students



47

SAT and AP students. A student survives transfer and graduation quite successfully until the

middle or end of fourth year in college. The transfer survival curves starts to go down much

before graduation survival curve at the beginning of second year showing that a student would

transfer before four years and even fall below the dropout survival curve especially after four

years. It is the only survival curve which goes close to zero. After four years, there is a huge drop

in the graduation survival curve and it continues to drop smoothly, as more and more students

aim to graduate after their fourth year. For the first four years, the graduation survival curve is

like the top of plateau, indicating that whoever has the intention of getting a degree would stay on

for four years or more. The dropout survival curve starts falling at the beginning of the time

period and continues to fall sharply and reaches stagnation after between five and six years,

pointing out that people do not wait long to dropout.

Figure 1.7.1: Survival Plots for SAT Students



48

Figure 1.7.2: Survival Plots for AP Students

I have stressed on the fact that AP credits are more correlated with college success

parameters relative to test scores. I based my results on the significance of AP credits and the

marginal effects. I addressed the question that whether AP credits is a better predictor of semester

GPAs than SAT scores for AP students by doing out of sample prediction. The results are

reported in Appendix 1.A (Table 1.A.1). I first ran Eq (2) without the variable AP credits on two-

third of observations for all eight semester GPAs. Then I predicted out of sample for the rest one-

third of the observations. Three statistics which measure the forecasting power of a model-Root

Mean Square Error, Mean Absolute Error and Theil Inequality Coefficient are calculated. I redid

out of sample prediction for the full model and the three statistics were always lesser than the

“Without AP credits” model (look at the difference column). The results assert the fact that for

AP students, Advanced Placement credits are a better predictor of semester GPAs. This is a very

strong result as I find evidence for predictive power of AP credits at all levels of college GPA.



49

I also derived a set of indifference curves-combinations of composite SAT score (SAT

Verbal and SAT Math) and High School GPA for SAT students. A similar set of indifference

curves for AP students was also derived showing the combinations of composite SAT score and

AP credits which produce a particular value of predicted semester GPA. Figure 1.A.1 and Figure

1.A.2 shows various combinations of academic ability variables which produce predicted

semester eight GPAs of 3 and 3.5. The patterns of curves show that the ability variables are

“good” items. In a nutshell more of ability variables are better. Higher High School GPA, SAT

scores and AP credits are correlated with higher college GPA. Therefore, for SAT students SAT

scores do a good enough job of predicting their success in college. While for AP students, AP

credits are better predictors than test scores. One interesting thing to observe in both the figures is

the range of composite SAT scores. The range is much wider for SAT students. This again goes

back to the issue of selectivity in the data analysis. Variability in academic variables within AP

students is much lesser compared to SAT students.





51

Predictors of Course Grades

Esha Sinha

AbstractThis study analyzes the correlation of Scholastic Aptitude Test verbal and math scoresand Advanced Placement grades in English and Mathematics with college grades in

Mathematics and English in 100, 200, 300 and 400 level courses. Course grades in Physical sciences-Biology, Chemistry and Physics were also analyzed to understand theefficacy of the respective subject’s Advanced Placement grades relative to Scholastic

Aptitude Test’s verbal and math scores. Controlling for demographic characteristics,time effects, high school effects, college faculty characteristics and college experience of

students using a fixed effects logistic model, the overall results suggest that AP gradesare more strongly correlated with college grades relative to SAT scores for students whohave both SAT score and AP grades. While for students who do not have AP grades in therelevant subject, SAT score is a good predictor of college grades.



52

1.INTRODUCTION

Researchers have questioned the validity of Scholastic Aptitude Test scores relative to

Advanced Placement grades in predicting college performance, viewing them as substitutes.

Which one is a better indicator of college success? The question had been answered by looking at

cumulative freshman GPA, sophomore GPA, persistence rates and graduation rates. Scholastic

Aptitude Test and Advanced Placement are two very different measures of a student’s academic

ability. SAT measures innate ability or inherent quality of student. It has three sections- verbal,

math and writing. It tests a student’s basic understanding in English and Mathematics and his

writing skills. AP program offer courses in mathematics, history, basic sciences etc. It is a year-

long or half-year-long commitment. The purpose is to train students in particular subjects so that

their college credits are waived off and they can get a head start in college. The tests (exams)

have sections in (are offered in) subject areas of English and Mathematics. Why not look at

grades in college courses of Mathematics and English to understand the predictive validity of AP

grades and SAT scores? This is a more focused approach to answer the question of validity.

Students taking the tests devote their time and energy. Colleges and Universities take into

account a host of factors including SAT and AP when considering applications for undergraduate

degrees. SAT scores and AP grades are signaling devices to admission authorities. As per the

National Council Research Report in 2002, AP grades are important criteria for admission people

at various universities and colleges 27. Are the admission authorities right in considering

standardized test scores and Advanced Placement course participation and grades when

evaluating college applicants? The second chapter takes a more focused approach to answer this

question by looking at determinants of college grades in English, Mathematics, Physics, Biology

and Chemistry.

27 Learning and Understanding; Improving Advanced Study of Mathematics and Science in U.S. HighSchools (2002). National Research Council.





54

admitted students and conduct market research 31. The report concentrated SAT and ACT and did

not look at AP program, Honors courses, International Baccalaureate Courses or SAT subject

tests. The committee recommended that admission policies be aligned with institutional goals

and the test scores should serve to further those goals. The current study being very limited, does

not answer the issue of alignment of tests with institutional goals. The fact remains that admission

policies across universities are not uniform and the institutions do make an effort to make it

transparent to public. Whether their efforts are adequate and ease the worry of college bound

students and their parents is a question which will have many possible answers. Even though

admission policies are not similar across institutions, the common thread running through most of

them is the consideration of test scores and subject-specific courses. They are uniform across

students in terms of content offered and tested on.

As the previously mentioned statistics showed that there is an increasing demand of

higher education and the question of accessibility is quite pertinent due to the fact that post

secondary education has become expensive. Average tuition and fee charges has increased by

186% for public four year institutions from 1978-79 to 2008-09. Private four year institutions

witnessed 154% increase and public two year institutions saw an increase of 119% in the same

period 32. As per Baum (2001), the cost of attending public four year institutions relative to family

incomes was 13% (42%, 6%) for middle-income families (low-income, high-income) in 1971-72.

For private four year institutions the respective percentages are 29%, 91% and 12%. In 1999-

2000, the cost of attending public four year institutions increased to 17% (61%, 5%) for middle-

income (low-income, high-income) families. The corresponding numbers in case of private four

year colleges are 44%, 162% and 14% 33. The numbers show that within 30 years, low-income

and middle-income families had to lighten their purse strings to put their kids in college. When

31 Myths and Tradeoffs: The Role of Tests in Undergraduate Admissions (1999).National Research Council.32 The College Board (2008). Enrollment Weighted33 Baum (2001) and Trends in College Pricing (1999), College Board.



55

the investment in higher education has become more expensive, the factors that control entry

should be investigated in terms of their validity in predicting college success.

Ordered logit was used to analyze the correlation of SAT scores and AP grades with

college grades because the right hand side variable consists of five distinct non-continuous

grades. A host of right hand side variables controlling for socio-economic characteristics of

students, the kind of college experience a student goes through, and course and faculty

characteristics. Ordered logit estimation is based on the assumption of proportionality and the

logit results indicated that the assumption of proportionality does not hold. The analysis moved to

fixed effect estimation using a logit model for grades A to F because it is important to control for

school and time effects. The left hand side variable is the grade received in lower level and upper

level courses in SM (Mathematics, Chemistry, Biological Sciences, Physics) and English.

For English and Math courses, AP grades are a stronger determinant of course grades

relative to SAT scores when it comes to students who have both subject AP grades and SAT

verbal and math scores. For students who only have SAT scores, it can predict performance in

college courses. The study also investigated science courses to understand if SAT math scores

have better explanatory power than science AP courses. The conclusions that hold for English

and Math courses hold for Biology and Chemistry courses and for lower level Physics courses.

Due to host of right hand side variables used in the fixed effects model to control for student

characteristics, the results give interesting facets about college and high school curriculum of

science, math and English courses and how related they are with each other. The results showed

the significance of correlation of demographic characteristics of students and faculty with course

grades. I could also draw interesting conclusions about SAT and AP curriculum. For Biology and

Math courses, the author investigated the gender peer effect by looking at percentage of female in

a course and found that it did have significant impact on grades.



56

2.LITERATURE REVIEW

Determinants of grades in college have been analyzed by Bridgeman and Wendler(1991),

Melican, Debebe and Morgan(1997), Krieg and Uyar(1997), Didia and Hasnat(1998), Morgan

and Ramist (1998), Buschena and Watts(1999), Cohn and Johnson (2006), Grant(2007), Keng

and Dodd (2008); and Xiong, Mattern and Shaw (2008). The kind of student population studied

in the above papers, their main research question and important results are presented in the

following table.



5 7

Table 2.2.1: Determinants of College Grades

Author(s), Year Main Research Question Sample Left Hand Side

Variable(s)

Right Ha

Variables

Bridgeman and

Wendler (1991)

Gender Difference in SAT scores

and grades in college math courses

Grades and SAT scores of

students in algebra, precalculusand calculus classes from nine

universities.

Grades in Algebra,

Precalculus andCalculus.

High Sch

Math sco

Debebe, Melican

and Morgan

(1997)

Comparing performance of college

level Economics students and AP

economics students

1994 AP Economics exam high

school students and 938

students (from 18 universities)

who took the requisite college

course in Economics

Comparison of the mean scores rece

Micro and AP Macro exam by AP E

school students and college students

Krieg and Uyar

(1997)

Determinants of student

performance in introductory

business and economics statistics

course.

289 students enrolled in six

sections (two sections per

semester) of business and

economics statistics course in

University of Iowa

Prerequisite course

exam score and the

total score of the four

exams given in the

course during the

semester

Math AC

timing, a

GPA, FT

student;

number o

if repeati

Didia and Hasnat

(1998)

Determinants of performance in

introductory finance course

210 students in seven sections

of Principles of Finance course

taught in Spring and Fall 1994.

Letter Grade ranging

from A to F.

Cumulat

of study

Average

courses t

accountin

economi

credit loa

Freshma

of studen

Morgan and

Ramist (1998)

College performance of students

with high AP exam grades

Looked at Mean Course Grades

in Non-Introductory Courses

Made comparisons between students

or above in AP exams and the studen



5 8

across 21 Universities. the introductory courses.

Buschena and

Watts (2001)

The importance of prerequisite

courses for courses in intermediate

microeconomics and agricultural

economics

Students in Intermediate

Microeconomics (Agricultural

Economics) classes from

Spring95 (Fall95) to

Spring97(Fall97) at Montana

State University

Grade in Intermediate

Microeconomics

(Agricultural

Economics)

GPA, SA

hours, G

prerequi

Percenta

the prere

Agr.Eco

Cohn and Johnson

(2006)

Importance of class attendance on

student performance

347 students in Principles of

Economics classes from

Fall97-Spring01 in University

of Southern California

Score in the tests and

final exam

administered in class

SAT, Co

Gender,

Percenta

attended

Credit H

Attempt.

Grant (2007) The kind of information revealed by

grades in terms of student and

instructor productivity

Principles of Economics

Classes from 1998 to 2001 in

University of Texas-Arlington

Letter Grade ranging

from A to F

GPA, SA

Informat

business

courses t

variables

demogra

Feldon, Gustainis

and Timmerman

(2007)

Performance of AP Biology

students who were placed out of

introductory courses in 300-level

biology course relative to students

who took the introductory course.Both groups of students were

majoring in Biological Sciences.

117 biology majors enrolled in

University of Southern

California Honors College for

the period 2002-2006.

Mean Grades in 300 level Biology c

compared across the two groups of s

Mann-Whitney test.

Keng and Dodd

(2008)

Performance of AP students relative

to non-AP students.

Groups of AP and non-AP

students (took AP exams and

Comparison of means of

First Year GPA, Overall GPA,





60

3. MY STUDY

Most of the above papers have looked at college grades to understand what determines

them and have used different sets of explanatory variables to understand which one causes

improvement in student performance. For explanatory variables, SAT scores (in some cases only

SAT math) were used as pre-college aptitude or ability indicator along with high school GPA,

controlling for gender, ethnicity and whether prerequisite courses were taken or not. The main

focus of Bridgeman and Wendler (1991) was on gender difference and they found that even

though females performed better than males on SAT they fall behind in getting good grades.

Debebe, Melican and Morgan(1997) looked at the effectiveness of AP Program by analyzing

performance on two AP Economics exams. They did not analyze college grades, but found

evidence that high school students receiving the benefits of AP Program outperformed college

students. Krieg and Uyar (1997) looked at ACT scores as determinant of college grades in

Economics and Business Statistics and found ACT math score to be a significant predictor of

grades after controlling for enrollment status, class timings and employment hours. Didia and

Hasnat (1998) did not control for SAT scores or AP grades in their model for college grades.

Morgan and Ramist (1998) looked at AP grades and its college success predictive power but did

not mention anything about the students in their sample having SAT scores or not.

Predictive power of performance in prerequisite courses was investigated by Buschena

and Watts (2001) and the results pointed out that SAT scores improved performance in

intermediate courses. Cohn and Johnson(2006) focused on class attendance as determinant of

final exam score and controlled for innate ability or aptitude by using SAT score. They found the

interesting result that higher SAT score was negatively correlated with class attendance. Xiong,

Mattern and Shaw(2009) controlled for both AP grades and SAT scores in their model for college

GPA, retention and type of institution selected by first-time freshman students. In the first



61

chapter, college GPA has been investigated using Tobit regression and probability of graduation,

transfer and attrition has been investigated using Logistic regression. Feldon, Gustainis and

Timmerman (2007); and Keng and Dodd (2008) analyzed the difference in mean grades among

various groups of students classified as per their AP exam and course taking behavior. These are

the only two studies which came close to investigating the correlation between AP grades and the

corresponding subject’s college course grades. The current study aims to fill the lacuna which

exists in the SAT and AP literature by looking at the correlation of SAT scores and AP grades

with college grades in mathematics, physical sciences and English.

The study assumes that course grades are one of the outputs of multi-product human

capital investment. The information revealed by course grades was explored by Grant(2007). He

found them to be too noisy and the average of grades (which removes all the noise) a better

indicator of student and instructor performance. College grades are an end product of student

motivation and ability, and instruction quality and college atmosphere. Barkley(1992) considered

undergraduate grades as market signal to potential employers of student ability, effort or both.

Callaway, Fuller and Schoenberger(1996) looked at college-acquired characteristics on

employment status and starting salaries of business majors. They found that academic

achievement in college, i.e., college grades play a significant role in determining employment

prospects and starting salaries. They reasoned that good grades can be viewed as employers as a

sign of initiative and commitment. Even high school grades can be a signal to prospective

employers. Miller(1998) using a fixed effects model concluded that high school grades can

provide information to employers about the quality of the interviewer. Curry(2007) using survey

data on employers, found that GPA plays an important role in the decision to hire a college

graduate. Briggeman, Henneberry and Norwood(2007) found from a survey on employers that

half of them used grades to make decision on an applicant’s character and communication skills.

The current study concentrates on the grades as an indicator of the academic progress made by



62

students during their undergraduate education. I assume that good grades indicate that the student

is gaining knowledge and understanding of subject(s) he or she is interested in pursuing. Whether

those grades have any kind of influence on job prospects or any other kind of future prospects the

student is keen on, is not being investigated here.

The study is based on one four year research intensive university. There is no inter-

university variation but definitely intra-university variation in terms of faculty and class

atmosphere. As the study is looking at SAT scores and AP grades and performance on SAT test

and AP exams are dependent on the high school a student attends, an econometric model is

needed to control for high school bias. Plus the data analysis is based on seven freshman cohorts

and so controlling for time effects is necessary. The econometric model used here is a two-sided

(high school and entry time) fixed effects logistic model for grades (A to F). This model takes

into account student and faculty demographics, effects of high school and different times of entry

into undergraduate education.



63

4.DATA DESCRIPTION

The current study investigates SAT and AP students separately because students taking

AP courses in school have a more clear idea of the kind of subject areas they would pursue in

college. Also the kind of training they received in those subjects would influence their

performance in college courses. If a comparison is being made between SAT scores and AP

grades, then one needs to analyze students who have taken both SAT and AP tests. The sample

consists of seven freshman undergraduate cohorts from a research-intensive public university.

The number of SAT students and AP students for each freshman cohort shows that a considerable

percentage of students do not take AP exams. Hence it is important to analyze the performance of

SAT and AP students separately.

Table 2.4.1: Number of freshman students who took only SAT test and/or took at least one AP exam

Freshman Cohort Number of students Only SAT Took SAT and AP exam

1997 2042 860 1118

1998 2198 996 1104

1999 2262 1034 1124

2000 2180 981 1104

2001 2462 1079 1291

2002 2296 1119 1110

2003 2542 1173 1269

Individual grades in 100, 200, 300 and 400 level courses are analyzed. The distribution of

grades across SAT and AP students for SM and English courses are shown in the following

tables. How are we defining SAT students and AP students? When we are investigating course

grades in Mathematics, SAT students encompass those who have not taken an AP exam in any of

the three AP courses in Mathematics (AP Calculus AB, AP Calculus BC, AP Statistics). AP

students refer to students who have taken any one of the AP courses. The definition is

analogously applied to courses in physical sciences and English. In physical sciences, AP courses

offered are AP Biology, AP Chemistry, AP Physics B, AP Physics C-Mechanical and AP Physics





65

Table 2.4.5: Physics Courses

SAT STUDENTS AP STUDENTS

Grade Grade

Course Level A B C D F A B C D F

400 level 100 59 13 2 2 38 20 4 6 0

300 level 111 94 37 21 3 49 46 17 10 7

200 level 17 13 7 7 2 11 8 1 1 2

100 level 866 920 854 881 485 281 234 157 110 53

Table 1.4.6: Mathematics Courses

SAT STUDENTS AP STUDENTS

Grade Grade

Course Level A B C D F A B C D F

400 level 145 137 92 104 57 301 184 110 100 46

300 level 472 466 363 427 322 917 671 424 415 231

200 level 722 910 912 1210 1239 710 732 566 526 296

100 level 1263 1469 1086 1167 1069 422 305 149 112 64

The data is a panel data of transfer students enrolling in Fall 1997 to Fall 2003 and they

are observed until Spring 2007. Students are followed from the point, they enter the University

until they graduate, transfer or attrite 34. It is a person-period dataset, with each student i having a

certain number of observations depending on the mode of exit (graduation, attrition, transfer)

from the dataset. A student is observed each semester and the dataset has information on courses




66

taken by a student in a semester. Course-related information such as gender, ethnicity, academic

rank of the instructor, average grade in course, kind of course (has a laboratory session or not),

course level and the department offering the course is also documented. Pre-college academic

variables- SAT scores, high school GPA, AP course and grades declared by student - are

available for freshman students only. There is information on enrollment status (fulltime or part-

time, freshman or transfer), gender, ethnicity and major(s) declared (field of the major). There is

also information on aid offered from various sources and kind of sources (sports scholarship or

other scholarship). The dataset has information on the kind of major chosen by individual student

during the application process and also the majors subsequently declared as they pursued their

undergraduate education. First (Second) Major refers to the first (second) major declared by

student. If the students change their major then their first and second major would be in separate

subjects or closely related field of study.

There is information available until the fifth declared major. The number of students

going until fifth major is very rare. Hence variables denoting third, fourth and fifth major choice

do not enter the regression due to lack of sufficient observations. Application major and first

declared major are highly correlated hence they do not enter the model together. Degree Major is

the field in which the student decided to get his or her degree in. It would be interesting to see the

interaction of first, second and degree major dummy variables with each other to see if switching

fields of study has any impact on performance.

There is a problem of self-selectivity in the current analysis, because the current analysis

is looking at freshman students of a particular university and not at applicant pool or students

across universities. A freshman cohort of a University is a selected group of students from the

pool of applicants. The results of the analysis cannot be generalized. If the characteristics of

freshman classes across the nation are similar to the characteristics of the freshman class of the





68

5. MODEL AND METHODOLOGY

Course grades range from A to F and hence they are ordered in ascending fashion

(starting from F). The dependent variable has an inherent ranking. Didia and Hasnat(1998);

Butler, Finegan and Siegfried(1998); Van Ness, Van Ness and Kamery (1999, 1999); Chan,

Miller and Tcha (2005); Grant (2007) and Kokkelenberg, Dillon and Christy (2008) have used

ordered probit or ordered logit models to analyze grades. I have applied the ordered logit model.

The score test on the proportionality assumption rejected the assumption of proportionality 35.

Hence I moved to fixed effects logistic model which would control for the kind of high school a

student attends and the time they entered the University. The left hand side variable is discrete,

“1” for getting A grade and “0” for for not getting A grade.

The two-sided fixed effects model for grade “A” controlling for school effects and cohort

effects is as follows.

Grade (A)i,j,t,h = Intercept + SAT Verbal Score i,h + SAT Math Score i,h + AP Grade i,h + Fulltime i,t

+ Residency i,t + Gender i + Others i + Black i + Hispanic i + Aid Offer i,t + Average Grade in

Course i,j,t + Gender of Instructor i,j,t + (First Major i,t or Second Major i,t or Degree Major i,t )+ u h

+v t + e i,j,t,h

i=student

j=course

t=time of entry in university

h=high school Eq(1)

Some of the right hand side variables are dummy variables. The coding is explained as

follows.

35 This test statistic is generated by SAS 9.1 Program.



69

Gender Coding Status Coding

Male 0 Fulltime 1

Female 1 Part-Time 0

Major Coding Gender of

Instructor

Coding

Major not in Course’s Subject 0 Male 0

Major in Course’s Subject 1 Female 1

Ethnicity Coding

Black 1 or 0 otherwise

Hispanic 1 or 0 otherwise

Asian 1 or 0 otherwise

Others(Non-resident, American

Indian, Pacific Islander)

1 or 0 otherwise

SAT scores on both verbal and math sections enter the regression. The papers

documented in literature review have included the relevant AP grade depending on the subject

area of course grade being analyzed. If one looked at course grades in English or Biology, AP

English or AP Biology grades were the explanatory variables. Performance in a course would be

correlated with the respective AP grade but also with AP grades in subject areas which closely

correspond to that of the course. Therefore performance in Biological Sciences may also be

influenced by AP grades in mathematics and other physical sciences. The issue of correlation

among AP grades is taken into consideration and highly correlated AP grades did not enter any

regression model together.

The dataset has scanty information on family income (as it is a self-reported variable) and

no information on parental educational qualifications. Hence as a proxy for economic background

of student, “financial aid offered” variable is used (Bailey and Weininger, 2002; Calcagno,







72

6.RESULTS 36 Table 2.6.1: Biology Courses: SAT Students: Grade A

Course Level400 300 200 100

Number ofObservations 1957 4774 1255 7128

Covariance Parameter Estimates Cov Parm Estimate Estimate Estimate Estimate

Residual 0.1693 0.1702 0.1446 0.1278

Fit Statistics -2 Res LogLikelihood

2169.2 5181 1220.2 5567.9

AIC 2171.2 5183 1222.2 5569.9AICC 2171.2 5183 1222.2 5569.9BIC 2176.8 5189.5 1227.3 5576.8

Variable Estimate StandardError Estimate Standard

Error Estimate StandardError Estimate Standard

Error

Intercept -1.5439 0.1533 -1.0250 0.1168 -1.6041 0.3205 -1.4200 0.1743

High School GPA -0.0004 0.000519 0.0003 0.0003 0.0010 0.0006 0.0001 0.0002

SAT Verbal 0.0006 0.0001 0.0003 0.0001 0.0007 0.0002 0.0007 0.0001

SAT Math 0.000287 0.000155 0.0005 0.0001 0.0005 0.0002 0.0006 0.0001

Fulltime -0.0457 0.08503 0.1227 0.0717 0.2451 0.2706 0.0246 0.1608

Offcampus -0.02371 0.02004 0.0268 0.0124 0.0645 0.0243 0.0178 0.0142

Female 0.0897 0.0196 0.0314 0.0124 0.0525 0.0282 0.0051 0.0092

Other 0.02303 0.02714 -0.0274 0.0179 0.0201 0.0330 0.0250 0.0139

Black -0.2055 0.04249 -0.1431 0.0296 -0.0242 0.0424 -0.0320 0.0173

Hispanic -0.1072 0.04429 -0.1174 0.0294 0.0223 0.0491 -0.0177 0.0187

Asian -0.06933 0.02567 -0.1271 0.0156 -0.0583 0.0293 -0.0354 0.0113

Average Grade 0.4797 0.01779 0.2264 0.0212 0.2698 0.0444 0.2947 0.0203

Instructor Gender -0.00476 0.02134 -0.0451 0.0133 0.0875 0.0485 -0.0184 0.0103

First Major 0.0670 0.0260 0.0902 0.0095

Degree Major 0.05087 0.02561 0.0427 0.0213

Tests of Fixed Effects

Effect F Value Pr > F F Value Pr > F F Value Pr > F F Value Pr > FHigh School GPA 0.59 0.44 0.93 0.33 2.97 0.08 0.41 0.52

SAT Verbal 18.97 <.0001 15.14 0.00 20.28 <.0001 144.06 <.0001

SAT Math 3.43 0.06 23.09 <.0001 6.97 0.01 83.31 <.0001

Fulltime 0.29 0.59 2.93 0.09 0.82 0.37 0.02 0.88

Offcampus 1.40 0.24 4.69 0.03 7.03 0.01 1.57 0.21

Female 21.05 <.0001 6.40 0.01 3.46 0.06 0.31 0.58

Other 0.72 0.40 2.33 0.13 0.37 0.54 3.24 0.07

Black 23.39 <.0001 23.32 <.0001 0.32 0.57 3.45 0.06

Hispanic 5.86 0.02 15.89 <.0001 0.21 0.65 0.90 0.34

Asian 7.29 0.01 66.11 <.0001 3.96 0.05 9.81 0.00

Average Grade 727.41 <.0001 114.19 <.0001 36.93 <.0001 211.33 <.0001

Instructor Gender 0.05 0.82 11.47 0.00 3.26 0.07 3.23 0.07

First Major 6.63 0.01 90.22 <.0001

Degree Major 3.94 0.05 4.04 0.04

36 For all the results reported in Section 6, shaded and bolded cells refers to significance at 1%level and a shaded cell refers to significance at 5% level.



73

Table 2.6.2: Biology Courses: AP Students: Grade ACourse Level 400 300 200 100

Number ofObservations

1200 2797 437 1976

Covariance ParameterEstimates

Cov Parm Estimate Estimate Estimate EstimateResidual 0.1812 0.1984 0.1804 0.1579

Fit Statistics

-2 Res LogLikelihood

1455.1 3525.4 557.4 2066.9

AIC 1457.1 3527.4 559.4 2068.9AICC 1457.1 3527.4 559.4 2068.9BIC 1462.2 3533.3 563.4 2074.5

Effect Estimate StandardError

Estimate StandardError



Intercept -1.0868 0.2378 -1.3349 0.1817 -0.7332 0.4881 -1.201 0.3297High School GPA -0.00024 0.000695 -0.00063 0.000525 0.001254 0.00138 0.000255 0.000532

SAT Verbal 0.000254 0.000221 0.000271 0.000145 -0.00076 0.000369 0.000221 0.000157SAT Math 0.00028 0.00022 0.000515 0.000155 0.000218 0.000335 0.000296 0.00017

AP Biology 0.02207 0.01443 0.06145 0.009886 0.1208 0.02334 0.06234 0.01106AP Calculus AB 0.02216 0.006232AP Calculus BC 0.04281 0.01095

AP Physics B -0.00368 0.01194 0.01817 0.008119AP Chemistry 0.01126 0.01045 -0.01469 0.007351

Fulltime -0.1325 0.1303 0.1513 0.09577 0.2437 0.3059 0.1947 0.2824Offcampus -0.00088 0.02563 0.02001 0.01738 0.0374 0.04781 0.03104 0.03317

Female 0.003144 0.02536 0.0623 0.01737 0.001886 0.05051 -0.01199 0.0193Other 0.03107 0.03432 -0.1066 0.02601 -0.1023 0.06921 0.004253 0.03054Black -0.1439 0.07414 -0.1896 0.05251 -0.1501 0.1162 -0.07244 0.04351

Hispanic -0.1916 0.08097 -0.08347 0.04898 -0.08966 0.1281 -0.05544 0.04539Asian -0.06003 0.03295 -0.1137 0.02099 -0.1168 0.05078 -0.04416 0.02214

Average Grade 0.4322 0.0229 0.2792 0.02938 0.216 0.08036 0.249 0.04129

Instructor Gender -0.06309 0.02851 0.005986 0.01879 -0.08141 0.1077 -0.04854 0.02251First Major 0.06711 0.02013 0.09852 0.01882Second Major -0.1033 0.04193 -0.3945 0.2184

Tests of Fixed EffectsEffect F Value Pr > F F Value Pr > F F Value Pr > F F Value Pr > F

High School GPA 0.12 0.73 1.46 0.23 0.82 0.36 0.23 0.63SAT Verbal 1.31 0.25 3.50 0.06 4.21 0.04 1.98 0.16SAT Math 1.62 0.20 11.06 0.00 0.42 0.52 3.04 0.08

AP Biology 2.34 0.13 38.63 <.0001 26.81 <.0001 31.79 <.0001AP Calculus AB 12.64 0.00AP Calculus BC 15.29 <.0001

AP Physics B 0.10 0.76 5.01 0.03AP Chemistry 1.16 0.28 3.99 0.05

Fulltime 1.03 0.31 2.50 0.11 0.63 0.43 0.48 0.49Offcampus 0.00 0.97 1.33 0.25 0.61 0.43 0.88 0.35

Female 0.02 0.90 12.87 0.00 0.00 0.97 0.39 0.53Other 0.82 0.37 16.80 <.0001 2.18 0.14 0.02 0.89Black 3.77 0.05 13.03 0.00 1.67 0.20 2.77 0.10

Hispanic 5.60 0.02 2.90 0.09 0.49 0.48 1.49 0.22Asian 3.32 0.07 29.33 <.0001 5.29 0.02 3.98 0.05

Average Grade 356.19 <.0001 90.34 <.0001 7.23 0.01 36.35 <.0001Instructor Gender 4.90 0.03 0.10 0.75 0.57 0.45 4.65 0.03

First Major 11.11 0.00 27.40 <.0001Second Major 6.07 0.01 3.26 0.07



74

Table 2.6.3: Chemistry Courses: SAT Students: Grade ACourse Level 400 300 200 100


Covariance Parameter EstimatesEstimate Estimate Estimate Estimate

Residual 0.1887 0.1958 0.1887 0.1538

Fit Statistics-2 Res LogLikelihood

1446.9 5235.9 2807.9 7081.3

AIC 1448.9 5237.9 2809.9 7083.3AICC 1448.9 5237.9 2809.9 7083.3BIC 1454 5244.3 2815.6 7090.2



ErrorIntercept -2.0337 0.2272 -1.1627 0.1423 -1.0494 0.2341 -1.3879 0.1628

High School GPA -0.0008 0.0004 0.0000 0.0003 0.0002 0.0004 0.0006 0.0002SAT Verbal 0.0002 0.0002 -0.0001 0.0001 0.0001 0.0001 0.0001 0.0001SAT Math 0.0007 0.0002 0.0008 0.0001 0.0013 0.0002 0.0014 0.0001Fulltime 0.1217 0.1070 0.1369 0.1115 0.1339 0.1788 -0.0401 0.1490

Offcampus -0.0831 0.0276 -0.0728 0.0147 -0.0187 0.0220 0.0167 0.0165Female 0.0230 0.0274 0.0002 0.0140 -0.0126 0.0189 0.0085 0.0097Other -0.0801 0.0415 -0.0285 0.0209 -0.0013 0.0277 0.0199 0.0149Black -0.1804 0.0652 -0.1918 0.0319 -0.0770 0.0405 -0.0002 0.0201

Hispanic -0.1216 0.0781 -0.0802 0.0354 -0.0782 0.0435 -0.0412 0.0222Asian -0.0586 0.0311 -0.0742 0.0168 -0.0545 0.0229 0.0104 0.0120

Average Grade 0.6012 0.0363 0.3495 0.0120 0.1283 0.0376 0.2446 0.0166Instructor Gender 0.0289 0.0326 -0.0434 0.0246 -0.0587 0.0194 0.0066 0.0156

First Major 0.0561 0.0319 0.1615 0.0253Second Major -0.1230 0.0426Degree Major 0.0364 0.0357


High School GPA 3.31 0.07 0.00 0.96 0.23 0.63 6.25 0.01SAT Verbal 1.81 0.18 0.23 0.63 0.41 0.52 1.44 0.23SAT Math 11.60 0.00 50.18 <.0001 76.88 <.0001 366.71 <.0001Fulltime 1.29 0.26 1.51 0.22 0.56 0.45 0.07 0.79

Offcampus 9.08 0.00 24.66 <.0001 0.72 0.40 1.03 0.31Female 0.70 0.40 0.00 0.99 0.44 0.51 0.76 0.38Other 3.73 0.05 1.86 0.17 0.00 0.96 1.78 0.18Black 7.65 0.01 36.19 <.0001 3.62 0.06 0.00 0.99

Hispanic 2.42 0.12 5.14 0.02 3.24 0.07 3.46 0.06Asian 3.55 0.06 19.48 <.0001 5.64 0.02 0.76 0.38


First Major 3.10 0.08 40.82 <.0001Second Major 8.32 0.00Degree Major 1.04 0.31



75

Table 2.6.4: Chemistry Courses: AP Students: Grade ACourse Level 400 300 200 100


538 931 468 608

Covariance Parameter EstimatesCov Parm Estimate Estimate Estimate Estimate

Residual 0.1853 0.2069 0.2096 0.2021

Fit Statistics


693.9 1260.7 677.5 835.9

AIC 695.9 1262.7 679.5 837.9

AICC 695.9 1262.7 679.5 837.9

BIC 700.2 1267.5 683.6 842.3

Effect Estimate StandardError




Intercept -2.1223 0.3599 -1.0655 0.3421 -0.8294 0.3880 -0.8746 0.3192High School GPA -0.0017 0.0012 0.0005 0.0012 0.0003 0.0015 0.0024 0.0011

SAT Verbal 0.0005 0.0002 0.0000 0.0002 0.0001 0.0003 -0.0008 0.0003SAT Math 0.0005 0.0003 0.0004 0.0003 0.0009 0.0004 0.0005 0.0004

AP Chemistry -0.0007 0.0198 0.0589 0.0150 0.1076 0.0213 0.1513 0.0239AP Biology -0.0262 0.0113

AP Calculus AB 0.0269 0.0110 0.0516 0.0117AP Calculus BC 0.0515 0.0154

AP Physics B 0.0438 0.0108Fulltime 0.0046 0.1560 0.0803 0.2289

Offcampus 0.0172 0.0405 -0.0792 0.0344 0.0543 0.0639 -0.1156 0.1042Female 0.1218 0.0406 0.0496 0.0322 0.0345 0.0450 0.0378 0.0395Other -0.1063 0.0798 -0.1233 0.0543 -0.1345 0.0790 -0.0597 0.0659Black 0.0109 0.1365 -0.0215 0.1070 0.0281 0.1532 -0.1041 0.1045

Hispanic -0.1189 0.1826 -0.2162 0.1467 -0.2200 0.2085 -0.1507 0.1101Asian -0.0917 0.0446 -0.0689 0.0352 -0.1052 0.0500 -0.0240 0.0435

Average Grade 0.6512 0.0515 0.3303 0.0287 0.1089 0.0774 0.3119 0.0692Instructor Gender -0.0352 0.0517 0.0872 0.0534 -0.0691 0.0502 -0.0231 0.0641

First Major -0.1112 0.0411 -0.1346 0.0331 -0.1405 0.0503 0.1313 0.0581


SAT Verbal 5.34 0.02 0.06 0.80 0.04 0.85 9.46 0.00SAT Math 2.38 0.12 1.45 0.23 4.40 0.04 1.71 0.19

AP Chemistry 0.00 0.97 15.51 <.0001 25.44 <.0001 40.09 <.0001AP Biology 5.40 0.02

AP Calculus AB 5.96 0.02 19.53 <.0001AP Calculus BC 11.16 0.00

AP Physics B 16.51 <.0001Fulltime 0.00 0.98 0.12 0.73

Offcampus 0.18 0.67 5.31 0.02 0.72 0.40 1.23 0.27

Female 8.98 0.00 2.37 0.12 0.59 0.44 0.92 0.34Other 1.78 0.18 5.17 0.02 2.90 0.09 0.82 0.37Black 0.01 0.94 0.04 0.84 0.03 0.85 0.99 0.32

Hispanic 0.42 0.52 2.17 0.14 1.11 0.29 1.88 0.17Asian 4.23 0.04 3.83 0.05 4.43 0.04 0.31 0.58


First Major 7.31 0.01 16.52 <.0001 7.80 0.01 5.11 0.02



76

Table 2.6.5: English Courses: SAT Students: Grade A

Course Level 400 300 200 100


Covariance Parameter Estimates

Cov Parm Estimate Estimate Estimate Estimate

Residual 0.1717 0.2123 0.1964 0.2006

Fit Statistics


1367.8 5948.8 4697.1 12101.2

AIC 1369.8 5950.8 4699.1 12103.2

AICC 1369.8 5950.8 4699.1 12103.2

BIC 1374.9 5957.3 4705.3 12110.4

Effect Estimate StandardError Estimate Standard


Error

Intercept -1.9134 0.2026 -2.2482 0.1686 -2.6490 0.1997 -2.6091 0.1635

High School GPA 0.0010 0.0006 0.0013 0.0004 0.0007 0.0004 0.0007 0.0002

SAT Verbal 0.0009 0.0002 0.0010 0.0001 0.0010 0.0001 0.0010 0.0001

SAT Math 0.0001 0.0002 -0.0001 0.0001 0.0001 0.0001 0.0001 0.0001Fulltime -0.0054 0.1170 0.3183 0.1237 0.1976 0.1575 -0.0930 0.1428

Offcampus -0.1069 0.0261 -0.0815 0.0143 -0.0581 0.0149 -0.0380 0.0168

Female 0.0773 0.0263 0.1017 0.0146 0.0771 0.0157 0.0954 0.0096

Other -0.0428 0.0321 0.0003 0.0196 0.0066 0.0212 0.0260 0.0149

Black -0.2115 0.0502 -0.1246 0.0296 -0.1608 0.0288 -0.0441 0.0212

Hispanic -0.1025 0.0566 -0.1085 0.0296 -0.1395 0.0304 -0.0755 0.0193

Asian -0.0525 0.0437 -0.0276 0.0220 -0.0543 0.0241 -0.0342 0.0127

Average Grade 0.5409 0.0308 0.5105 0.0276 0.6628 0.0293 0.7177 0.0178

Instructor Gender 0.0249 0.0247 0.0958 0.0161 0.0239 0.0145 0.0084 0.0092Degree Major 0.0586 0.0255

Tests of Fixed Effects


SAT Verbal 24.26 <.0001 85.34 <.0001 79.82 <.0001 224.59 <.0001

SAT Math 0.22 0.64 0.26 0.61 0.32 0.57 0.80 0.37

Fulltime 0.00 0.96 6.62 0.01 1.57 0.21 0.42 0.52

Offcampus 16.72 <.0001 32.34 <.0001 15.14 0.00 5.12 0.02

Female 8.68 0.00 48.29 <.0001 24.13 <.0001 98.90 <.0001

Other 1.78 0.18 0.00 0.99 0.10 0.76 3.05 0.08

Black 17.75 <.0001 17.74 <.0001 31.17 <.0001 4.34 0.04Hispanic 3.28 0.07 13.45 0.00 21.11 <.0001 15.26 <.0001

Asian 1.45 0.23 1.58 0.21 5.07 0.02 7.26 0.01

Average Grade 308.10 <.0001 342.55 <.0001 513.35 <.0001 1619.70 <.0001

Instructor Gender 1.02 0.31 35.28 <.0001 2.73 0.10 0.82 0.37

Degree Major 5.26 0.02



77

Table 2.6.6: English Courses: AP Students: Grade A

Course Level 400 300 200 100Number of

Observations865 2367 2160 3717

Cov Parm Estimate Estimate

Estimate Estimate

Residual 0.1605 0.21 0.2123 0.2004Fit Statistics


962.5 3122.7 2881.1 4679.6

AIC 964.5 3124.7 2883.1 4681.6

AICC 964.5 3124.7 2883.1 4681.6

BIC 969.2 3130.5 2888.8 4687.8

Effect Estimate Standar d Error

Estimate

Standar d Error

Estimate Standar d Error

Estimate Standar d Error

Intercept -1.5833 0.3090 -1.0990 0.2838 -2.3628 0.2630 -2.4559 0.1392

High School GPA -0.0003 0.0007 -0.0002 0.0005 -0.0001 0.0006 0.0008 0.0004

SAT Verbal 0.0003 0.0003 0.0007 0.0002 0.0013 0.0002 0.0009 0.0001

SAT Math 0.0003 0.0002 -0.0002 0.0002 0.0001 0.0002 0.0001 0.0001

AP EnglishLanguage 0.0009 0.0095 0.0189 0.0068 0.0071 0.0074 0.0098 0.0059

AP EnglishLiterature

0.0408 0.0132 0.0316 0.0090 0.0328 0.0097 0.0381 0.0076

Fulltime 0.2077 0.2036 -0.4131 0.2300 0.2226 0.1755

Offcampus -0.0301 0.0282 -0.0445 0.0195 -0.0248 0.0220 -0.1447 0.0348

Female 0.0330 0.0322 0.0850 0.0215 0.0497 0.0231 0.0831 0.0163

Other 0.0194 0.0356 0.0157 0.0254 0.0032 0.0272 -0.0297 0.0236

Black 0.0853 0.0748 -0.1059 0.0488 -0.1308 0.0484 -0.0187 0.0438

Hispanic -0.0793 0.0802 -0.0803 0.0501 -0.1272 0.0552 -0.0902 0.0394

Asian -0.0077 0.0439 -0.0425 0.0307 -0.0447 0.0322 -0.0214 0.0216

Average Grade 0.4541 0.0420 0.4960 0.0359 0.5440 0.0430 0.6626 0.0291Instructor Gender 0.0020 0.0285 0.0693 0.0233 -0.0189 0.0201 -0.0037 0.0150

First Major 0.0576 0.0200

Second Major 0.0358 0.0298

Degree Major 0.0256 0.0344 0.0357 0.0337Tests of Fixed Effects


SAT Verbal 1.61 0.20 14.85 0.00 48.51 <.0001 43.30 <.0001

SAT Math 1.49 0.22 1.23 0.27 0.11 0.74 0.31 0.58

AP EnglishLanguage

0.01 0.92 7.78 0.01 0.93 0.34 2.76 0.10

AP EnglishLiterature

9.56 0.00 12.44 0.00 11.52 0.00 25.30 <.0001

Fulltime 1.04 0.31 3.23 0.07 1.61 0.20

Offcampus 1.13 0.29 5.20 0.02 1.28 0.26 17.34 <.0001

Female 1.05 0.31 15.60 <.0001 4.61 0.03 26.04 <.0001Other 0.30 0.59 0.38 0.54 0.01 0.91 1.59 0.21

Black 1.30 0.25 4.70 0.03 7.30 0.01 0.18 0.67

Hispanic 0.98 0.32 2.58 0.11 5.31 0.02 5.25 0.02

Asian 0.03 0.86 1.92 0.17 1.93 0.17 0.99 0.32

Average Grade 117.20 <.0001 190.74 <.0001 159.96 <.0001 517.47 <.0001Instructor Gender 0.00 0.94 8.82 0.00 0.89 0.35 0.06 0.80

First Major 8.30 0.00Second Major 1.44 0.23Degree Major 0.56 0.46 1.00 2351.00



78

Table 2.6.7: Math Courses: SAT Students: Grade A

Course Level 400 300 200 100


Covariance Parameter Estimates


Residual 0.1568 0.1318 0.0865 0.1341

Fit Statistics

-2 Res LogLikelihood 618.8 2051.7 2849

5751.3

AIC 620.8 2053.7 2851 5753.3

AICC 620.8 2053.7 2851 5753.3

BIC 625.1 2059.5 2857.9 5760.1

Variable Estimate Standard

ErrorEstimate Standard



ErrorIntercept -0.7190 0.4280 -0.4722 0.1306 -0.3133 0.0989 -0.7037 0.1186

High School GPA -0.0007 0.0006 -0.0014 0.0003 -0.0005 0.0002 0.0002 0.0002SAT Verbal 0.0002 0.0002 -0.0005 0.0001 -0.0004 0.0000 -0.0003 0.0001

SAT Math 0.0000 0.0002 0.0006 0.0001 0.0005 0.0000 0.0006 0.0001

Fulltime 0.1505 0.3984 0.0846 0.1106 0.1205 0.0934 -0.0031 0.1108Offcampus -0.0008 0.0364 -0.0471 0.0158 -0.0239 0.0102 -0.0099 0.0114

Female -0.0306 0.0360 -0.0254 0.0181 0.0266 0.0074 0.0260 0.0093Ethnicity Dummy

Other -0.0081 0.0495 0.0003 0.0211 0.0101 0.0113 0.0167 0.0150Black -0.1918 0.0997 -0.0925 0.0375 -0.0644 0.0149 -0.0535 0.0151

Hispanic -0.1376 0.0881 -0.0608 0.0335 -0.0494 0.0150 -0.0422 0.0140Asian -0.0155 0.0462 -0.0318 0.0203 0.0189 0.0092 -0.0130 0.0142

Average Grade 0.2688 0.0420 0.2245 0.0171 0.1150 0.0109 0.2861 0.0110Instructor Gender 0.0390 0.0574 0.0251 0.0232 -0.0071 0.0076 0.0274 0.0096


Third Major 0.0764 0.0293


High School GPA 1.24 0.2652 22.04 <.0001 10.67 0.0011 0.83 0.3632SAT Verbal 1.17 0.2797 29.71 <.0001 72.77 <.0001 27.43 <.0001SAT Math 0.02 0.8832 51.39 <.0001 104.71 <.0001 86.86 <.0001Fulltime 0.14 0.7057 0.59 0.4444 1.67 0.1968 0.00 0.9778

Offcampus 0 0.9822 8.95 0.0028 5.49 0.0191 0.76 0.3820

Female 0.73 0.3948 1.96 0.1618 13.07 0.0003 7.81 0.0052Other 0.03 0.8707 0 0.9901 0.81 0.3682 1.25 0.2638Black 3.7 0.055 6.1 0.0136 18.80 <.0001 12.50 0.0004

Hispanic 2.44 0.119 3.29 0.07 10.80 0.0010 9.15 0.0025Asian 0.11 0.7376 2.46 0.1172 4.26 0.0389 0.84 0.3605






79

Table 2.6.8: Math Courses:AP Students:Grade ACourse Level 400 300 200 100


786 29843354 1121

Covariance ParameterEstimatesCov Parm Estimate Estimate Estimate EstimateResidual 0.1895 0.1795 0.1492 0.2088


1014.83459.2

3269.11519.3

AIC (smaller isbetter)

1016.83461.2

3271.11521.3

AICC (smaller isbetter)

1016.83461.2

3271.11521.3

BIC (smaller isbetter)

1021.53467.2

3277.21526.3

Variable Estimate Standard




ErrorIntercept -0.9593 0.3676 -1.3841 0.1824 -0.6287 0.1914 -1.4403 0.5100High School GPA 0.0011 0.0010 -0.0004 0.0004 -0.0006 0.0004 0.0017 0.0008

SAT Verbal 0.0006 0.0002 -0.0002 0.0001 -0.0004 0.0001 0.0000 0.0002SAT Math -0.0001 0.0004 0.0008 0.0001 0.0006 0.0001 0.0006 0.0002

AP Calculus BC 0.0574 0.0128 0.0489 0.0064 0.0357 0.0054 0.0691 0.0116AP Calculus AB 0.0756 0.0139 0.0783 0.0069 0.0890 0.0075 0.0949 0.0155

AP Statistics -0.0037 0.0133 -0.0045 0.0072 0.0147 0.0072 0.1087 0.0261AP Biology 0.0098 0.0040

AP Chemistry 0.0225 0.0121 0.0156 0.0055 0.0037 0.0055 0.0356 0.0142Fulltime -0.3184 0.2540 0.2403 0.1512 0.1241 0.1736 0.2848 0.4608

Offcampus -0.0718 0.0336 -0.0076 0.0186 0.0271 0.0259 -0.0485 0.0390Female -0.0042 0.0349 0.0544 0.0181 0.0844 0.0142 0.1140 0.0285

Ethnicity DummyOther -0.0285 0.0465 0.0307 0.0229 0.0066 0.0222 -0.0311 0.0445Black 0.3806 0.2291 0.0188 0.0918 -0.0442 0.0500 -0.0184 0.0897

Hispanic -0.1993 0.1683 -0.0159 0.0598 -0.0538 0.0426 -0.0629 0.0768Asian -0.0705 0.0404 0.0260 0.0195 -0.0122 0.0161 -0.0060 0.0343

Average Grade 0.3585 0.0367 0.3043 0.0203 0.1855 0.0195 0.2747 0.0519Instructor Gender 0.0379 0.0541 0.0081 0.0247 0.0447 0.0154 0.0391 0.0357



High School GPA 1.25 0.26 0.75 0.39 2.80 0.09 4.51 0.03SAT Verbal 8.11 0.00 2.77 0.10 14.93 0.00 0.03 0.86SAT Math 0.04 0.84 33.62 <.0001 27.03 <.0001 6.93 0.01

AP Calculus BC 20.21 <.0001 58.45 <.0001 44.55 <.0001 35.56 <.0001AP Calculus AB 29.45 <.0001 129.81 <.0001 140.29 <.0001 37.34 <.0001

AP Statistics 0.08 0.78 0.38 0.54 4.17 0.04 17.29 <.0001AP Biology 5.99 0.01

AP Chemistry 3.45 0.06 7.90 0.01 0.45 0.50 6.32 0.01Fulltime 1.57 0.21 2.52 0.11 0.51 0.47 0.38 0.54

Offcampus 4.56 0.03 0.17 0.68 1.10 0.29 1.55 0.21Female 0.01 0.90 9.06 0.00 35.57 <.0001 16.02 <.0001

Ethnicity DummyOther 0.37 0.54 1.80 0.18 0.09 0.77 0.49 0.48Black 2.76 0.10 0.04 0.84 0.78 0.38 0.04 0.84

Hispanic 1.4 0.24 0.07 0.79 1.59 0.21 0.67 0.41Asian 3.04 0.08 1.79 0.18 0.57 0.45 0.03 0.86





80

Table 2.6.9: Physics Courses: SAT Students: Grade ACourse Level 400 300 200 100


181 270 47 4442

Covariance Parameter EstimatesCov Parm Estimate Estimate Estimate EstimateResidual 0.1891 0.2129 0.1528 0.1435


264 402.9 86.5 4078.4

AIC 266 404.9 88.5 4080.4AICC 266 405 88.7 4080.4BIC 269.1 408.5 90.1 4086.8

Variable Estimate SE Estimate SE Estimate SE Estimate SE

Intercept -2.8951 0.5349 -1.5520 0.6000 -0.9011 0.6761 -0.8046 0.1122High School GPA 0.0001 0.0024 -0.0024 0.0012 -0.0043 0.0030 -0.0007 0.0003

SAT Verbal 0.0007 0.0005 0.0001 0.0004 0.0029 0.0008 -0.0004 0.0001SAT Math -0.0001 0.0005 0.0007 0.0004 -0.0023 0.0008 0.0007 0.0001Fulltime 0.6627 0.2596 0.1471 0.4724 0.0328 0.0925

Offcampus 0.1428 0.0765 -0.0588 0.0587 -0.1577 0.1301 0.0178 0.0134Female 0.0384 0.0800 0.0906 0.0701 -0.2653 0.1352 -0.0015 0.0128Other -0.1619 0.1147 0.0293 0.0848 -0.0593 0.1709 -0.0356 0.0174Black -0.5283 0.2481 -0.1387 0.0277

Hispanic 0.2185 0.1696 0.1634 0.1412 0.0792 0.3048 -0.0720 0.0308Asian -0.0344 0.1091 -0.0914 0.0926 0.1838 0.1887 -0.0020 0.0145

Average Grade 0.6388 0.1002 0.4445 0.1070 0.4977 0.1775 0.3120 0.0208Instructor Gender -0.5759 0.4681 -0.1037 0.0631

First Major 0.2201 0.0851Second Major 0.1571 0.0755 0.1737 0.0616 0.1008 0.1327


High School GPA 0.00 0.97 3.90 0.05 2.04 0.16 6.07 0.01SAT Verbal 1.71 0.19 0.04 0.84 15.06 0.00 26.63 <.0001SAT Math 0.06 0.81 2.95 0.09 8.41 0.01 85.42 <.0001Fulltime 6.52 0.01 0.10 0.76 0.13 0.72

Offcampus 3.49 0.06 1.00 0.32 1.47 0.23 1.77 0.18Female 0.23 0.63 1.67 0.20 3.85 0.06 0.01 0.91Other 1.99 0.16 0.12 0.73 0.12 0.73 4.16 0.04Black 4.53 0.03 25.18 <.0001

Hispanic 1.66 0.20 1.34 0.25 0.07 0.80 5.46 0.02Asian 0.10 0.75 0.98 0.32 0.95 0.34 0.02 0.89

Average Grade 40.67 <.0001 17.25 <.0001 7.86 0.01 225.66 <.0001Instructor Gender 1.51 0.22 2.70 0.10

First Major 6.68 0.01Second Major 4.33 0.04 7.96 0.01 0.58 0.45



81

Table 2.6.10: Physics Courses: AP Students: Grade ACourse Level 400 300 200 100

Number ofObservations Used

72 136 25 891


Residual 0.2039 0.1921 0.09096 0.2016


131.2 212.7 50.9 1173.8

AIC 133.2 214.7 52.9 1175.8AICC 133.2 214.8 53.2 1175.8BIC 135.3 217.6 53.6 1180.5

Effect Estimate SE Estimate SE Estimate SE Estimate SE

Intercept -2.3947 1.2509 0.1604 0.6013 -1.3453 1.1519 -0.7741 0.1967High School GPA -0.0020 0.0050 -0.0038 0.0020 -0.0074 0.0057 -0.0011 0.0007

SAT Verbal 0.0013 0.0011 0.0020 0.0006 0.0028 0.0010 -0.0002 0.0002SAT Math 0.0004 0.0014 -0.0022 0.0006 0.0018 0.0015 0.0010 0.0002

AP Physics C-Mech 0.0325 0.0198 -0.1590 0.0402 0.0358 0.0113AP Physics C-E&M -0.0470 0.0432

FulltimeOffcampus 0.1803 0.1375 0.0115 0.0828 -0.0447 0.1814 0.0824 0.0408

Female -0.1512 0.2183 -0.1156 0.1074 -0.2420 0.1856 -0.0094 0.0352Other 0.2506 0.3730 0.0982 0.1540 0.3295 0.4160 -0.0115 0.0509Black -0.2568 0.1852

Hispanic 0.0066 0.0927Asian 0.2044 0.1443 0.0663 0.1045 -0.0023 0.1872 0.1061 0.0364

Average Grade 0.5253 0.1737 0.2291 0.1337 -0.1300 0.1914 0.2203 0.0543Instructor Gender 0.2408 0.3229 -0.2365 0.2636


High School GPA 0.16 0.69 3.55 0.06 1.73 0.21 2.47 0.12SAT Verbal 1.36 0.25 12.68 0.00 8.09 0.01 1.02 0.31SAT Math 0.08 0.77 13.21 0.00 1.40 0.25 21.07 <.0001

AP Physics C-Mech 2.70 0.10 15.69 0.00 10.04 0.00AP Physics C-E&M 1.18 0.28

FulltimeOffcampus 1.72 0.19 0.02 0.89 0.06 0.81 4.07 0.04

Female 0.48 0.49 1.16 0.28 1.70 0.21 0.07 0.79Other 0.45 0.50 0.41 0.53 0.63 0.44 0.05 0.82Black 1.92 0.17

Hispanic 0.01 0.94Asian 2.01 0.16 0.40 0.53 0.00 0.99 8.51 0.00

Average Grade 9.15 0.00 2.94 0.09 0.46 0.51 16.46 <.0001Instructor Gender 0.56 0.46 0.81 0.37



82


Biology Courses

SAT Students : SAT scores are positively significant until 300 level courses and only SAT verbal

score is significant at the 400 level. High School GPA is not at all significant even though

positive except at 400 level. Being a female (staying off-campus) brings in good grades and they

are significant at 400 and 300 (300 and 200) level courses. Being a non-white lowers your

chances of getting the top grade in Biology courses. Average grade in the course is the only

variable other than SAT Verbal score that is significantly positive throughout. It has the largest t-

statistic showing that it has the most explanatory power. Having a female instructor at 300 level

courses will lower student’s grades keeping other things same. If Biology is a student’s first

major (degree major) it improves his performance for 100 and 200 (300 and 400) level courses.

The interaction of major terms was not found to be significant. Fixed effects were found to be

significant for the SAT scores and average grade in course irrespective of the course levels

providing evidence that the SAT scores are very much dependent on the high school a student

attends and average grade in courses varies over time.

AP students : SAT scores lose their significance once AP grades are introduced in the model for

100 and 400 level courses. AP Biology grades are positive at all course levels but significant until

300 course level. Having AP grades in mathematics help improve one’s performance in lower

level courses but for upper level courses, AP grades in physics (chemistry) are positively

(negatively) correlated with course grades. Female students are expected to perform better than

their male peers. Non-whites are lagging behind whites in biology courses. Average grade in

course has the highest t-statistic throughout. Female instructors lower student’s performance.

Having Biology as first major (second major) increases chances of getting a good grade in 100

and 300 (200 and 400) level courses. Degree major was significant but less significant than first



83

major and second major for 300 and 400 level courses respectively. Interaction terms were not

significant AP students. AP Biology grade and average grade in course have significant fixed

effect again providing evidence that participation and performance in AP exams is significantly

dependent on high schools AP curriculum.

Chemistry Courses

SAT students : High School GPA is positively significant at 100 level courses only. SAT Math

score is positively significant throughout while SAT Verbal score is not significant at all. Living

off-campus, being non-white and having a female instructor harms ones chances of getting A in

Chemistry. Having academically good peers improves ones performance in class. If Chemistry is

a student’s first major he or she performs well in 100, 200 level courses, while declaring

Chemistry as second major (degree major) improves student’s performance in 300 (400) level

courses. Average grade in course and SAT Math score continue to have significant fixed effects.

AP students : As for SAT students, high school GPA is significant at 100 level. SAT scores are

not significant for all course levels except SAT verbal score for 100 and 400 level and the sign

switches from negative to positive as one move up the course level. AP Chemistry is positively

significant until 300 course level and turns negative (not significant) at 400 course level. Having

AP Biology (Mathematics, Physics) grade lowers (raises, raises) 200 level (100 and 200 level,

300 level) course grades in Chemistry. One interesting result is that for 100 and 200 level

Chemistry courses there are no part-time students. The result for staying off-campus and being a

female are same as for SAT students. Being a non-white does not significantly reduce chances of

getting A in Chemistry except if you are an Asian taking 400 and 200 level courses. Higher class

grade average pushes up student’s potential performance. First major is the only one significant

or relatively more significant than second or degree major for all course levels. The surprising





85

throughout only for SAT students taking English courses. It shows that high school courses are

not very science or math intensive. High School GPA is a weighted average of all the courses

taken in high school and there is no information available on its breakup. Another explanation is

that the kind of curriculum followed by high schools is not very closely related to kind of course

topics covered in college courses. Hence there is definite break-up in the linkage between high

school and college courses when it comes to SM courses.

Mathematics Courses

SAT Students : High School GPA (SAT Verbal, SAT Math) is significantly negative (negative,

positive) except at 100 and 400 (400, 400) level courses. Living off-campus lowers performance

and females perform better than males at lower course levels. Non-white students lag behind

white students except Asian students perform better only at 200 level. The sign on gender of

instructor is positive (except at 200 level) but significant only at 100 level. Third Major enters as

explanatory variable only in case of Math courses because declaring math as first major is a rare

phenomenon. Students are most likely to declare math as their second or third major and their

influence is significantly positive at 200 and 300 level courses respectively. Fixed effects are

significant for SAT scores and average grade in course. Average grade in course has the highest t-

statistic.

AP Students : The sign on High School GPA (SAT Verbal, SAT Math) is positive (positive,

positive) except at 200 and 300 levels (200 level, 400 level). High School GPA (SAT Verbal;

SAT Math) is significant at 100 level (200 and 400 levels; 100, 200 and 300 levels) only. AP

grades in Mathematics enter the regression together because of their low correlation among

themselves. AP grades in Calculus are positively significant throughout unlike the significance of

AP grades in physical sciences when it came to science courses. AP Statistics is positively









89

Other variables introduced were interaction of student and instructor gender dummy

variables with “percent female” variable. The idea was to look into the fact whether being a

female student (instructor) and sitting in a (teaching a) course which has large number of females

would improve that student’s performance. The surprising result was that the interaction terms

were not significant. The results of percent female model are reported in the appendix. They point

out that having more females in math and biology courses improves a student’s performance

irrespective of the student’s gender. The positive coefficient on student gender dummy for math

and biology courses show that females perform better than males in class. Hence having more

women in a class would raise the average performance and extort all students irrespective of

gender to perform better. Therefore there is a gender peer effect working here. The negative sign

for percent female variable in case of 300 level math courses is not what I expected. I do not

know the reason for such a result.





91

Time to Degree of Different Kinds of Transfer Students

Esha Sinha

Abstract

This chapter analyzes time to degree of non-transfer students and transfer students-horizontal, vertical and reverse. The aim is to understand the impact of various kinds oftransfer process on time to degree. Two longitudinal datasets have been used in this

study. Both are student-period datasets, one following the educational pathway of students enrolled in 4-year research intensive university; the second is a survey on arandomly selected group of individuals, documenting their transition from school towork. The results of the regressions ran on two different datasets, corroborate eachother. Students who attend a single institution graduate faster relative to students whoattend more than one institution. Being a female, white, fulltime student and staying on-campus reduces time to degree for transfer students. Aid offer or financial assistance inany form helps in achieving a degree. Presence of articulation agreements across institutions

can help reduce time to degree for transfer students.









95

I’m testing one of the aspects of “transfer shock” by looking at time taken to finish a

bachelor degree. Two longitudinal datasets have been used in this study. Both are student-period

datasets, one following the educational pathway of students enrolled in 4-year research intensive

university; the second is a survey on a randomly selected group of individuals, documenting their

transition from school to work. The first dataset is used to analyze performance of horizontal and

vertical transfer students in the 4-year institution they have transferred to. The second dataset

looks at transfer students i.e. students who have attended more than one institution in their pursuit

for bachelor degree, and non-transfer students i.e. students who have started and ended their

baccalaureate degree in one institution.

Students who attend a single institution have the lowest time to degree i.e. they graduate

faster relative to transfer students. Among transfer students, vertical transfers who have an

associate degree take longer to graduate relative to horizontal and reverse transfers. This result

can be attributed to the fact that a student needs to accumulate certain amount of credits to

transfer up i.e. transfer from a 2-year college to a 4-year college. The results also show that

presence of articulation agreements across institutions can fasten degree achievement rates. This

result is very significant as larger numbers of students are attending more than one institution.

Therefore it is crucial that this process works smoothly. Transfer students should not be penalized

in their search for better options elsewhere.



9 6

2. LITERATURE REVIEW

Progress of transfer students in terms of accumulation of credits, persistence and ultimately attainment of u

had been investigated by previous researchers. A brief summary of previous papers is presented below.

Table 3.2.1: Literature Review on Performance of Transfer Students

Author (Year)Journal/WP/Publication

Main ResearchQuestion

Sample Left Hand SideVariables

Right HandSide Variables

Lee, Mackie-Lewis, Marks(1993)

American Journal ofEducation

Comparison of probability ofattainment of

bachelor degree ofcommunity college

students whotransferred to 4-

year collegesrelative to studentswho started in 4-

year colleges.

Random sample of422 transferstudents and

sample of 1899 4-year college

students fromHigh School and

Beyond Survey of1980

Attainment ofdegree,

Aspiration toattend graduateschool, Actualenrollment in

graduate school.

Studentdemographic and

academiccharacteristics,

Transfer Collegecharacteristics

Andrew Nutting(2004)

CHERI Working Paper

Correlation ofTime of transferfrom communitycollege to 4-year

college with probability ofgetting degree,

time to degree andcredits earned.

Student Data Filecontaining

enrollment data of64 campuses of

State University of New York system

Probability ofgetting degree,Time to degree

and Creditsearned.

Terms enrolled incommunity

college, Timetaken off, Credits

accumulated

Peter and Kataldi(2005)

NCES Report

Correlation between multiple

institution

1996-01Beginning

Postsecondary

Probability of persistence in

college and

First collegecontrols, type of

multiple





9 8

campuses anddepartments of 4-

year colleges

college and 4-yearcollege, TransferCollege controls,4-year college’s

campus anddepartment

transfer studentshare and 6-yeargraduation rate of

freshmanstudents.

Long and Kurlaender(2009)

Educational Evaluationand Policy Analysis

Comparison of probability ofattainment of

bachelor degree ofcommunity college

students whotransferred to 4-

year collegesrelative to studentswho started in 4-year colleges in

Ohio public highereducation system.

Longitudinaldataset spanningnine years, Fall1997 to Spring2007 on Ohio public higher

education systemfrom Ohio Boardof Regents (OBR)

College Credits,Degree

Completion

Student ability(ACT score),

demographics andfamily

background





100

degree and the kind of progress made in various institutions in terms of GPA, credits

accumulated, getting a degree etc. Almost all the previous studies had access to student level data

over a span of time and it helped them analyze the progress made by transfer students starting at

2-year colleges and finishing their degree in 4-year colleges. The current study goes beyond

studying vertical transfer students and also looks at time to degree for lateral and reverse transfer

students.

Various factors influencing probability of attainment of degree has been investigated by

Lee, Mackie-Lewis, Marks (1993), Nutting(2004,2008) and Long and Kurlaender(2009). They

looked at the performance of community college students relative to native students. Lee,

Mackie-Lewis, Marks (1993) used a longitudinal survey and they concluded that attendance in

community college did not hamper the chances of getting a bachelor degree for transfer students.

Nutting (2004,2008) used student enrollment data of State University of New York’s (SUNY) 64

campuses. He concluded that the longer a transfer student delays transferring up from a

community college, it reduces the student’s chances of getting a degree. He also found that non-

technical college campuses which have large share of transfer students improve graduation

prospects of transfer students, but reduces chances of degree attainment for native students at the

department level. Long and Kurlaender(2009) used enrollment data files of Ohio Public Higher

Education System. Their results were opposite to those found by Lee, Mackie-Lewis, Marks

(1993): community college students were more likely to drop out and not finish degree relative to

native students. The conflicting results can be attributed to different time frames the authors

investigated and different kinds of controls used in regression models. Lee, Mackie-Lewis, Marks

(1993) looked at educational choices made by high school students in 1980s while Long and

Kurlaender(2009) looked at the 10-year period of 1997-2007. Time to degree of community

college students has been one of the main research questions in Nutting(2004) and Peter and

Kabaldi(2005). Nutting (2004) addressed the issue of time taken by community college students



101

to transfer up and how it negatively influenced their time to degree using SUNY enrollment data.

Peter and Kabaldi(2005) used two longitudinal surveys to trace multiple enrollment patterns and

found evidence that enrolling in multiple institutions at the same time increases time taken to

graduate with a bachelor degree. My study makes a comparison between students who attended

more than one postsecondary institution versus who attended a single postsecondary institution

and the impact of such a choice on their time taken to get a bachelor degree. The analysis is not

restricted to only community college students. It also looks at horizontal transfers (4-year

institution to another 4-year institution) and reverse transfers (4-year institution to 2-year

institution).

My work makes use of longitudinal survey data and enrollment information of a

university, while the previous researchers have either enrollment data or survey data. This chapter

is using two different datasets- the first is a longitudinal student-course dataset and the second is a

longitudinal survey of a representative sample of 12 to 16 years old children and youth. The first

dataset is used to analyze the performance of vertical and horizontal transfer students. How much

time was taken by the transfer students to get a bachelor degree in the 4-year public university

they transferred to? Does it make a significant difference if the student transferred in from a 4-

year college? The 4-year public university is part of a statewide system of universities, university

centers, technological colleges and community colleges. The chapter also looked into system

effect, i.e. if a student transfers in from an institution outside the system, does it influence the

student’s prospects of finishing in time. Articulation agreements of a statewide system encourage

the transfer process within the system but discourage students coming from colleges and

universities outside the system.

The second dataset being a representative sample of school going children of United

States covers a wider range of colleges and universities and makes it possible to study all three



102

kinds of transfer processes - vertical, horizontal and reverse transfers. I looked only at those

individuals who have a bachelor degree and they fall into two board categories: a) started and

finished their bachelor degree in one institution b) started their educational career in one

institution and finished in another. I couldn’t get access to the NLSY97 database on educational

institutions which contain information on colleges and universities IPEDS (Integrated Post

Secondary Education Data System) ID which can be linked to IPEDS data. Those files were

restricted and required special access. Access to such information would have been helpful in

terms of controlling for transfer college quality because it does influence a transfer student’s

college grades, an interesting result found by Dills and Hernandez-Julian (2008).

The kind of econometric methodology used earlier has ranged from OLS to Hazard

Models. Studies analyzing probability of graduation and persistence to degree had used logistic

regression. For college grades, ordered probit and for time to degree, OLS methodology had been

used. Persistence to degree has been studied using discrete time hazard model too. This chapter is

investigating time to degree using the methodology of Cox proportional hazard (duration) model

for student dataset and Ordinary Least Squares for survey data.

There is a problem of self-selectivity because one half of the study is looking at transfer

students of a particular university and not at applicant pool or students across universities. The

econometric analysis on university data is not based on a random sample of students. Hence, the

results of the analysis cannot be generalized. The results of the econometric analysis based on the

longitudinal survey data (which is a random sample of school going children and youth) can be

generalized.



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4. DATA DESCRIPTION

The current study is based on two datasets. One is a longitudinal dataset covering ten

years of student data of a research-intensive four-year public university in New York State. The

data is a panel data of transfer students enrolling in Fall 1997 to Fall 2003 and they are observed

till Spring 2007. Students are followed from the point, they enter the University till they graduate,

transfer or attrite 38. It is a person-period dataset, with each student i having a certain number of

observations depending on the mode of exit (graduation, attrition, transfer) from the dataset. A

student is observed each semester and the dataset has information on courses taken by a student in

a semester. Course-related information such as gender, ethnicity, academic rank of the instructor,

average grade in course, kind of course (has a laboratory session or not), course level and the

department offering the course is also documented. Pre-college academic variables-SAT scores,

high school GPA, AP course and grades declared by student are available for freshman students

only. There is information on enrollment status (fulltime or part-time, freshman or transfer),

gender, ethnicity and major(s) declared (field of the major). There is also information on aid

offered from various sources and kind of sources (sports scholarship or other scholarship). The

dataset neither provides information on age of the student nor about the high school

(characteristics of the school). It provides the name of the high school. Marital status, family

income and ethnicity are self-reported variables and therefore there are many missing items under

these three variables. The dataset has information on students as long as they are enrolled in the

university. Once they have graduated or transferred out or left the university due to various

reasons (taking time off from study or show up in some other university after semester(s)), the

dataset does not follow up on the student. This dataset is used to analyze the performance of

transfer students once they have transferred into a 4-year college.




104

The second one is a selected sample of individuals from a longitudinal survey-National

Longitudinal Survey of Youth, 1997 (NLSY97). NLSY97 has finished 11 rounds starting from

year 1997 to 2007 39. The NLSY97 consists of a nationally representative sample of 8984 youths

who were 12 to 16 years old as of December 31, 1996. The sample is designed to be a

representative sample of United States Most of the survey respondents in round one of the survey

were in high school. It asks the survey participants and their parents (Questionnaire to parents

were provided only in Round 1 of NLSY, which makes it a unique feature of NLSY97) questions,

the answers to which show the “rites of passage” of students from school to college to work and

their choices concerning marriage and children 40. Also in round one, Computer Adaptive Version

of Armed Services Vocational Aptitude Battery (CAT-ASVAB) was administered by Department

of Defense (DOD) to the survey respondents over the summer and fall of 1997 to winter of 1998.

Schools of sampling areas were also surveyed in 1996. A census of the schools in the sampling

areas was conducted. The school survey questionnaire asked the schools to provide information

on characteristics of the school such as type of school, grades offered, facilities available at

school, and characteristics of the staff such as fulltime/part-time teachers, demographic

composition of staff and their educational qualification. A second survey was conducted in 2000

which included the schools surveyed in 1996, vocational schools in primary sampling units and

high schools which NLSY97 respondents attended after they moved out of primary sampling unit

in which they were located when originally surveyed. As survey respondents grew in age,

subsequent rounds of NLSY97 included questions on college and employment. The schooling

section of survey questionnaire has items on a) educational attainment –highest grade attained,

SAT and ACT scores; b) experiences-percentage of peers planning to go to college or work; c)

coursework- learning programs, AP coursework etc. The college section has items on a) college

39 The 12 th round took place in 2008 for which the data is yet to be released.40 http://www.bls.gov/nls/y97summary.htm





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National Longitudinal Survey of Youth 1997

The following table describes the educational pipeline from National Longitudinal

Survey of Youth 1997. For 8954 individuals in NLSY Round One, 6648 graduated from high

school. Out of them 593 earned an associate degree, 1580 graduated with bachelor’s degree and

100 of them had both associate and bachelor degree (100 individuals are part of 593 associate

degree holders and 1580 bachelor degree holders). Out of 1480 “only bachelor degree” recipients,

482 started and finished their post-secondary education in different institutions. 143 out of 481

either started their educational career in a 2-year college (vertical transfer) or transferred to 2-year

College after starting in a 4-year college (reverse transfer). The remaining 339 transferred from a

4-year college to another 4-year college (horizontal or lateral transfer). The numbers show that

the number of individuals moving from one institution to another without getting any kind of

credential from the previous institution is much larger than the number of individuals who

transfer up with a credential.

Table 3.4.2: Educational Pipeline based on NLSY 97

Characteristic Number

Interviewed in Round One of NLSY97 8984Received High School Diploma 6648

593Received Associate DegreeHave Bachelor Degree 1001578Have Associate Degree 100Vertical Transfer Without Associate Degree 101

Reverse Transfer 42Horizontal Transfer Without Degree 339

Received Bachelor Degree

Stayed in One Institution 996

It is important to note here the distinction between the two datasets in terms of the

information available. The university data has information on students who are enrolled and there

is no way to know the kind of experience they had in their previous institution except their





108

Time to Graduation (tte) of studentsFigure 3.4.1: Who have transferred from 2-year College (System) with an Associate degree

Figure 3.4.2: Who have transferred from 2-year College (System) without an Associatedegree



109

Figure 3.4.3: Who have transferred from 4-year College (System) with a degree

Figure 3.4.4: Who have transferred from 4-year College (System) without a degree



110

Figure 3.4.5: Who have transferred from 2-year Instate(New York) College (Outside System)

Figure 3.4.6: Who have transferred from 4-year Instate (New York) College (Outside System)



111

Figure 3.4.7: Who have transferred from 2-year Out of state College (Outside System)

Figure 3.4.8: Who have transferred from 4-year Out of state College(Outside System)



112

The following boxplots are helpful in comparing the time to degree for bachelor degree holders

with various characteristics.

Time to Degree (tte) of Bachelor Degree holder students (in order as they appear in Figure 3.4.9).

1. Have an Associate Degree

2. Do not have an Associate Degree and transferred from 2-year institution

3. Do not have an Associate Degree and transferred from 4-year institution

Figure 3.4.9: Boxplot of Time to Degree of Bachelor Degree Holder Students by PreviousDegree (University Data)







115

Figure 3.4.12: Time to Degree (ttd) of Bachelor Degree Holder Students (NLSY 97)

Figure 3.4.1 to Figure 3.4.8 show that vertical transfers with an associate degree take the longest

to finish a degree, as they need to accumulate certain amount of credits to transfer up and may

end up staying in 2-year institutions for a longer time to do so. Also transfer students from

outside the system take longer to graduate pointing to evidence that articulation agreements can

smooth the transfer process and reduce the costs associated with it. Figure 3.4.12 shows that non-

transfer student take lesser time to graduate relative to students who have attended more than one

institution, a result similar to what was concluded by Peter and Kabaldi(2005). Among transfer

students, on average reverse and horizontal transfers take least time to graduate.



116

5.1 MODEL AND METHODOLOGY

Timely college graduation is investigated using Cox proportional hazard (duration) model which

is applied on the first dataset . The hazard model is written as

hazard of graduation of student i in time period t = λ(ti) = exp(- X i’µ ) λ 0(t) Eq(3)

The above expression says that the hazard (probability) of graduation of student i at time t

depends on the value of X 1. X1 matrix consists of covariates, Transfer GPA, gender, ethnicity,

dummy variables controlling for origin institution, aid offer and residency status. The function

λ 0(t) is the baseline hazard, which represents individual heterogeneity (Greene, 2003). The

intuitive explanation is if all the covariates take the value zero for a student, λ 0(t) is the student’s

risk of graduating. Cox model is semi-parametric and called proportional hazard model, because

hazard for any individual is a fixed proportion of hazard for any other individual. Say, for

students i and k,

λ(ti) / λ(tk) = exp(- X i’µ ) / exp(- X k ’µ ). Eq(4)

Λ0(t) cancels out, hence Cox model doesn’t have to assume anything about the distribution of

hazard function. It does assume that a student exits the dataset only once and doesn’t show up

again and encounters only one kind of exit. In the data used in this paper, each student has distinct

kind of exit from the dataset. A student can exit the dataset by graduating or dropping out

(attrition). The third possible event is that the student stays enrolled till Spring 2007 (the last

point in time the dataset covers). Graduation and Persistence are positive events. Attrition is a

non-positive event. The dataset has information on students as long as they are enrolled in the

university, nothing about their educational path after they leave the university to take time off or

join another college or university after a semester.

Looking only at the probability of graduation can be misleading because the three events are

competing outcomes and should be analyzed using a competing risk model. Such a model helps



117

in calculating the probability of graduation, attrition and persistence in each semester starting

from the semester the student enters the university and takes into account the interdependence

which (may) exist among these three outcomes and indicates the variables which are important in

a students decision to choose among the above three outcomes. Therefore, time to graduation,

persistence and attrition has been investigated using a competing risk framework. Time taken to

graduate is analyzed through the model of competing risks using techniques of event history

analysis. As mentioned above, graduation, persistence and attrition are interdependent events;

therefore a competing risk approach (which takes into consideration interdependent events) is

taken to investigate time to degree. Event-history techniques had been used for competing risk

models by Ronco(1995), Denson and Schumacker (1996) and DesJardins et al.(2006).

Ronco(1996) looked into different types of student departure (graduation, transfer or dropout).

She based her analysis on 1635 first-time fall 1987 college students who were followed till spring

1994 and found that the risk of transfer to a two-year college was almost as high as the risk of

dropout throughout the enrollment period and that provisionally admitted students and those with

low GPA’s were at greater risk of dropping out. Denson and Schumacker (1996) used database

from Dallas Public Schools to study the different modes of departure from school of students who

were starting ninth grade for first time. They found that students are at risk of withdrawing or

dropping out from school until the end of their senior year, when graduation is the most likely

outcome Males relative to females were more likely to withdraw or dropout and females are more

likely to graduate by the second semester of eleventh grade compared to males. DesJardins et

al,(2006) investigated the issue of multiple withdrawals from college and the periods of multiple

enrollment in college on probability of graduation. They followed first-time freshman students of

University of Minnesota-Twin Cities entering in fall 1984, 1986 and 1991 for six years. Students

who withdrew from college once had much lesser probability of graduation; longer enrollment

spells increased the risk of graduation and higher ACT scores, college GPAs, coming from

middle- or high-income family increased chances of reenrollment.



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5.2 MODEL AND METHODOLOGY

From NLSY97 we selected individuals who have a bachelor’s degree and/or have an

associate degree; horizontal, vertical or reverse transfers without a degree; and who started and

ended in the same 4-year institution, which brings our sample size to 1580 individuals. In this

case all the individuals have witnessed the event of graduation, so there are no censored variables.

Therefore there is no need to go for event history analysis. The left hand side variable is time to

degree calculated using the Eq(1). I calculated the number of days the student was enrolled in the

institution till receipt of degree and divided it by 365.25 days. This method helped in expressing

the period of enrollment in number of years and also made it continuous. I took the approach of

counting days of enrollment to calculate time to degree so as to get a more accurate picture of the

time taken by transfer students to graduate. Transfer students can enroll either in Fall or Spring

semester and can graduate in the following Spring, Summer or Fall semester. The starting and

ending points of enrollment period is not a whole number. It is generally a couple of months or

couple of years plus some months. The left hand side variable denotes time to degree which is left

and right censored. It will never be less than zero and can never possibly go beyond fifteen.

Figure 3.4.9 point out that the time to degree variable is continuous within no particular range,

therefore a simple econometric analysis involving Ordinary Least Squares is sufficient in this

case. Same approach has been taken by Nutting (2004, 2008) as mentioned in Section 2.

The right hand side variables are gender, ethnicity, CAT-ASVAB percentile score, SAT

Verbal score, SAT Math score, High School GPA, expectations of the individual student to finish

bachelor degree, peer effect in terms of percentage of high school peers aiming for college,

fulltime or part-time status, residency status, cumulative college GPA, percentage of tuition paid

by loans and scholarships, high school type and student teacher ratio. Gender is coded as “1” for

male and “2” for female. Ethnicity is coded as “1” for Black, “2” for Hispanic, “3” for Mixed

race and “4” for Non-Black and Non-Hispanic. A student may move between fulltime and part-



119

time status in a college. In the NLSY 1997 dataset, there are students who have changed their

status while enrolled in one institution. While there are students who haven’t changed their

fulltime or part-time status during the entire period they were enrolled in an institution. To take

into account this behavior, the explanatory variables denoting status of student is “percentage of

terms the student is fulltime in a college”. Residency status is coded as “1” if staying in campus

or other facilities provided by college or University and “0” otherwise. In terms of equation, the

full model is outlined as follows

Time To Degree i = α + βg*Gender i + βe*Ethnicity i + βsv*SAT Verbal i + βsm*SAT Math i +

βas*ASVAB i + βhgpa*High School GPA i + βcnc*Percent Chance will finish Bachelor Degree by

30years i + βpc*Percentage of HS peers planning to go to college i + βes1*Percentage of terms

fulltime in College One i+ βrs1*Residency Status in College One i + βes2*Percentage of terms

fulltime in College Two i + βrs2*Residency Status in College Two i + βcgpa*Cumulative GPA

from College One i + βptl1*Percent of Tuition in College One paid by Loan i + βpts1*Percent of

Tuition in College One paid by Scholarship/ Grant i + βptl2* Percent of Tuition in College Two

paid by Loan i + βpts2* Percent of Tuition in College Two paid by Scholarship/Grant i + βht*Type

of High School i +βhstr*Student Teacher Ratio of High School i Eq (5)

1. For Students who attended single institution (4-year college)

Time To Degree i = α + βg*Gender i + βe*Ethnicity i + βas*ASVAB i + βhgpa*High School GPA i +

βcnc*Percent Chance will finish Bachelor Degree by 30years i + βpc*Percentage of HS peers

planning to go to college i + βes*Percentage of terms fulltime i + βrs*Residency Status i +

βcgpa*Cumulative College GPA i + βptl1*Percent of Tuition in College paid by Loan i +





1 2 1

6. RESULTS Table 3.6.1: Time to Degree, Attrition and Persistence (University Data)

Degree Attrition Number of Observations Used 3320 3320

Model Fit Characteristics

Without With Without With CriterionCovariates Covariates Covariates Covariates Co

-2 LOG L 36115.112 35799.6 12167.55 11806.21

AIC 36115.112 35827.6 12167.55 11834.21

SBC 36115.112 35909.2 12167.55 11899.6

Parameter Standard Hazard Parameter Standard Hazard ParamVariable

Estimate Error Ratio Estimate Error Ratio

Transfer GPA 0.050 0.049 1.052 -0.218 0.082 0.804

2-Year College -0.049 0.088 0.952 0.566 0.148 1.762

Has Previous Degree -0.461 0.066 0.631 0.076 0.114 1.079

Transfer College part of SUNY 0.091 0.069 1.095 0.069 0.138 1.072

Instate College -0.111 0.065 0.895 -0.059 0.125 0.943

System Effect=SUNYColl*2*year*Instate

0.067 0.060 1.069 -0.053 0.103 0.948

Female 0.212 0.040 1.237 -0.116 0.072 0.891

Other -0.532 0.055 0.587 -0.311 0.099 0.733

Black -0.355 0.090 0.701 0.137 0.160 1.146

Hispanic -0.268 0.100 0.765 0.105 0.169 1.111

Asian -0.193 0.065 0.825 -0.242 0.128 0.785

Fulltime 0.714 0.087 2.043 0.057 0.126 1.059

Offcampus -0.104 0.053 0.901 -0.751 0.081 0.472

Aidoffer -8.E-06 4.E-06 1.000 -1.E-04 8.E-06 1.000





123


Table 3.6.1 provides the results for the duration model. The darkened rows show the

variables which are significant at 1% level and the less darkened rows shows the variables which

are significant at 5% level. The columns of interest are that of hazard ratio. Hazard Ratio greater

than one indicate that a unit increase in the covariate results in increase of the probability of the

outcome (person’s chance of not witnessing the event goes down). Being transfer students, the

dataset does not provide information on SAT scores, high school GPA and AP grades. Increase in

transfer GPA reduces time to degree. Horizontal transfer or students transferring in from a 4-year

college take lesser time to graduate. Transfer students from 2-year colleges which are part of the

SUNY system take lesser time to graduate relative to students who come from colleges which are

neither part of SUNY system nor are from an in-state institution. Transferring in with an associate

degree or if the transfer college is a 2-year college, it increases the time taken by students to

achieve a degree. A female (fulltime, non-white, off-campus) student, would take less (less,

more, more) time to graduate.

Transferring in from a 2-year college or having an associate degree or if the student

transfers in from a SUNY institution, the individual is more likely to leave without finishing

degree even though the associate degree and SUNY institution variables are not significant. The

system effect is positive as it reduces the possibility of attrition. Hence transferring to a campus

which is within the system provides the advantage of transferring in credits smoothly (due to

articulation agreements) and the college atmosphere is similar to the one faced by transfer

students in the transfer institution. Others (non-white, non-Hispanic, non-Black, non-Asian) and

Asian transfer students have greater chances of non-attrition. Being a full-time student increases

chances of both graduation and attrition, but the variable is significant only in the event of

graduation. Staying off-campus reduces chances of both graduation and attrition and is significant

at 5% and 1% respectively for the events of graduation and attrition. Therefore there are opposing

effects of staying outside college campus. It reduces chances of attrition relatively more than



124

graduation. Therefore students staying outside dormitories are more likely to graduate than leave

without a degree.

Factors improving persistence among transfer students are transfer GPA, coming from in-

state transfer college, being a black and residency status being off-campus. The result is very

similar to the event of graduation. Even though this group of transfer students has not graduated

yet, they are still enrolled and that is a positive event.

Tables 3.6.2 and 3.6.3 provide the OLS results based on NLSY 1997 data. Transfer

students had attended more than one institution; hence variables denoting their experience in their

second college are included as explanatory variables in the regression. Non-transfer students have

a simplistic model and the results are comparable to time to degree analysis done on freshman

students in the first chapter. Reverse transfers, vertical transfers with and without degree take

more time to finish their bachelor degree on average relative to horizontal transfers as seen from

Table 3.6.2 and the Boxplot in Section 4. Gender and ethnicity are not significant for transfer

students and ethnicity is significant for only non-transfer students. The signs on gender and

ethnicity parameters suggest that a female and non-black takes lesser time to finish a degree.

Academic variables (SAT scores, ASVAB score, High School GPA) reduce time to degree for

both transfer and non-transfer. ASVAB scores were more significant for non-transfer students

relative to SAT scores. High School GPA was not significant for non-transfer students. For

transfer students cumulative college GPA at first institution is significant in reducing their time to

achieve bachelor degree. For non-transfer students, the sign on cumulative college GPA is the

opposite as for non-transfer students.

Percentage of total tuition paid (in college while enrolled) in loan or scholarship/grant is

an indicator of a student’s family’s financial condition and any changes in it. Transfer students

had attended a 2-year and 4-year college. Either of these colleges were their first or second

college. Therefore four explanatory variables denoting the percentage of their total tuition in both



125

colleges being paid from loan or/and scholarship or grant enters the model for transfer students.

The variables controlling for a student’s family income is not significant for transfer students, but

is significant in case of non transfer students. Being a fulltime student and staying in campus

reduces time taken to graduate. The explanatory variables were percentage of time enrolled in

college as fulltime and whether staying in campus or not. Being in fulltime status and staying off-

campus reduces time to degree. Peer effect and student’s attitudes were investigated by variables

“percent of peers planning to attend college” and “percent chance one would have bachelor

degree by age 30”. Peer effect was significantly negative for transfer students. Student’s attitude

did not reduce time taken to finish degree, even though not significant. High School academic

factors have been controlled for in the regression along with institutional factors- type of high

school (public or private) and student teacher ratio of high school. Only student teacher ratio of

high school was found to be significant. The explanatory powers of the models are not high for

both transfer and non-transfer students. Even though the author controlled for factors determining

graduation and time taken to graduate, as summarized in the literature review (Section 2) and as

available in NLSY 1997; the results point out that there is more than what meets the eye. Not so

obvious parameters can determine a student’s educational pathway and its successful completion,

which are beyond the scope of this chapter.

The time to degree was run separately for fulltime and part-time students. The results are

reported in Appendix 3.A (Table 3.A.1). The variable denoting the enrollment status of students

was the most significant variable in the time to degree model (see Table 3.6.1). Separate models

run for fulltime and part-time students show that the characteristics of fulltime students drive the

overall results, i.e. the significance of explanatory variables. Sign and significance of explanatory

variables for fulltime students are equal to the time to degree model run for all students. For part-

time students, the ethnicity dummy denoting “others” is the only significant variable.



126

8. CONCLUSION

The third chapter investigates the performance of transfer students (who start their post-

secondary education in one institution and end in another) and non-transfer students (who start

and end their post-secondary education in one institution). Using two datasets factors enhancing

faster degree achievement rates were investigated. The first dataset is enrollment data of a public

4-year university and covers the 10 year period of 1997 to 2007. The second dataset is a random

sample of Bachelor degree holders from National Longitudinal Survey of Youth 1997 from

Round One to Round 11 spanning 10 years from 1997 to 2007.

The hypothesis about vertical and horizontal transfer students was found to be true from

the data analysis. Vertical transfer students take longer time to graduate relative to horizontal

transfer students. The regression models controlled for gender, ethnicity, previous academic

achievement, economic conditions and degree of campus involvement of students. The results of

the regressions running on two different datasets corroborate each other, i.e. a female and a white

takes less time to finish; staying off-campus and being part-time increases time to degree.

Variables controlling for economic condition was not found significant for transfer students, but

the negative sign on them denote that availability of financial aid in form of loan or scholarship

fastens degree achievement rates.

The results also show that presence of articulation agreements across institutions can help

reduce time to degree. This result is very important as the option of transfer is getting popular

among students, especially vertical transfer. As the number of high school graduates continue to

rise along with their aspirations and as college costs go up, college students will look for options

beyond a single institution. Therefore it is crucial that this process works smoothly and transfer

students do not pay any penalty in their search for better options.





128

Figure 1.A.1: Predicted Semester GPA for SAT Students

Indifference Curve of Predicted GPA for SAT Students

0

200

400

600

800

1000

1200

1400

83.2875 91.3945693 97.6141026

High School GPA

C o m p o s i t e S A T = S A T V e r b a l + S A T M a t h

SemesterSemester



129

Figure 1.A.2: Predicted Semester GPA for AP Students

Indifference Curve of Predicted GPA for AP Students

0

200

400

600

800

1000

1200

1400

0 4 8

AP Credits

C o m p o s

i t e S A T =

S A T V e r b a

l + S A T M a

t h

Sem

Sem



130

APPENDIX 2.A

Table 2.A.1: Biology Courses: SAT Students:Grade A:Percent Female Model


Observations 1845 4725 1241 6994Covariance Parameter Estimates



-2 Res LogLikelihood 2050.9 5132.5 1200.8 5564.1

AIC 2052.9 5134.5 1202.8 5566.1AICC 2052.9 5134.5 1202.8 5566.1BIC 2058.4 5141 1207.9 5572.9

Solution for Fixed EffectsVariable Estimate SE Estimate SE Estimate SE Estimate SEIntercept -1.597 0.163 -0.980 0.123 -1.882 0.334 -1.549 0.181

High School GPA 0.000 0.001 0.000 0.000 0.001 0.001 0.000 0.000SAT Verbal

6.E-04 1.E-04 4.E-04 9.E-05 8.E-04 2.E-04 7.E-04 6.E-05SAT Math 3.E-04 2.E-04 5.E-04 1.E-04 5.E-04 2.E-04 6.E-04 7.E-05Fulltime -0.017 0.089 0.122 0.073 0.260 0.270 0.036 0.161

Offcampus -0.024 0.021 0.030 0.012 0.064 0.024 0.018 0.014Female 0.081 0.021 0.032 0.013 0.031 0.029 0.003 0.009Other 0.016 0.028 -0.027 0.018 0.019 0.033 0.026 0.014Black -0.209 0.044 -0.143 0.030 -0.025 0.043 -0.032 0.017

Hispanic -0.098 0.046 -0.117 0.030 0.023 0.049 -0.017 0.019Asian -0.061 0.026 -0.127 0.016 -0.069 0.029 -0.036 0.011

Average Grade 0.484 0.018 0.220 0.021 0.280 0.045 0.291 0.020Instructor Gender

-0.006 0.022 -0.045 0.013 0.088 0.050 -0.011 0.011

First Major 0.106 0.029 0.090 0.009Degree Major 0.057 0.026 0.041 0.021

Percent Female0.058 0.064 -0.043 0.060 0.227 0.091 0.198 0.077

Test of Fixed EffectsEffect F Value Pr > F F Value Pr > F F Value Pr > F F Value Pr > F

High School GPA 0.85 0.3579 0.78 0.3767 4.290 0.039 0.550 0.457SAT Verbal 18.570 <.0001 16.070 <.0001 25.670 <.0001 144.330 <.0001SAT Math 2.520 0.112 21.520 <.0001 6.470 0.011 85.070 <.0001Fulltime 0.030 0.853 2.820 0.093 0.930 0.336 0.050 0.821

Offcampus 1.370 0.242 5.630 0.018 6.760 0.010 1.690 0.193Female 15.100 0.000 6.290 0.012 1.150 0.284 0.100 0.754Other

0.330 0.563 2.220 0.136 0.320 0.572 3.410 0.065Black 22.670 <.0001 23.170 <.0001 0.350 0.555 3.540 0.060Hispanic 4.670 0.031 15.600 <.0001 0.220 0.640 0.820 0.365

Asian 5.310 0.021 64.940 <.0001 5.500 0.019 10.270 0.001Average Grade 693.630 <.0001 104.670 <.0001 39.070 <.0001 205.270 <.0001

Instructor Gender 0.070 0.797 11.490 0.001 3.100 0.078 0.960 0.327First Major 13.020 0.000 90.560 <.0001

Degree Major 4.680 0.031 3.770 0.052Percent Female 0.820 0.366 0.520 0.470 6.180 0.013 6.590 0.010





132

Table 2.A.3: Math Courses:SAT Students:Grade A:Percent Female ModelCourse Level 400 300 200 100

Number ofobservations 482 2307 6999 6799



-2 Res LogLikelihood 519.2 1957.9 2855.4 5716.5

AIC (smaller isbetter) 521.2 1959.9 2857.4 5718.5

AICC (smaller isbetter) 521.2 1959.9 2857.4 5718.5

BIC (smaller isbetter) 525.4 1965.6 2864.3 5725.4



ErrorIntercept -0.743 0.421 -0.4715 0.1369 -0.3069 0.09999 -0.846 0.122

High School GPA 3.E-05 6.E-04 -0.00145 0.000307 -0.00049 0.000151 2.E-04 2.E-04SAT Verbal 1.E-04 2.E-04 -0.00051 0.000092 -0.00038 0.000045 -3.E-04 6.E-05SAT Math 2.E-04 2.E-04 0.000665 0.000091 0.000464 0.000046 6.E-04 6.E-05Fulltime 0.163 0.388 0.06668 0.1158 0.1212 0.09341 -0.018 0.111

Offcampus -0.013 0.038 -0.05417 0.0162 -0.02413 0.01027 -0.003 0.011Female -0.049 0.041 -0.03228 0.01875 0.02712 0.007449 0.019 0.009Other -0.021 0.053 0.002139 0.0215 0.01004 0.01127 0.017 0.015Black -0.179 0.103 -0.0962 0.03817 -0.06433 0.01487 -0.058 0.015

Hispanic -0.142 0.089 -0.05432 0.03526 -0.04928 0.01505 -0.047 0.014Asian -0.022 0.047 -0.03423 0.0205 0.0189 0.009174 -0.011 0.014

Average Grade 0.268 0.046 0.2253 0.01746 0.1155 0.01093 0.280 0.011Instructor Gender 0.050 0.062 0.02632 0.02355 -0.00635 0.007784 0.021 0.010

Second Major 0.0847 0.02425Third Major 0.07808 0.03047

Percent Female -0.195 0.104 0.0592 0.07948 -0.02091 0.04481 0.281 0.055

Tests of Fixed EffectsEffect F Value Pr > F F Value Pr > F F Value Pr > F F Value Pr > FHigh School GPA 0 0.9623 22.09 <.0001 10.55 0.0012 0.77 0.3816

SAT Verbal 0.21 0.6446 30.71 <.0001 72.14 <.0001 28.59 <.0001SAT Math 0.5 0.4783 53.33 <.0001 103.09 <.0001 95.15 <.0001Fulltime 0.18 0.6752 0.33 0.5646 1.68 0.1943 0.03 0.8681

Offcampus 0.11 0.7349 11.18 0.0008 5.52 0.0188 0.05 0.8197Female 1.48 0.2248 2.96 0.0852 13.26 0.0003 4.14 0.042Other 0.16 0.6849 0.01 0.9207 0.79 0.3728 1.29 0.2565Black 2.99 0.0845 6.35 0.0118 18.7 <.0001 14.74 0.0001

Hispanic 2.56 0.1104 2.37 0.1236 10.72 0.0011 11.16 0.0008Asian 0.22 0.6391 2.79 0.0951 4.24 0.0394 0.65 0.4214


Second Major 12.2 0.0005Third Major 6.57 0.0105

Percent Female 3.55 0.06 0.55 0.4564 0.22 0.6408 26.34 <.0001



133

Table 2.A.4: Math Courses:AP Students:Grade A:Percent Female Model


Observations 715 2909 3342 1088Covariance Parameter Estimates



-2 Res LogLikelihood 936 3352.4 3201.5 1463.4

AIC 938 3354.4 3203.5 1465.4AICC 938 3354.4 3203.5 1465.4BIC 942.6 3360.4 3209.6 1470.3

Solution for Fixed Effects



ErrorIntercept -0.888 0.381 -1.339 0.191 -0.850 0.192 -1.622 0.517

High School GPA 5.E-04 1.E-03 -3.E-04 4.E-04 -6.E-04 4.E-04 2.E-03 8.E-04SAT Verbal 5.E-04 2.E-04 -2.E-04 1.E-04 -4.E-04 9.E-05 1.E-04 2.E-04SAT Math

4.E-05 4.E-04 7.E-04 1.E-04 6.E-04 1.E-04 7.E-04 2.E-04AP Calculus BC 0.056 0.013 0.051 0.006 0.046 0.005 0.071 0.012AP Calculus AB 0.071 0.015 0.081 0.007 0.100 0.008 0.097 0.016

AP Statistics -0.005 0.014 -0.004 0.007 0.019 0.007 0.113 0.027AP Biology 0.011 0.004

AP Chemistry 0.034 0.013 0.016 0.006 0.006 0.005 0.037 0.014Fulltime -0.310 0.255 0.217 0.161 0.108 0.172 0.276 0.458

Offcampus -0.081 0.035 0.000 0.019 0.021 0.026 -0.060 0.040Female 0.004 0.038 0.071 0.019 0.070 0.014 0.102 0.029

Ethnicity DummyOther -0.020 0.049 0.035 0.023 0.000 0.022 -0.024 0.045Black 0.378 0.232 0.058 0.094 -0.047 0.050 0.028 0.092

Hispanic -0.214 0.169 -0.015 0.060 -0.062 0.042 -0.039 0.077Asian -0.066 0.042 0.028 0.020 -0.017 0.016 -0.002 0.035

Average Grade 0.344 0.039 0.312 0.021 0.167 0.019 0.264 0.056Instructor Gender 0.062 0.059 0.010 0.025 0.026 0.015 0.021 0.039

Third Major 0.147 0.051Percent Female 0.038 0.117 -0.259 0.078 0.673 0.086 0.165 0.149

Test of Fixed EffectsEffect F Value Pr > F F Value Pr > F F Value Pr > F F Value Pr > F

High School GPA 0.25 0.6194 0.46 0.4974 2.81 0.0937 5.66 0.0176SAT Verbal 4.72 0.0301 2.53 0.1119 18.85 <.0001 0.29 0.5894SAT Math 0.01 0.9101 33.09 <.0001 30.06 <.0001 8.8 0.0031

AP Calculus BC 17.7 <.0001 62.28 <.0001 70.81 <.0001 37.28 <.0001AP Calculus AB 23.21 <.0001 134.23 <.0001 172.43 <.0001 38.92 <.0001

AP Statistics 0.12 0.7327 0.33 0.5656 7.19 0.0074 17.04 <.0001AP Biology 7.61 0.0058

AP Chemistry 6.76 0.0095 7.76 0.0054 1.03 0.3113 6.74 0.0096

Fulltime 1.48 0.2247 1.82 0.1769 0.39 0.5301 0.36 0.5473Offcampus 5.17 0.0233 0 0.9832 0.66 0.4176 2.27 0.1323

Female 0.01 0.9094 14.54 0.0001 24.7 <.0001 12.38 0.0005Other 0.18 0.6756 2.28 0.1313 0 0.9977 0.28 0.5941Black 2.66 0.1031 0.38 0.5357 0.9 0.343 0.09 0.7616

Hispanic 1.6 0.2069 0.06 0.8071 2.11 0.146 0.25 0.6176Asian 2.49 0.1148 2.06 0.1518 1.15 0.2835 0 0.9578



Percent Female 0.1 0.7472 10.87 0.001 61.85 <.0001 1.22 0.2695



134

APPENDIX 3.A

Table 3.A.1: Time to Degree by Enrollment Status of StudentsTime to Degree for Part-Time

StudentsTime to Degree for Fulltime

StudentsNumber of

Observations234 3086

Without With Without WithCriterionCovariates Covariates Covariates Covariates

-2 LOG L 1340.231 1313.445 33629.727 33376.024AIC 1340.231 1339.445 33629.727 33402.024SBC 1340.231 1378.84 33629.727 33477.059

Parameter Standard Hazard Parameter Standard HazardVariableEstimate Error Ratio Estimate Error Ratio

Transfer GPA 0.0243 0.1824 1.025 0.0592 0.0506 1.0612-Year College

-0.0890 0.3932 0.915 -0.0551 0.0912 0.946Has Previous Degree -0.3133 0.2887 0.731 -0.4803 0.0680 0.619Transfer College part

of SUNY-0.1128 0.3823 0.893 0.0992 0.0707 1.104

Instate College -0.2851 0.3780 0.752 -0.1086 0.0659 0.897System Effect=SUNYColl*2*year*Prev_Deg

0.1307 0.2920 1.14 0.0683 0.0620 1.071

Female 0.0402 0.1834 1.041 0.2303 0.0417 1.259Other -1.0053 0.2190 0.366 -0.4926 0.0570 0.611Black -0.4896 0.4741 0.613 -0.3382 0.0922 0.713

Hispanic -0.6557 0.6011 0.519 -0.2478 0.1015 0.781Asian -0.1323 0.3509 0.876 -0.1903 0.0668 0.827

Offcampus 0.0524 0.7328 1.054 -0.1053 0.0529 0.900

Aidoffer 0.0000 0.0000 1 0.0000 0.0000 1.000



135

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Documents

Indicators of College Success of Freshman and Transfer Undergraduate Students