Determinants of Persistence of Graduate Studentspersistence include student aptitude and achievement, financial support, and demographic characteristics, as well as characteristics

Determinants of Persistence of Graduate Students

in Ph.D. Programs

Gregory M. Attiyeh

GRE Board Report No. 9518R

April 1999

This report presents the findings of a research project funded by and canied out under the auspices of the Graduate

Record Examinations Board

Educational Testing Service, Princeton, NJ 08541

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Copyright 0 1999 by Educational Testing Service. All rights reserved.

Acknowledgments

I would like to thank Rocco Russo and the AAU/AGS Project for Research on Doctoral Education for making data available for this study. I would also like to thank Richard Attiyeh and Mary O’Neil from the University of California San Diego for their suggestions and assistance.

Abstract

This study utilizes longitudinal data on individual students enrolled in doctoral programs fi-om 1989 to 1993 to identify patterns and determinants of their persistence. For each of five disciplines (biochemistry, economics, English, mathematics, and mechanical engineering), a survival model is specified to explain student persistence through the first four years of graduate study. Variables hypothesized to explain persistence include student aptitude and achievement, financial support, and demographic characteristics, as well as characteristics of the programs in which students were enrolled. The statistical estimates reveal significant differences across disciplines, but several general results are apparent: a student with given characteristics is more likely to persist at more selective institutions; other things being equal, a student is more likely to persist if he or she has greater financial support, higher GRE Verbal or Quantitative scores, and a master’s degree. Student citizenship, gender, ethnicity, and age are not consistently related to persistence across disciplines.

Introduction

This study utilizes longitudinal data on individual students enrolled in doctoral programs to identify patterns and determinants of their persistence. A large percentage of doctoral students withdraw from doctoral programs before completing their programs, and so considerable attention has been focused in recent years on the persistence, or retention, of Ph.D. students. Retention of these students is seen as a key element both in the success of students and in the effectiveness of doctoral programs. If it is possible to understand why students resign from graduate programs prematurely, it may also be possible both to formulate improved admissions criteria and to establish effective advising programs. In turn, this could lead to higher graduation rates and more efficient use of institutional resources.

Our effort to understand the determinants of persistence was motivated in part by the seminal work of Bowen and Rudenstein (1992)‘. Their study, which analyzed data for six fields at ten institutions, yielded the following findings:

For six fields (English history, political science, economics, mathematics, and physics) in nine leading universities, the completion rate for students beginning graduate study between 1972 and 1976 was only 48 percent.

For men in the nine university sample, the completion rate declined Corn 63 percent for the 1962-66 entering cohort to 49 percent for the 1972-76 cohort.

For six fields at six leading universities for the 1972-76 entering cohort, 87 percent persisted into their second year of study, 70 percent advanced to candidacy, and 57 percent eventually received the Ph.D.

For six fields at ten universities, competition rates for students who had institutional support (fellowships and assistantships) ranged from 50 to 100 percent higher than for students who were self-supporting.

At the one institution for which data were available, students with teaching assistantships were more likely to advance to candidacy than students with fellowships.

At eight leading universities, students in mathematics and physics had substantially higher completion rates than students in the humanities and social sciences. Also, math and science students supported primarily with research assistantships had higher completion rates than students with other forms of support.

The earlier literature on graduate education contains several studies which focused on measuring and predicting success in doctoral programs. Two of these are of particular relevance to this study. In 1988, Zwick and Braun used a longitudinal database of students at Northwestern University to investigate the progress of those students toward advancement to candidacy and graduation in fourteen fields of study. This study

involved three separate approaches. First, the authors compared success in graduate school among demographic groups. They found little difference with respect to advancement to candidacy, but foreign students had a substantially higher graduation rate than did domestic students. In their second approach, Zwick and Braun used survival analysis to model students’ progress and found substantial differences among disciplines in the probability of advancing to candidacy and graduating within given time intervals. Finally, using simple correlation analysis to test for a relationship between success in reaching these milestones and both undergraduate GPA and GRE scores, they found no systematic relationship between success and these predictor variables.

In 199 1, Zwick expanded on the Zwick and Braun study by analyzing the graduate careers of Ph.D. students in eleven disciplines at three universities. Although it followed a similar methodological approach, this later study paid greater attention to differences in advancement and graduation rates among demographic groups. It found higher rates for foreign relative to domestic students, men relative to women, and whites relative to under-represented minorities. Like Zwick and Braun, Zwick found substantial differences across disciplines and little association between advancement and graduation, on the one hand, and undergraduate GPA and GRE scores, on the other.

Following on these earlier studies, our analysis of graduate student persistence relies heavily on the database being developed by the Association of American Universities / Association of Graduate Schools (AAU/AGS) Project for Research on Doctoral Education (hereafter, AGS Project). The project has been collecting data on enrolled doctoral students in five fields since 1989 in order to provide a basis for analyzing the flow of students in and out of graduate programs offered by the schools that make up the AAWAGS. The institutions participating in the AGS Project accounted for 42 percent of the Ph.D.s awarded in the United States in 1989. Of the 58 schools that were AAU members in 1989,48 have provided some data to the project. Data from 3 1 of these institutions for 1989 through 1994 are used in this study.

The specific objectives of this study are as follows:

l Construct a longitudinal database from the AGS Project database that can be used to analyze persistence of doctoral students.

l Identify patterns of persistence by disciplinary field through the first several years of study.

l Determine the extent to which these patterns of persistence are explained by aptitude/achievement, financial support, and demographic variables.

l Determine how well persistence at each transition point can be predicted from data available at time of admission.

This report on the study’s methods and results is organized as follows. First, we give a brief description of the study’s database. Next, we describe the patterns of persistence evident in the database. Then, we report on a multivariate statistical analysis

3

of the data. In the final section, we summarize the study’s findings and identify firther work that can be done to better utilize the AGS Project’s database and to better understand the determinants of persistence.

Description of the Database

As indicated above, the information utilized in this study is derived primarily fkom the AGS Project database. Since 1989, the project has been collecting data from AAU member institutions on enrolled doctoral students in five fields: biochemistry, economics, English, mathematics, and mechanical engineering. The resulting database is unique in that it contains a wealth of information on individual students over multiple years during the course of their study. Meaningful use of this database, however, requires that the following limitations be fully considered:

Not all AAU institutions have participated in the AGS Project.

Some participating institutions provided data for only some of the years, either because they entered the project late or left it early.

Some participating institutions were unable to provide data on key variables relevant to this study.

Some of the data provided by participating institutions contained obvious reporting errors.

Most institutions did not indicate a reason (e.g., graduation, withdrawal, leave of absence) why a student was no longer enrolled.

As a result, the data extracted from the AGS Project’s database for use in this study includes only seven institutions with data for all six possible years. Further, it includes eleven institutions with enrollment data for only two or three years, and it excludes many records of students that were missing key variables or had obvious reporting errors.

Students in the database are followed from their first year of study through transition points until they (1) drop out,2 (2) data on them is no longer provided by their institutions, or (3) they reach their fourth year of study. Persistence through a transition point is defined as being enrolled at the beginning of one academic year of study and also being enrolled at the beginning of the next academic year. Students are not followed beyond their fourth year because at that point it is impossible to distinguish between students who drop out and those who graduate. It is assumed that no students in the database graduate with less than four years of study.

Because of data limitations, students who take leave are considered to be withdrawn even though they may return in a later year. Institutions that provided data to the AGS Project did not distinguish leaves of absence fi-om withdrawals. Furthermore, many students who take leave do not return; they are withdrawn, even though this is not known by the institution or even the student at the time of leave-taking. Moreover, for most institution-cohorts in the database, there were not enough years of data to identify returning leave takers.3

5

Students who transfer from one institution to another are treated as dropping out. Clearly, students could not be followed who transfer either to institutions not in this database or to institutions in the database that did not provide data during the year of transfer. It is possible that some transfers between participating institutions could be identified, but no attempt to do this was made.

Taken together, these inadequacies limit the explanatory power of the data.4 Results should be viewed as suggestive, and readers are cautioned not to over-interpret these findings. Additional efforts to obtain more complete data from the participating institutions and to extend the longitudinal database would ,help to overcome many of these limitations.

Table 1 shows the size of each entering cohort by participating institution. It is possible to follow some students through three transitions points -- first to second, second to third, and third to fourth year of study -- as with the 1989, 1990, and 199 1 cohorts at UCLA. It is possible to follow other students through only one or two transition points, as with the 1989 cohort at Arizona or the 1989 cohort at Kansas, respectively.

6

Table I

Number of First-Year Students

Institution 1989 1990 1991 1992 1993 Total

University of Arizona Brown University University of California-Berkeley University of California-Los Angeles University of California-San Diego California Institute of Technology Case Westem Reserve University Columbia University Cornell university University of Florida U of Illinois At Urbana - Champaign University of Kansas University of Maryland - College Park University of Missouri-Columbia New York University Ohio State University University of Oregon University of Pennsylvania Pennsylvania State University University of Pittsburgh Purdue University Rice University University of Rochester Rutgers State University-New Brunswick University of Southern California Syracuse University University of Texas - Austin Tulane University University of Virginia University of Washington Washington University

57

134

9

130 62

145 35

98

103

60 156 44 97

54 78

57 24

129 138

38

108 61 22 26

70

164 37

110

140

63

58

69

122 141

12

197 127

41 21

77 42

179 48

90

197

62

46 67

149 31

39

79 147 39

207 119 46 18

42 192 137 53

63 63 50 60

150 156

112 80

121 125 53 64

83 86

109 58 70

118

52 70 67 54

87 43

2 93

109 53

75 59 28

102

116 116 48

95 42

596 625 160 90 47

130 335 152 794 120 112 461 207 674 111 196 334 141 122 167 184 389 191 30

360 24

446 651 152

Total 1,357 1,494 1,678 1,714 1,895 8,138

Overall, there are 8,138 students in the database. Of these, 3,883 can be followed through only one transition point, 2,332 through only two transition points, and 1,923 through all three transition points. Consequently, there are 8,138 observations of students going through the first transition point, 4,255 through the second transition point, and 1,923 through the third. Table 2 provides a breakdown of these observations by field.

Table 2

Number of Observations by Transition Point

Field of Study 1st to 2nd Year

Biochemistry 784

Economics 1,653

English 2,233

Math 1,764

Mech. engineering 1,704

All fields 8,138

Transition Point

2nd to 3rd Year 3rd to 4th Year

477 287

739 319

1,243 572

967 449

829 296

4,255 1,923

Total

1,548

2,711

4,048

3,180

2,829

14,3 16

For each student in the database, in addition to enrollment status by year of study, the following information was obtained or derived from the AGS Project database: age, gender, citizenship, ethnicity (for U.S. citizens), Graduate Record Examination (GRE) General Test scores, master’s degree (if any), bachelor’s degree institution, tuition and fees, amount of financial support, and form of financial support. For the purposes of this study, the ethnicity of U.S. citizens in the database is defined as Asian American, under-represented minority (African American, Hispanic American, Native American), or other.

As many students as possible were linked to the Educational Testing Service (ETS) GRE database in order to fill in missing information on GRE scores and to add information on undergraduate grade point average? In addition, information was obtained from Barrons on the avera institutions. !

e Scholastic Aptitude Test (SAT) score of students’ bachelor’s degree Finally, the program rating and faculty size of the program in which each

student was enrolled were obtained from the National Research Council (1995) study of doctoral programs.

The demographic characteristics of the 8,138 first-year students in the database are shown in Table 3. One striking feature of Table 3 is the demographic makeup of the group of students enrolled in English programs. Compared to the other fields, more women, fewer international students, fewer Asian Americans, and more underrepresented minorities are enrolled in English programs.

Table 3

First-Year Enrollment by Demographic Group

Biochem.

Economics

English

Math

Mech. eng.

All fields

Gender

Male Female

457 327

58% 42%

1,220 433

74% 26%

931 1,302

42% 58%

1,325 439

75% 25%

1,535 169

90% 10%

5,468 2,670

67% 33%

Citizenship

Non S.

512 272

65% 35%

753 900

46% 54%

2,027 206

91% 9%

1,054 710

60% 40%

1,024 680

60% 40%

5,370 2,768

66% 34%

Ethnicity of U.S. Citizens

Asian Underrep. Amer. Minori&* Other

45 26 441

9% 5% 86%

49 54 650

7% 7% 86%

69 169 1,789

3% 8% 88%

64 64 926

6% 6% 88%

99 63 862

10% 6% 84%

326 376 4,668

6% 7% 87%

* Underrepresented minoirites include African Americans, Hispanic Americans, and Native Americans.

Patterns of Persistence

The simplest analysis involves reporting the persistence of students with various characteristics through transition points. For each transition point, Table 4 shows the number of students enrolled by year of study and by field, as well as the number who persist through the transition point to enroll the next year. The persistence rate for each transition point (pii), which is the percent of students enrolled in the i’h year of study who are still enrolled in the]” year, is also shown by field of study. In reading Table 4, it is important to understand that the number of students enrolled in Year 2 at the close of Transition Point 1 is larger than the number of students enrolled in Year 2 at the beginning of Transition Point 2. This censoring occurs because some institutions report enrollments for the first and second year of study but do not report enrollments for the third or later years of study.’ Similarly, the number enrolled in Year 3 at the close of Transition Point 2 is also larger than the number of students enrolled in Year 3 at the beginning of Transition Point 3.

Table 4

Persistence Through Transition Points by Field

1 Transition Point 1 1 Transition Point 2 1 Transition Point 3

Field of

_dY

Biochemistry Economics English Math Mech. eng. All fields

Enrolled

Yr. 1 Yr. 2 P 12

784 669 85% 1,653 1,121 68% 2,233 1,770 79% 1,764 1,330 75% 1,704 1,218 71% 8,138 6,108 75%

Enrolled

Yr. 2 Yr. 3 P23

477 422 88% 739 519 70%

1,243 871 70% 967 728 75% 829 492 59%

4,255 3,032 71%

Enrolled

Yr. 3 Yr. 4 P 34

287 251 87% 319 258 81% 572 495 87% 449 333 74% 296 211 71%

1,923 1,548 80%

The variation in the persistence rate across fields and transition points is substantial. In Table 4, for example, compare ~12 for biochemistry to ~12 for economics, and, for English, compare p23 to p34. The significance of these differences becomes evident when persistence across multiple transition points is considered. It is possible to derive the persistence rates across two or three transition points implied by the persistence rates shown for individual transition points in Table 4. For example, the imputed persistence rate Corn the first to the third year of study 0713) is simply the product ofpI andp23. Similarly, the persistence rate from the first to the fourth year of study (pl4) is the product ofpl2,p23, andp34. These persistence rates are shown in Table 5. For all fields, ~14 averages 43 percent, but there is a large difference across fields, with ~14 ranging Corn 30 percent for mechanical engineering to 66 percent for biochemistry8

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Table 5

Imputed Persistence Through Multiple Transition Points

Field of

studv

Biochemistry Economics English Math Mech. eng. All fields

YearltoYear2 I

09121

85% 68% 79% 75% 71% 75%

YearltoYear3 I

(PJ

75% 48% 56% 57% 42% 53%

YearltoYear4

CPlr) **

66% 39% 48% 42% 30% 43%

l

PI3 ‘PI2 xP23 ** PI4 =P12 xP23 xP34

Table 6 provides a comparison of persistence rates for men and women by field of study. Although these gender differences are generally small, they demonstrate the importance of disaggregation by field of study when describing patterns of persistence across demographic groups. For example, the Year 1 to Year 4 persistence rate (~114) for all fields taken as a group is higher for women (45% versus 42%), but for each individual field taken separately, ply is higher for men. The explanation for what seems to be a paradox is that women are more heavily concentrated in fields that have above-average persistence rates. Whether women continue to show a lower persistence rate after controlling for aptitude/achievement variables is a question that is considered below in the discussion of the multivariate statistical analysis of the data.

Table 6

Persistence Rates by Gender

Field of

studv

Biochemistry

Economics

English

Math

Mech. eng.

All Fields

YearltoYear2

@Id)

Male Female

88% 81%

69% 66%

81% 78%

75% 77%

71% 73%

75% 76%

Year 1 to Year 3

@13)

Male Female

78% 71%

48% 46%

57% 55%

57% 55%

43% 38%

53% 55%

Year 1 to Year 4

@rl)

Male Female

73% 57%

39% 38%

49% 48%

43% 40%

31% 26%

42% 45%

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The difference in persistence between domestic and international students is shc:vn in Table 7. For all fields as a group, pl4 for domestic students (45%) is substantially higher than for international students (38%). This difference, however, is not consistent across disciplines. In the field of English, for example, U.S. students have a much higher Year 1 to Year 4 persistence rate (49%) than do international students (33%), but in mechanical engineering, ~14 for U.S. students is only 29% compared to 33% for international students. Again, the question of whether these differences can be accounted for by other variables in the database or whether they actually reflect differences intrinsic to citizenship is discussed later in this report.

Table 7

Persistence Rates by Citizenship

Field of

study

Year 1 to Year 2

(P12)

U.S. Other

YearltoYear3

(Pi3)

U.S. Other

Year 1 to Year 4

(PII)

U.S. Other

Biochemistry 88% 81%

Economics 75% 61%

English 81% 63%

Math 78% 72%

Mech. eng. 73% 69%

All Fields 79% 68%

79% 69%

55% 42%

57% 44%

59% 53%

41% 44%

56% 48%

68% 62%

44% 34%

49% 33%

43% 41%

29% 33%

45% 38%

Among U.S. citizens, it is of interest to compare the persistence of students Corn different ethnic groups. Table 8 shows persistence rates for Asian Americans, underrepresented minorities (AfKcan Americans, Hispanic Americans, and Native Americans),g and all other U.S. citizens. For all fields taken as a group, under-represented minorities have the highest persistence rate through one, two, and three transition points. There are, however, some marked differences across fields. In biochemistry, for example, under-represented minorities had substantially lower persistence rates than either Asian Americans or other ethnic groups. In economics, underrepresented minorities had a lower pl2 than both Asian Americans and Other U.S. students, apl3 that was above that for Asian Americans but lower than that for Other U.S. students, and a pl4 above both other groups. In all other fields, underrepresented minorities consistently had the highest persistence rates.

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Table 8

Persistence of Domestic Students by Ethnicity

Field

Biochemistry

Economics

English

Math

Mech. eng.

All Fields

Year 1 to Year 2 6,~)

Under- Asian rep. Amer Minor, Other

78% 81% 79%

89% 77% 88%

80% 69% 76%

81% 85% 81%

73% 80% 78%

72% 86% 73%

Year 1 to Year 3 613)

Under- Asian rep. Amer Minor. Other

50% 58% 56%

79% 47% 81%

41% 53% 56%

58% 60% 56%

53% 66% 59%

32% 48% 41%

Year 1 to Year 4 614)

Under- Asian rep. Amer Minor. Other

40% 50% 45%

63% 36% 71%

41% 50% 43%

47% 51% 49%

40% 52% 42%

25% 48% 28%

Given the current strong interest in the predictive validity of the GRE, the question arises whether there is any association between persistence and performance on the GRE. Some interesting findings can be seen in Table 9, which shows persistence rates for students with GRE General Test verbal and quantitative ability scores above and below the median for their program. These rates are shown separately for domestic and international students.

GRE performance appears to be most strongly associated with persistence from the first to the fourth year of study ($14). An overall positive association is reflected in the rates for all fields taken as a group. U.S. students with GRE quantitative scores in the upper half of their program have a higher average Year 1 to Year 4 persistence rate (49%) than students with scores in the lower half (43%). Similarly, U.S. students who score above the median on the GRE verbal test have a hi

B her average ~14 (50%) than students

with a GRE verbal score below the median (42%). ’ The difference in pld for students with scores above and below the median on both the quantitative and verbal tests is even higher - 5 1% compared to 3 9%.

The same pattern applies to both domestic and international students in most of the disciplines. One striking exception is that international students in mechanical engineering programs with above-median GRE quantitative scores have a dramatically lower p14. Similarly, international students in biochemistry with above-median GRE verbal scores have a lowerpld. Lastly, the persistence rate for domestic biochemistry students appears to be unrelated to GRE performance.

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Table 9

Persistence Rates of Domestic and International Students by GRE Score

Domestic Stud1

Fields

Biochem. Upper Half Lower Half

Economics Upper Half Lower Half

English Upper Half Lower Half

Math Upper Half Lower Half

Mech. Eng. Upper Half Lower Half

All Fields Upper Half Lower Half

1ts

Year 1 to Year 2 (pl2)

Ouant. Verbal 0 & V

89% 88%

85% 69%

82% 80%

84% 75%

78% 74%

82% 77%

88% 89%

82% 72%

82% 79%

86% 77%

82% 74%

83% 77%

89% 89%

87% 67%

82% 79%

84% 72%

82% 73%

83% 75%

Year 1 to Year 3 (p 13)

Ouant. Verbal 0 & V

86% 77%

64% 48%

55% 57%

67% 55%

48% 37%

60% 53%

80% 85% 80% 78%

57% 69% 52% 49%

58% 57% 51% 52%

71% 71% 56% 51%

48% 49% 40% 35%

60% 61% 53% 51%

Year ltoYear4(p14)

Ouant. Verbal 0 & V

70% 69%

51% 39%

49% 49%

51% 35%

35% 25%

49% 43%

68% 70%

47% 42%

51% 42%

51% 40%

35% 28%

50% 42%

70% 70%

54% 38%

50% 43%

52% 32%

36% 24%

51% 39%

International Sl ldents

Fields

Year 1 to Year 2 (*12)

Ouant. Verbal 0 & V

Biochem. Upper Half Lower Half

Economics Upper Half Lower Half

English Upper Half Lower Half

Math Upper Half Lower Half

Mech. Eng. Upper Half Lower Half

All Fields Lower Half Upper Half

81% 86%

64% 67%

63% 68%

81% 76%

67% 68%

70% 71%

90% 91% 81% 85%

66% 65% 65% 66%

71% 69% 58% 62%

95% 100% 78% 75%

66% 64% 67% 67%

72% 71% 70% 70%

Year 1 to Year 3 (p13)

Ouant. Verbal 0 & V

73% 72% 81% 65% 71% 67%

45% 50% 52% 43% 43% 43%

50% 60% 59% 51% 38% 41%

56% 83% 85% 56% 55% 55%

40% 46% 43% 46% 42% 45%

50% 56% 56% 49% 49% 48%

63% 45% 46% 60% 65% 61%

37% 50% 52% 34% 34% 33%

42% 53% 53% 35% 19% 24%

46% 72% 74% 38% 41% 38%

28% 36% 39% 35% 30% 36%

41% 47% 48% 37% 38% 36% c

YearltoYear4(,14)

Ouant. Verbal 0 & V

14

A central issue concerns the extent to which persistence is influenced by the level of financial support. Table 10 shows persistence rates by field according to the level of financial support available in the first year of study. Three levels of support are shown: no support (none); positive support, but less than the median amount awarded in the student’s field of study at his or her institution (low); and positive support equal to or greater than that median amount (high). Persistence rates systematically increase with level of support.

Table 10

Persistence by Level of First-Year Financial Support

Biochem.

Economics

English

Math

Mech. eng.

All Fields

YearltoYear2(pj2) Level of Support

None Low* Hi**

61% 84% 89%

63% 69% 71%

73% 81% 84%

58% 76% 81%

62% 71% 78%

66% 76% 80%

Year 1 toYear (p13)

Level of Support

None Low” Hi**

42% 74% 80%

36% 52% 56%

44% 58% 65%

37% 56% 65%

39% 39% 48%

40% 54% 62%

Year 1 toYear4(pi4) Level of Support

None LOWS Hi**

28% 64% 72%

25% 43% 48%

37% 49% 57%

23% 40% 51%

22% 27% 41%

29% 43% 53%

l Below institution’s median financial support. l * At or above institution’s median financial support.

For all fields taken together, the persistence rate from Year 1 to Year 4 (pld) is 29% for students with no support, 43% for students with less than the median amount of support, and 53% for students with support equal to or greater than the median amount of support. Although it is clearly plausible that the amount of financial support is an important determinant of persistence, it is also likely that higher levels of support are given to more able students. Consequently, the results in Table 10 may reflect student ability as well as the amount of financial support. This issue will be explored in some detail in the statistical analysis below.

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Multivariate Analysis

As suggested in the preceding section, there are many factors that are associated with persistence. Given that many of these factors are also likely to be correlated with one another, multivariate statistical methods were applied to the data to determine which factors, if any, influence persistence when all of the others are held constant. The relationship between persistence through the three observed transition points and variables identified as potential determinants of persistence were estimated.

The Explanatory Variables

Four groups of variables were examined to determine their influence on persistence:

0 institutional characteristics

l student aptitude/achievement

l financial support

0 student demographic characteristics

A fifth set of variables was created to account for missing data.

Institutional characteristics. Because the data include students from 3 1 institutions, it was necessary to take into account differences in institutional characteristics . The institutional variables hypothesized to influence a student’s persistence were:

l the graduate program’s student-faculty ratio during the student’s first year.

l the graduate program’s rating for program effectiveness in the 1993 National Research Council (NRC) study of doctoral programs.

l the average GRE score (quantitative, verbal and analytical scores combined) of students enrolled in the program. l1

All three of these variables were presumed to reflect the excellence and selectivity of the student’s program. For a given student, it was assumed that the greater the excellence of the program, the greater the value of continuing in the program. At the same time, it was held that the more selective the program, the greater the difficulty of being successful. Thus, it was difficult to hypothesize apriori whether these variables have a positive or negative influence on persistence.

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Student aptitude/achievement. It was hypothesized that the greater a student’s academic aptitude and achievement, the more likely he or she is to remain enrolled through any transition point. The measures of a student’s aptitude and achievement available in the data set are:

l quantitative score on the GRE General Test

l verbal score on the GRE General Test

l analytical score on the GRE General Test

0 undergraduate grade point average self-reported on the GRE application

Because persistence is likely to be influenced by a student’s ability relative to others in his or her program, each of the four variables above was measured as a deviation from the mean value for students in that program.

In addition to these variables, the following variables were included as indicators of student aptitude and achievement:

0 average SAT score of the student’s undergraduate institution. (This variable is intended to serve as a measure of the quality of the student’s pre-doctoral education.)

l whether the student had a master’s degree when entering the doctoral program (1 if yes, 0 if no.)

Financial support. It is widely believed that financial support is a determinant of persistence because it makes graduate study affordable and it provides an incentive to remain enrolled. Also of interest is the form in which financial support is provided: Does it matter whether financial support takes the form of a fellowship, a research assistantship, or a teaching assistantship? To assess the influence of financial support on persistence, the following variables were included in the analysis:

l The net amount of financial support provided to a student during the first year of study. (For the purposes of the study, financial support equals the total amount of support less the amount of tuition and fees paid by the student. For example, if a student receives exactly enough to cover tuition and fees, then the net amount of financial support equals zero. If a student receives a teaching assistantship of $12,000 and pays tuition and fees in the amount of $4,000, then the net amount equals $8,000. Finally, if a student receives no financial support and pays tuition and fees of $4,000 Corn his or her own funds, then the net amount of support equals -$4,000.)

l All or part of the student’s financial support in the first year of study is in the form of a research assistantship (1 if yes, 0 if no)

l All or part of the student’s financial support in the first year of study is in the form of a teaching assistantship (1 if yes, 0 if no)

17

In this study, only first-year financial support was included in the analysis, and therefore the effects of any changes to the level or form of financial support over the course of a student’s tenure are not captured. The reasoning behind this simplification is as follows: financial support beyond the first year is undoubtedly influenced to a large degree by performance in the program; student performance is likely to be an important factor in determining persistence; and the data set does not provide independent information on doctoral performance; consequently, it would be difficult to distinguish between post-first-year financial support having an influence from post-first year financial support being determined by the same factors that influence persistence. An effort to disentangle the relationship between later financial support and graduate program performance and their influence on persistence needs to be undertaken in future analysis of the AGS Project data.

Student demographic characteristics. When a student’s financial support, measured aptitude/achievement, and the characteristics of his or her doctoral program are held constant, does the student’s age, gender, ethnicity, or citizenship influence persistence? To help answer this question, the following variables were defined:

l The age of the student at the beginning of his or her first year.

l The student is female (1 if yes, 0 if no).

l The student is Asian American (1 if yes, 0 if no).

l The student is a member of an under-represented minority group (1 if African American, Hispanic American, or Native American; 0 if no).

l The student is a citizen of a country other than the U.S. (1 if yes, 0 if no).

If any of these variables proved to be significant in explaining persistence, something inherent in the experience of students with that characteristic or differential treatment of students with that characteristic by the graduate program could be the cause. It would be beyond the scope of this study to distinguish between these two explanations. However, the absence of significance for any of these characteristics would suggest that neither of these alternatives applies.

Missing observation dummies. In addition to the four sets of variables described above, another set of variables was created to account for missing data on one or more variables in some of the records in the data set. Rather than deleting all records which have missing observations (and thereby losing information contained in other variables for which data are available), a dummy variable was created that corresponds to each explanatory variable that has missing data. When an observation was missing for a variable, that variable was set to zero, and the dummy variable took on the value 1; otherwise the variable took on its actual value and the dummy variable was equal to zero (Kmenta, 1979).

18

Determinants of Net Financial Support

Because of the importance of the interrelationship between financial support and the various student characteristics in determining persistence, two specifications of the persistence model were estimated. The first specification - the restricted specification - includes all of the explanatory variables except the financial aid variables; the second - the unrestricted specification - includes all of the explanatory variables. For a variable that is correlated with both persistence and financial support, a comparison of the estimates for the two specifications helps to separate its direct influence on persistence from any indirect influence that results from its effect on financial support. Before considering the estimation of the persistence model, it is useful to consider the way in which net financial support is influenced by the other explanatory variables in the persistence model.

The interest in better understanding the nexus of persistence, financial support, and student characteristics is motivated, first by the fact that institutions wish to know whether the various student characteristics on which they base their admissions decisions have a direct influence on persistence. Second, it is important for graduate program administrators to know how financial support directly influences student persistence because it is one of the variables under their control. And third, because student aptitude/achievement and financial support are positively correlated, their separate direct effects on persistence need to be disentangled in order for graduate programs to make sound decisions about admissions and financial support.

The way in which the student characteristics influence financial support can be seen in Tables 11 .a through 11 .e, which report the results of a multiple regression relating the amount of financial support to the institutional and student characteristics for each field. The overall picture that emerges is that students with higher aptitude/achievement tend to have greater financial support. In all fields other than biochemistry, one or more GRE scores has a positive and significant coefficient: GRE quantitative, verbal, and analytical in economics; GRE verbal in English; GRE quantitative in mathematics; and GRE verbal in mechanical engineering. The student’s undergraduate GPA also has a positive and significant coefficient in all fields other than biochemistry. Perhaps none of these variables has a significant coefficient for biochemistry because many departments in the biological sciences provide nearly equal amounts of support to all students enrolled in their graduate programs, as they tend to have sufficient amounts of training grants, research grants, and teaching assistantships. Several other features of the overall picture also emerge:

l Foreign students receive significantly less support than domestic students in two fields.

l Students fkom under-represented minority groups receive significantly more support than majority students in three fields.

l Asian American students receive significantly more support in one field and significantly less support in another field than do other students.

19

l Older students receive significantly less support in three fields.

Although the data make clear that student characteristics are important determinants of how financial support is awarded, the modest proportion of the variance in financial support explained by the regression model in Table 11 suggests that there is a substantial amount of independent variation in student aptitude/achievement and financial support. Consequently, it should be possible to identify their separate effects on persistence.

20

Table 1I.a

Financial Support Ordinary Least Squares Estimates for Biochemistry

Coefficient Std. Error p-value Mean

Intercept

Institutional Variables Student/facutly NRC program rating Average GRE (Q+V+A)

Aptitude/achievement variables * * + GRE quantitative GRE verbal (domestic) For_GRE verbal GRE analytical Undergraduate GPA Master’s degree Average SAT (UG inst.)

Demographic Variables Female Underrepres. minority Asian American Non-U. S. citizen

Age Missing Observation Variables

Missing GRE Missing GPA Missing student/faculty Missing age Missing SAT

10,53 1.5 6,437.2 0.1018 1.000

-89.9 126.1 0.4759 1.802 3,43 1.2 718.6 0.0000 ** 3.658

-5.9 2.9 0.0455 ** 1903.890

-3.6 3.5 0.8476 -0.377 0.5 3.0 0.4341 -0.108

-4.1 5.2 0.4344 -14.772 -0.5 3.1 0.5633 -0.95 1

-155.4 625.4 0.5981 0.003 358.4 612.4 0.2792 0.139

-0.4 4.4 0.5400 188.5 14

-281.6 403.6 0.4853 0.404 707.2 1,156.2 0.5407 0.028

-1,259.0 866.0 0.1460 0.059 -361.1 570.1 0.5265 0.337 -41.0 55.5 0.4599 24.930

-1,224.2 604.8 0.0430 ** 0.145 -959.7 475.0 0.0433 ** 0.400 -308.4 1,449.8 0.83 16 0.014

-24,167.6 5,824.5 0.0000 ** 0.001 -886.8 4,854.2 0.8550 0.828

* Indicates signifkance at the 10 percent level l * Indicates significance at the 5 percent level

l ** p-values for GRE quantitative, verbal, analytical and undergraduate GPA are for one-sided hypothesis

tests. These variables are expressed as deviations from their program means.

21

Table I1.b

Financial Support Ordinary Least Squares Estimates for Economics


Intercept Insitutiaaal Variabtm

Student/facutly NRC program rating Average GRE (Q+V+A)

Aptitude/aahievematt va&bled”“+

GRE quantitative GRE verbal (domestic) For_GRE verbal GRE analytical Undergraduate GPA Master’s degree Average SAT (UG inst.)

Demographic Variabltzs

Female Underrepres. minority Asian American Non-U. S. citizen

Age Mking Obervath Vatiablm

Missing GRE Missing GPA Missing student/faculty Missing age Missing SAT

12,233.g 7,289.1 0.0933 * 1.000

-38.0 199.1 0.8487 3.053 -970.6 3 12.3 0.0019 ** 2.962

0.9 2.8 0.7407 1903.652

7.8 3.7 0.0177 ** 0.414 8.1 2.9 0.0024 ** 2.367

9.4 4.4 0.0304 ** -20.449

10.5 2.7 0.0000 ** 1.878 3,585.7 648.5 0.0000 ** -0.003

505.1 504.9 0.1586 0.231 -6.3 4.8 0.9057 153.305

-89.6 451.7 3,916.l 1,168.2 -334.4 1,184.4

-670.3 577.1 -84.8 48.3

0.8428 0.252 0.0008 ** 0.036 0.7777 0.030

0.2454 0.5 16

0.0793 * 26.288

-977.0 571.0 0.0871 * -1,097.9 521.5 0.0353 **

-358.8 2,162.0 0.8682

-6,700.8 5,366.5 0.2118

0.188 0.525 0.006 0.000 0.863

R-Sauared 0.1376

l Indicates signifkance at the 10 percent level +* Indicates significance at the 5 percent level

l ** p-values for GFU3 quantitative, verbal, analytical and undergraduate GPA are for one-sided hypothesis


22

Table I1.c

Financial Support Ordinary Least Squares Estimates for English


Intercept

Institutional Variables Student/facutly NRC program rating Average GRE (Q+V+A)

Aptituddachievement variables * + *

GRE quantitative GRE verbal (domestic)

For_GRE verbal

GRE analytical

Undergraduate GPA Master’s degree Average SAT (UG inst.)

Demographic Variables

Female Underrepres. minority

Asian American

Non-U.S. citizen

Age

Missing Observation Variables Missing GRE Missing GPA

Missing student/faculty

Missing age Missing SAT

4,256.6 5,361.2 0.4272 1.000

-1JB3.8 60.6 0.0000 ** 3.730 -36.2 203.9 0.8591 3.513 -2.2 2.3 0.3479 1877.507

-0.3 2.0 0.5612 -2.119 10.6 2.4 0.0000 ** 0.461

3.0 6.5 0.6452 -2.085

0.2 2.2 0.4594 -1.166 1,534.6 428.6 0.0002 ** -0.002 1,245.2 357.6 0.0002 ** 0.242

2.7 2.7 0.1532 267.141

183.6 305.5 0.5478 0.579 6,3 16.4 603.3 0.0000 ** 0.079

2,083.l 853.2 0.0146 ** 0.030

928.1 579.0 0.1090 0.076 31.3 27.7 0.2578 27.333

-35.8 487.6 0.9414 0.114 -309.8 351.5 0.3782 0.275

-4J25.5 1,828.6 0.0241 ** 0.004

- 1,000.3 4,940.3 0.8395 0.000 3,973.3 3,072.g 0.1960 0.766

R-Sauared 0.1908

* Indicates significance at the 10 percent level *+ Indicates significance at the 5 percent level

*** p-values for GREZ quantitative, verbal, analytical and undergraduate GPA are for one-sided hypothesis


23

Table 1l.d

Financial Support Ordinary Least Squares Estimates for Math


Intercept

Institutional Variables Student/facutly NRC program rating

Average GRE (QW+A)

Aptitude/achievement variables * * *

GRE quantitative GRE verbal (domestic) For_GRJZ verbal

GRE analytical Undergraduate GPA

Master’s degree Average SAT (UG inst.)


Female Underrepres. minority Asian American

Non-U. S. citizen

Age

Missing Observation Variables

Missing GRE Missing GPA


Missing age Missing SAT

-21,475.5 5,394.g 0.0001 ** 1.000

-628.9 196.0 -1,538S 217.2

21.0 2.0

0.0013 ** 2.061 0.0000 ** 3.399 0.0000 ** 2003.698

8.6 4.3 0.0236 ** 0.122 4.5 2.4 0.0296 ** 0.949

-4.1 3.6 0.2598 -19.874

4.4 2.6 0.0425 ** 0.590 1,640.8 515.1 0.0007 +* 0.003

192.6 406.9 0.3180 0.230 -2.0 3.2 0.7332 198.768

-558.9 375.3 0.1365 0.254

4,506.8 910.5 0.0000 ** 0.037

429.8 870.0 0.6213 0.039

-630.9 462.8 0.1728 0.387

-197.7 36.0 0.0000 ** 25.470

-1,611.8 411.2 0.0001 ** 0.264

-258.1 401.2 0.5201 0.461

3,350.4 2,759.4 0.2247 0.002

-6,508.7 3,482.4 0.0616 * 0.002

-2,275.3 3,628.6 0.5306 0.822

R-Sauared 0.1732

l Indicates significance at the 10 percent level l * Indicates significance at the 5 percent level



24

Table 1l.e

Financial Support Ordinary Least Squares Estimates for Mechanical Engineering


Intercept

Institutional Variables Student/facutly NRC program rating Average GRE (QtV+A)

Ap tituddachievement variables * **

GRE quantitative GRE verbal (domestic) For_GRE verbal

GRE analytical Undergraduate GPA Master’s degree Average SAT (UG inst.)


Female Underrepres. minority

Asian American

Non-U. S. citizen

Age

Missing Observation Variables Missing GRE Missing GPA

Missing student/faculty Missing age Missing SAT

-l&703.5 7JO3.6 0.0271 ** 1.000

-1,021.3 116.1 0.0000 ** 10.1 379.1 0.9787

18.6 2.9 0.0000 **

4.119 3.493

1905.03 1

-5.3 4.8 0.8650 -1.017 11.5 2.9 0.0000 ** 2.3 18 12.6 4.8 0.0091 ** -16.686 -0.7 2.9 0.5918 -0.746

3,524.6 632.2 0.0000 ** 0.003 594.9 525.6 0.1289 0.239

-1.4 4.5 0.6224 188.141

1,211.7 635.0 1,743.l 1,057.4

-2,961.0 843.6

-2,236.1 537.5

-281.1 51.9

0.0564 * 0.097

0.0993 * 0.036 0.0004 ** 0.056

0.0000 ** 0.396 0.0000 ** 25.759

96.9 525.3 0.8536 -950.0 482.9 0.0492 **

-6,123.6 3,587.6 0.0878 *

-3,115.l 5,073.l 0.5392

0.223 0.480

0.002 0.000 0.83 1

R-Sawed 0.2118

* Indicates significance at the 10 percent level ** Indicates significance at the 5 percent level

*** p-values for GRE quantitative, verbal, analytical and undergraduate GPA are for onesided hypothesis


25

Estimation of the Persistence Model

The approach taken to the statistical analysis for each field of study was to estimate a model that explains actual persistence through the three transition points QQJ, ~23, ~34) as a function of the explanatory variables. It was assumed that the explanatory variables influence the likelihood of a given student persisting through any of the three transition points in the same way (conditional on the student being enrolled at the beginning of the transition point). However, the inclusion of dummy variables for the second and third transition points is equivalent to having a separate intercept for each transition point and makes it possible to incorporate unequal persistence rates for the three transition points.

This approach permits the application of discrete time survival analysis to graduate student persistence. It treats each transition point as having a stochastic binary outcome for which the probability of persistence of any student is determined by the values of the explanatory variables for that student and a constant term for the particular transition point. Implicit in the estimation is that, for each individual, the likelihood of persistence depends on an index: the higher its value, the more likely that the individual will persist. This index is modeled as a linear function of the explanatory variables and an error term drawn from a logistic distribution. For each field, maximum likelihood estimates of this model were obtained for two specifications - one with and one without the financial support variables. The statistics are reported in Tables 12.a through 12.e.

26

Table 12.a

Logit Estimates for Biochemistry

Restricted WlKtStl-iCted

Coefficient p-value Coefficient p-value Mean

Intercept 2.6874 Yr2 to Yr3 0.1971 Yr3 to Yr4 0.0242

Institutional Variables StudentIfacutly 0.1346 NRC program rating 0.2472

Average GRE (Q+V+A) 0.0006

Aptitude/achievement variables ** * GRR quantitative GRE verbal (domestic)

For_GRE verbal

GRE analytical

Undergraduate GPA

Master’s degree

Average SAT (VG inst.)

Financial Aid Variab Les

First-year net support

Research Assistantship

Teaching Assistantship


Female

Underrepres. minority

Asian American

Non-U.S. citizen

Aae


Missing GRE

Missing GPA


Missing age

Missing SAT

0.0002 0.4560 0.0005 0.3729 -0.377 -0.0015 0.895 1 -0.0015 0.8974 -0.108

0.0006 0.7602 0.0010 0.65 12 -14.772

0.0008 0.2602 0.0008 0.2702 -0.95 1

-0.2696 0.8340 -0.268 1 0.8291 0.003

0.2232 0.1794 0.2121 0.1960 0.139

-0.0025 0.8991 -0.0025 0.9064 188.514

-- _- 0.059 1 0.0000 +* 9.380 -- -- -0.2562 0.1956 0.344 -- -- -0.1945 0.3715 0.280

-0.5793 0.0003 l * -0.5776 0.0003 ** 0.404

-1.23 18 0.0026 l * -1.2800 0.0022 ++ 0.028

-0.1769 0.6076 -0.0433 0.9022 0.059

-0.0957 0.6653 -0.1059 0.6391 0.337

0.0154 0.4880 0.0213 0.3430 24.930

-0.3975 0.0801 * -0.3323 0.1509 0.145

-0.6149 0.0010 l * -0.6064 0.0013 ** 0.400

12.1784 0.9573 12.2492 0.9571 0.014

-17.6667 0.9966 -16.2748 0.9968 0.00 1

-2.8214 0.1914 -2.8363 0.1875 0.828

Log likelihood -570.8 -562.4 0.0382 ++

(hrestr. vs. Restr.)

0.3360 2.4464 0.3934 1.000 0.2733 0.1331 0.4647 0.308 0.9086 -0.035 1 0.8691 0.185

0.0131 ++ 0.1578 0.0052 ++ 1.802 0.3974 0.0354 0.9121 3.658

0.6325 0.0008 0.5166 1903.890

* Indicates significance at the 10 percent level +* Indicates significance at the 5 percent level



27

Table 12. b

Logit Estimates for Economics

Restricted Unrestricted


Intercept -3.0705 Yr2 to Yr3 0.07 16 Yr3 to Yr4 0.6529

Institutional Variables Student/facutly -0.0539 NRC program rating -0.0056

Average GRE (Q+V+A) 0.002 1

Aptitude/achievement variables***


For_GRE verbal

GRE analytical

Undergraduate GPA

Master’s degree

Average SAT (VG inst.)

Financial Aid Variables First-year net support




Female


Asian American

Non-U. S. citizen

Age


Missing GRE

Missing GPA


Missing age

Missing SAT

0.0021 0.0044 +* 0.0019 0.0119 ++ 0.414 0.0004 0.2610 0.0003 0.3058 2.367

-0.0006 0.4947 -0.0009 0.33 10 -20.449 0.0007 0.1111 0.0005 0.2089 1.878

0.223 1 0.0589 l 0.1271 0.1907 -0.003

0.1483 0.0933 * 0.1203 0.1439 0.23 1

0.0005 0.3 105 0.0006 0.2869 153.305

--

-_

--

--

-_ 0.0078 0.1110 1.504

0.6042 0.0023 l * 0.070

0.5565 0.0000 ** 0.297

-0.1127 0.2627 -0.1260 0.2144 0.252

0.1824 0.4867 0.2639 0.3203 0.036

-0.0903 0.7357 0.0209 0.9382 0.030

-0.2198 0.0888 * -0.1448 0.2690 0.516

-0.0038 0.7155 o.do15 0.8904 26.288

-0.2386

-0.2455

0.422 1

0.3874

0.0502 +

0.0351 l *

0.5294

0.7439

-0.2632 0.0334 l *

-0.2 140 0.0690 l

0.3352 0.6185

0.5008 0.6749

Log likelihood -1601.9 -1579.8 0.0001 *+

(Unrestr. vs. Restr.)

0.0648 ’ -3.7439 0.0260 *+ 1.000 0.4657 0.0336 0.7348 0.273 0.0000 +* 0.5826 0.0002 +’ 0.118

0.2270 -0.d386 0.3935 3.053 0.9417 0.0429 0.57 14 2.962

0.0018 l * 0.002 1 0.0017 ** 1903.652

0.188

0.525

0.006

0.000

0.863

* Indicates significance at the 10 percent level l * Indicates significance at the 5 percent level

*+* p-values for GRE quantitative, verbal, analytical and undergraduate GPA are for one-sided hypothesis


28

Table 12.~

Logit Estimates for English



Intercept -3.6174 Yr2 to Yr3 -0.5572 Yr3 to Yr4 0.3882

Institutional Variables Studentifacutly -0.0620 NRC program rating 0.1048


Aptitude/achievement variables ***


For_GRE verbal

GRE analytical

Undergraduate GPA

Master’s degree

Average SAT (UG inst.)

Financial Aid Variables





Female


Asian American

Non-U.S. citizen

Age


Missing GRE

Missing GPA


Missing age

Missing SAT

-0.0007 0.8989 -0.0007 0.89 10 -2.119 0.0019 0.0017 ** 0.0016 0.0072 ** 0.46 1

-0.0009 0.587 1 -0.00 12 0.4613 -2.085

0.0002 0.3612 0.0002 0.3645 -1.166 -0.0023 0.508 1 -0.0560 0.6873 -0.002 0.4895 0.0000 ** 0.4223 0.0000 +* 0.242 0.0009 0.0838 + 0.0010 0.0674 * 267.141

-- -- 0.038 1 0.0000 ** 1.813 -- -- 0.4999 0.0419 l * 0.036 _- _- 0.2136 0.0554 * 0.333

-0.1084 0.1838 -0.1267 0.1245 0.579 0.1822 0.2655 -0.0329 0.8489 0.079

-0.0370 0.873 7 -0.0350 0.8830 0.030 -0.640 1 0.0000 l * -0.669 1 0.0000 ** 0.076

0.0140 0.0664 + 0.0 145 0.0604 l 27.333

0.025 1 0.8434 0.0049 0.9695 0.114 -0.2159 0.0208 ** -0.2090 0.0268 ** 0.275 -0.9304 0.1016 -0.6540 0.2669 0.004 -1.0347 0.4739 -0.9032 0.5326 0.000 1.0961 0.1623 1.1521 0.1491 0.766

Log likelihood -2064.3 -2030.3 0.0000 l *


0.0099 l * -4.6112 0.0017 +* 1.000 0.0000 *+ -0.6092 0.0000 ++ 0.307 0.0042 +* 0.3515 0.0101 ++ 0.141

0.0000 ** -0.0 124 0.4591 3.730 0.0527 * 0.0999 0.0619 + 3.513 0.0031 ** 0.0022 0.0006 ** 1877.507

* Indicates significance at the 10 percent level l * Indicates significance at the 5 percent level



29

Table 12.d

Logit Estimates for Math



Intercept -7.1912 Yr2 to Yr3 -0.0791 Yr3 to Yr4 -0.2266

Institutional Variables Student/facutly -0.2585 NRC program rating 0.1714


Aptitude/achievement variables*** GRE quantitative GRE verbal (domestic)

For_GRE verbal

GRE analytical

Undergraduate GPA

Master’s degree


Financial Aid Variab Ies





Female


Asian American

Non-U. S. citizen

Age


Missing GRE

Missing GPA


Missing age

Missing SAT

Log likelihood

0.0008 0.2267 0.0005 0.33 14 0.122 0.0019 0.0011 *+ 0.0018 0.0020 *+ 0.949

-0.003 1 0.0015 ++ -0.003 1 0.0018 ** -19.874

0.0005 0.2 183 0.0003 0.3401 0.590

0.2137 0.0569 * 0.1488 0.1374 0.003

0.1787 0.0520 * 0.1659 0.0674 l 0.230

0.0010 0.1319 0.0011 0.0957 + 198.768

__

__

__

-- 0.0478 0.0000 +* 6.648 -- -0.3040 0.1377 0.049 -- -0.0724 0.4844 0.553

-0.0365 0.7123 -0.0055 0.9559 0.254

0.74 17 0.0047 l * 0.522 1 0.0490 l * 0.037

-0.0117 0.9579 -0.0134 0.9523 0.039

0.0373 0.7616 0.0736 0.5554 0.387

-0.0145 0.1091 -0.0060 0.5161 25.470

-0.2466 0.0207 ** -0.1623 0.1375 0.264

0.0494 0.643 1 0.0495 0.6469 0.461

16.0839 0.995 1 15.8523 0.9952 0.002

-1.2390 0.1740 -1.1037 0.2297 0.002

1.0362 0.2777 1.1979 0.2095 0.822

-1718.7 -1693.7 0.0000 **

0.0000 *+ -6.2338 0.0000 l * 1.000 0.4058 -0.1296 0.1789 0.304 0.0700 l -0.304 1 0.0162 l * 0.141

0.0000 ** -0.2229 0.0000 ++ 2.061 0.0017 l * 0.2527 0.0000 ++ 3.399

0.0000 l * 0.0028 0.0000 l * 2003.698


l Indicates significance at the 10 percent level l * Indicates significance at the 5 percent level l ** p-values for GRE quantitative, verbal, analytical and undergraduate GPA are for one-sided hypothesis

tests. These variables are expressed as deviations Corn their program means.

30

Table 12.e

Logit Estimates for Mechanical Engineering



Intercept -3.4217 Yr2 to Yr3 -0.5992 Yr3 to Yr4 -0.1339

Institutional Variables Student/facutly -0.0528 NRC program rating 0.323 1


Aptitude/achievement variables *** GRE quantitative GRE verbal (domestic)

For_GRE verbal

GRE analytical

Undergraduate GPA

Master’s degree


Financial Aid Variables First-year net support




Female


Asian American

Non-U. S. citizen

Age


h4issing GE

Missing GPA


Missing age

Missing SAT

0.0003 0.3950 0.0004 0.3597 -1.017 0.0018 0.0023 ** 0.0016 0.0071 *+ 2.318

-0.0002 0.8353 -0.0006 0.5906 -16.686 0.0000 0.5305 -0.000 1 0.5332 -0.746 0.3054 0.0142 ** 0.2131 0.0652 * 0.003

0.8002 0.0000 ** 0.7811 0.0000 ** 0.239 -0.0009 0.8191 -0.0009 0.8258 188.14 1

-- -- 0.0277 0.0000 +* 4.268 __ -_ -0.0252 0.8265 0.321 -_ -_ -0.038 1 0.7588 0.200

0.0107 0.9398 -0.0 150 0.9161 0.097 0.6721 0.0103 ** 0.6276 0.0177 l * 0.036

-0.1552 0.3986 -0.0797 0.6683 0.056 0.1082 0.3683 0.1703 0.1625 0.396 0.03 50 0.0033 l * 0.0439 0.0004 l * 25.759

0.0185 0.8747 0.0268 0.8205

-0.293 1 0.0061 *+ -0.2796 0.0093 **

-0.3973 0.73 10 -0.2527 0.8279

-0.7852 0.4800 -0.7759 0.4862

Log likelihood -1676.1 -1664.1 0.0075 ++


0.0317 ++ -3.065 1 0.0570 l 1.000 0.0000 l * -0.6275 0.0000 l * 0.293 0.3527 -0.1394 0.3368 0.105

0.0377 ++ -0.026 1 0.3181 4.119 0.0001 l * 0.3 188 0.0002 *+ 3.493 0.0092 l * 0.0013 0.0529 l 1905.03 1

0.223

0.480

0.002

0.000

0.83 1

l Indicates significance at the 10 percent level *+ Indicates significance at the 5 percent level



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Model performance diagnostics show that the model does a reasonable job of explaining persistence. Likelihood ratio statistics indicate that, in each field of study, the explanatory variables are jointly highly statistically significant. Likelihood ratio tests also indicate that, in each field of study, the unrestricted model statistically outperforms the restricted model. That is, a model which includes first year financial support variables better explains persistence through the first several years of study.

A more tangible measure of model performance is the extent to which model estimates can be used to distinguish groups of students with high persistence from groups of students with low persistence. This comparison entails using the estimated coefficients to compute the predicted probability of persistence for each student in the sample, then reordering the sample from estimated-most-persistent to estimated-least- persistent. If the predicted retention rates are adequately reflective of student persistence, then, for students who are estimated most persistent, one should observe a greater proportion of students who actuaZZy persist into the second, third, and fourth years than for students who are estimated least persistent. The magnitude of this difference indicates the degree of model performance.

Figure 1 shows the actual survival curves (mean persistence rates into years 2, 3, and 4) for two groups: the group of students that are ranked “above 7Sth percentile” and the group of students that are ranked “below 25* percentile” within field of study using estimates from the unrestricted model. (These survival curves combine all five fields of study. That is, each percentile group combines the students from all five disciplines that are categorized within field by that percentile.) In addition, the survival curve for the entire sample is included to provide a benchmark.

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Figure I

Comparison of Actual Persistence Rates for Students Predicted to be Most and Least Persistent: Unrestricted Model

-m-75th P + 1 *25thp-

-All

Predicted Rank

100%

90%

80%

70%

60%

50%

40%

30%

20%

Year 1 Year 2 Year 3 Year 4

Year 1 Year 2 Year 3 Year 4 75thp+ 100% 86% 72% 63% 25thP- 100% 61% 33% 22% All 100% 75% 53% 43%

The survival curves portray a measurable difference in retention rates between these groups. In particular, the group of students predicted to exceed the 75* percentile persisted into the fourth year with approximately one and one-half times the frequency than the average for all students, and with nearly three times the frequency for students predicted to be in the 2? percentile. In this respect, the model successfully identifies students that persist into the second, third, and fourth years on the basis of aptitude/achievement, financial support, and demographic characteristics.

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Figure 2

Comparison of Actual Persistence Rates for Students Predicted to be Most and Least Persistent: Restricted and Unrestricted Models

+75th P+

--A--25thP-

- l x - 75th P R&i&d

-4X-2!3hP R&CCtt3d

‘I

100%

90%

80%

70%

60%

50%

40%

30%

20%



75th p Restricted 100% 85% 70% 60% 25th p Restricted 100% 64% 38% 27% All 100% 75% 53% 43%

Figure 2 shows the survival curves for the 25* and 75& percentile groups for both the restricted and unrestricted models. The difference between the two sets of curves reflects the impact of including financial support variables. The fact that the survival curves for the unrestricted model lie farther away from the mean survival curve (smooth uninterrupted line) than do the survival curves for the restricted model (dashed lines) illustrates the unrestricted model’s superiority in distinguishing high and low persistence. Given the earlier finding that financial support is strongly influenced by other variables in the persistence model (see Determinants of Net Financial Support), it should not be surprising that the difference in overall performance between the restricted and unrestricted models is modest.

Turning to the role of individual explanatory variables, examination of Tables 12.a through 12.e shows that many of the variables hypothesized as possibly influencing persistence do play a significant role. But, as the following sections show, there are clear differences among fields as to whether and how the explanatory variables influence persistence.

Variation Across Transition Points. As explained earlier, the model was constructed to allow for the likelihood of a student persisting across a transition point to vary across the three observed transition points. The coefftcients on the “Year 2 to Year 3” and “Year 3 to Year 4” dummy variables indicate whether there are differences in the

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conditional probability of persistence among the transition points. No significant difference among these conditional probabilities exists for biochemistry, but there are significant differences in the other fields. For economics, the probability of dropping out is significantly lower in the third year than in the first or second year. For English, the probability of dropping out is least in the third year, and it is significantly greater in the second year than in the first. For mathematics, the probability of dropping out is significantly greater in the third year than in the first or second year. Finally, for mechanical engineering, the probability of dropping out is significantly higher in the second year than in the first or third year. It is possible that these patterns reflect underlying differences in the programmatic structure of the disciplines.

Institutional variables. As discussed earlier, the three institutional variables were chosen to measure the quality and selectivity of the program in which a student is enrolled. To the extent that one believes that higher quality, more selective programs can be expected to engender higher persistence rates for students of given characteristics, the coefficient on “Enrollment/Faculty” should be negative and the coefficients on ‘NRC program rating” and on “Average GRE (Q+V+A)” of the first year cohort should be positive. For the unrestricted specification, the coefficient on “student/faculty” is positive and significant for biochemistry, but negative for all the other fields, although it is negative and significant only for mathematics.” Again using the unrestricted specification, the “NRC program rating” coefficient is positive but not significant for biochemistry and economics, and positive and significant for the remaining three fields. Finally, the “Average GRE (Q+V+A)” coefficient is positive for all fields and significant for all but biochemistry. Although the results are not entirely consistent across fields, they do suggest that a student, given his or her aptitude/achievement, demographic characteristics, and financial support, is more likely to persist through a transition point at a more highly rated, more selective program, especially as measured by “Average GRE (Q+V+A).”

Antitude/Achievement Variables. The assumption underlying the inclusion of these variables in the model is that the higher a student’s aptitude/achievement, the greater the likelihood that the student will persist through a transition point. Consequently, a one-tailed test for significance is used. An interesting array of statistics is evident in Tables 12.a through 12.e:

l Biochemistry - None of the aptitude/achievement variables is significant for either the restricted or the unrestricted specification.

0 Economics - The “GRE quantitative” variable is significant in both specifications. That is, it influences persistence even after controlling for its indirect effect as a determinant of students’ financial support. To gain a sense of the magnitude of the impact that the GRE quantitative score has on persistence, consider the effect of a 100 point difference in GRE quantitative score. Other things (including financial support) being equal, an economics student with a GRE quantitative score that is 50 points above the mean has a conditional persistence rate from Year 1 to Year 4 (pld) equal to 0.42, whereas a student with a GRE quantitative score that is 50 points less than the mean has a conditionalp of 0.36. No other aptitude/achievement variables have

35

significant coefficients in the unrestricted model. The student’s “Undergraduate GPA” and “Master’s degree” are significant in the restricted, but not in the unrestricted, specification; that is, unlike “GRE quantitative,” no direct influence of these two variables on persistence was detected.

l English - Both “GRE verbal” and “Master’s degree” are significant in both specifications. The statistics in Table 12.~ for the unrestricted specification imply that a difference of 100 points in GRE verbal score, centered around the mean, results in a 6-percentage-point difference in the conditionalpJ4, and the difference between having and not having a master’s degree results in a 13-percentage-point difference in

pJ4. The average SAT score of the student’s undergraduate institution has a significant coefficient in both specifications.

0 Mathematics - The significant positive coefficient on “GRE verbal” (domestic) and the significant negative coefficient on the interaction term “Foreign*GRE verbal” imply that “GRE verbal” is significant for domestic students, but not for students who are not U.S. citizens. l3 For a U.S. student, the conditionalpJ4 is 0.43 for a GRE verbal that is 50 points above the mean, and 0.37 for a GRE verbal score that is 50 points below the mean. Surprisingly, “GRE quantitative” is not a significant explanatory variable for the persistence of students in mathematics in either the restricted and unrestricted specifications. The “Master’s degree” variable does-have a positive significant coefficient in both specifications; based on the unrestricted specification, having a master’s degree adds 6 percentage points to the conditional pJ4. Unlike “GRE verbal” and “Master’s degree,” “Undergraduate GPA” is significant only in the restricted model, and “average SAT” is significant only in the unrestricted model.

l Mechanical engineering - “GRE verbal, ” “Undergraduate GPA,” and “Master’s degree” all have significant positive coefficients in both specifications. A loo-point difference in GRE verbal implies a 4-percentage- point difference in the conditional pJ4, and having a master’s degree adds a sizable 23 points to the conditionalpJ4. As with mathematics, “GRE quantitative” is not significant in either specification.

Although there are important differences in the results across fields, it is possible to draw some general conclusions from the results for the aptitude/achievement variables. First, the results for biochemistry notwithstanding, it is apparent that the GRE General Test scores measure student characteristics that play a role in determining persistence. The size of the direct impact is not large, but this is not surprising, given that the differences in GRE scores among enrolled students tend to be small; that is, students with low GRE scores are unlikely to be admitted unless they possess some other indicator of high aptitude or achievement.

Also, the fact that it is the GRE verbal, not the GRE quantitative, score that is associated with persistence in mathematics and mechanical engineering programs is interesting. This result suggests that the verbal test does measure attributes relevant to performance in quantitative fields. But the insignificance of the GRE quantitative score in these two fields need not imply that the GRE quantitative test does not measure

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performance attributes. This result could be attributed to the small variance of the GRE quantitative variable - the result of scores being bunched near the maximum possible value; indeed, the median GRE quantitative in the data set is 780 for mathematics and 760 for mechanical engineering compared to a maximum score of 800. Consequently, rather than being a reflection of differences in students’ quantitative aptitudes, the observed variance is likely to have a relatively large random component. In future work with the AGS Project data, it would be useful to obtain the students’ GRE Subject Test scores from Educational Testing Service for inclusion in the analysis, because those results are likely to contain more information on differences in students’ quantitative skills and preparation.

A second general conclusion regarding the role of aptitude/achievement variables is that the undergraduate GPA of a student does not appear to have a major influence on persistence, even though the selectivity of the student’s undergraduate institution is controlled for with the inclusion of the average SAT score of students attending that institution. In the restricted specification, “Undergraduate GPA” has a significant coefficient for three fields, but in the unrestricted specification there is significance in only one field (mechanical engineering at the 90% confidence level). In part, the largely insignificant role of “Undergraduate GPA” may be the result of its being self-reported on the GRE application as well as the limited availability of this data (information on this variable was available for only 40 percent of the observations). But the difference between the results for the restricted and unrestricted specifications suggests that the influence of “Undergraduate GPA” on persistence is felt largely through its effect on decisions by graduate programs about the amount of financial support to award students.

Third, the fact that having a master’s degree before entering a Ph.D. program is significant in three fields suggests that master’s degree programs play an important role in preparing and identifying students who are likely to persist in doctoral programs. Perhaps students who decide to enter doctoral programs after master’s programs are better prepared for and have a greater commitment to the field than students who enter doctoral programs directly from bachelor’s programs.

Financial Supnort Variables. The role of financial support in determining persistence is captured in the model by (1) the amount of the student’s financial support awarded and (2) whether the support includes a research or teaching assistantship. For reasons already discussed, these variables reflect only first-year financial support - that is, the amount of support awarded before performance in graduate school is known. The results in Tables 12.a through12.e on these variables, summarized below, reflect the impact of financial support independent of measured aptitude/achievement and other variables in the model.

l Biochemistry, mathematics, and mechanical engineering - In these fields, the greater the net amount of financial support a student receives in the first year of study, the more likely he or she is to persist through a transition point, but whether that support takes the form of either a research assistantship or a teaching assistantship (rather than a fellowship, the default alternative) does not matter. The difference in the conditionalpld from having $5,000 in net financial support above the mean rather

37

than $5,000 below the mean is 0.17 for biochemistry, 0.15 for mathematics, and 0.18 for mechanical engineering.

Economics - The amount of net financial support does not have a statistically significant positive effect on persistence, but a student’s having a research or teaching assistantship is preferable to having a fellowship in terms of influence on persistence. Having a given amount of financial support in the form of an research or teaching assistantship rather than a fellowship adds 0.19 and 0.17, respectively, to the conditional ~14 for economics students.

English - Both the net amount of support and whether it is a research or teaching assistantship rather than a fellowship has a significant positive effect on a student’s persistence. For an English student, a $10,000 difference in net support, centered around the mean, adds 12 percentage points to the conditional ~14.

The statistics for the financial support variables make it clear that financial support has an important influence on a student’s persistence independent of any role that a student’s personal characteristics might play. l4

Demographic Variables. These variables were included in the model to ascertain whether demographic characteristics explain any observed variation in persistence after controlling for the characteristics of the institution, measures of students’ aptitude/ achievement, and financial support. The coefficients on these variables in Tables 12.a - 12.e do not reveal any systematic patterns across disciplines.

A foreign student with given other characteristics is significantly more likely than a domestic student with the same characteristics to drop out of an English program, but this is not so in the other four fields. The results in Table 12.~ imply that the conditional probability of a student persisting from Year 1 to Year 4 of an English program is 0.5 1 if the student is domestic, but only 0.3 1 if the student is foreign. ls

A female student with given other characteristics is significantly more likely than a male student with the same characteristics to drop out of a biochemistry program, but this is not so in the other fields. The implication of Table 12.a is that the conditional ~14 for a male biochemistry student is 0.77, but for a female it is only 0.64.

A domestic student with given other characteristics who is from an under-represented minority group is significantly less likely than a domestic student who is not a member of an under-represented minority group to drop out of a mathematics or mechanical engineering program, more likely to drop out of a biochemistry program, and neither more nor less likely to drop out of an economics or English program. The respective values for the conditional ~14 for domestic nonminority and minority students are 0.42 and 0.57 in mathematics and 0.28 and 0.48 in mechanical engineering, while they are 0.74 and 0.40 in biochemistry.

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l A domestic student who is Asian American and has given other characteristics is neither more nor less likely to drop out of a program in any of the five fields of study than a domestic student who is not Asian American.

l Older students are significantly less likely than younger students with the same characteristics to drop out in English and mechanical engineering programs, but this is not so in the other three fields. The implied difference in the conditional probability of persistence resulting Corn a five-year age difference is only 0.02 for English and 0.05 for mechanical engineering.

The absence of consistent patterns across disciplines in the conditional relationship between student persistence and demographic characteristics can be taken as an indication that there is neither pervasive, preferential institutional behavior toward students from particular demographic groups, nor or there prevalent differences among demographic groups with respect to their ability to adapt and survive in graduate school. Although the differences in the results are substantial in particular instances, persistence seems to be more consistently linked to student aptitude/achievement characteristics and to financial support than to demographic characteristics.

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Summary and Conclusions

In this study, a model was specified to explain the relationship between student persistence through the first four years of graduate study and a number of variables including characteristics of the programs in which students are enrolled, the academic aptitude and achievement of the students, the financial support awarded to the students, and the demographic characteristics of the students. Discrete-time survival analysis techniques were used to fit the model to a data set derived from the AGS Project database. The data set consists of records for 8,138 students enrolled for at least two years in five disciplines at 3 1 graduate schools. The estimated model correctly explains approximately two thirds of the observed outcomes for these students across one or more of three possible year-to-year transition points. Many of the explanatory variables had statistically significant coefficients, and many of these implied substantial effects on student persistence across transition points.

The estimated model suggests the following general conclusions:

A student is likely to have a higher persistence rate at more selective graduate programs in four of the five disciplines, given that student characteristics and levels of financial support are held constant.

A student with a higher GRE quantitative ability score or GRE verbal ability score is likely to have a higher persistence rate in four of the five disciplines, given that other student characteristics, the levels of financial support and the characteristics of the student’s graduate program are held constant.

A student entering a doctoral program with a master’s degree is likely to have a higher persistence rate than a student without a master’s degree in three of the five disciplines, other things being equal.

A student with a greater amount of net financial support in the first year of study is likely to have a higher persistence rate in four of the five disciplines, other things being equal.

In the fifth discipline, the amount of financial support is not significant, but a student with support in the form of an assistantship rather than a fellowship is likely to have a higher persistence rate, other things being equal.

An older student is likely to have a slightly higher persistence rate in three fields, other things being equal.

Other demographic characteristics - citizenship, gender, and ethnicity - have sizable effects on persistence in some instances, but no consistent pattern across disciplines is evident.

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Although this study has revealed a significant relationship between persistence and a number of explanatory variables, more work can be done to build a robust understanding of persistence in doctoral programs. First, data for the years since 1994 should be added to the data set so that more cohorts can be followed into their fourth year of study and beyond. Second, information on whether a student has graduated should be incorporated into the data set so that persistence past the fourth year and degree completion can be analyzed. l6 Third, ETS data on GRE Subject Test scores should be incorporated into the data set, so that measurement of aptitude and prior achievement can be enhanced. ” Fourth, methods for appropriately analyzing data on financial support beyond the first year should be developed to expand understanding of how financial support influences persistence. These enhancements should extend substantially our knowledge of the graduate education process and the determinants of persistence, time to degree, and graduation rates.

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References

Bowen, W. G., & Rudenstein, N. L. (1992). In pursuit of the Ph.D. Princeton, NJ: Princeton University Press.

Espenshade, T. J., & Rodriguez, G. (1995). Foreign graduate students in U.S. doctoral nrograms in sciences and the humanities. New York: Alfred P, Sloan Foundation.

Kmenta, J. (1979). On the problem of missing measurements in the estimation of economic relationships. In E. G. Charatsis (Ed.), Proceedings of the Econometric Societv European Meeting 1979. Amsterdam: North-Holland.

National Research Council. (1995). Research-doctorate programs in the United States. Washington, DC: National Academy Press.

Willingham, W. W. (1974). Predicting success in graduate education. Science, 183,273-278.

Zwick, R. (1991). An analvsis of graduate school careers in three universities: Differences in attainment patterns across academic nrograms and demoaranhic grouns (GRE Board Professional Report 86-21P; ETS Research Report 91-7). Princeton: NJ: Educational Testing Service.

Zwick, R., & Braun, H. I. (1988). Methods of analyzing the attainment of graduate school milestones: A case studv (GRE Board Professional Report 86.3P; ETS Research Report 88-30). Princeton, NJ: Educational Testing Service.

Footnotes

’ Their analysis was extended by Espenshade and Rodriguez (1995).

2 Includes students who have withdrawn or have taken leave with the possibility of returning at a later date.

3 To account for returning leave takers we would either have to increase the dimensions of each year’s outcome to three (persist, exit and return, exit permanently) or expand the definition ofpersisr to include cases where the student returns within a fixed number of years. Either option is impractical given the limitations of the data but may become possible with an extended data set. Nevertheless, treating all student exits as permanent exits does cause underestimation of persistence rates. The impact of this, however, is expected to be minimal. Within the sample, 1.8% of students who leave return in the subsequent year (ranging from 0.7% for biochemistry to 2.2% for economics). These return rates imply that reported two- year persistence rates underestimate actual persistence rates by an average of less than half of one percentage point, and reported four-year persistence rates underestimate actual persistence rates by an average of less than one percentage point.

4 In addition, there are a number of qualitative variables (for example, socio-economic status) that, in principle, could influence persistence. Inclusion of such variables was beyond the scope of this study.

5 Data from the GRE database was matched to the AGS Project database by ETS. Confidentiality of students in both databases was preserved.

6 Averages reported by Barrons are provided by institutions; differences in institutional reporting practices may lead to inaccuracies in the data.

’ For example, for all fields, out of the 6,108 students who were identified as enrolling in the second year of study, information about whether they did or did not enroll in the subsequent year was available for only 4,255 cases. The remaining 1,853 cases, therefore, were excluded from the calculation of the persistence rate from Year 2 to Year 3.

* Bowen and Rudenstein, and Espenshade and Rodriguez, also found large differences across fields with respect to completion rates. Their results show higher completion rates in the sciences than in the humanities and social sciences.

’ It would have been interesting to disaggregate the under-represented minority category into separate groups. This would have resulted, however, in a small number of observations for each field and group, which would have lead to highly unreliable estimates.

lo Espenshade and Rodriguez find a strong association between completion rates and the GRE quantitative ability score, but little to no association between completion rates and the GRE verbal ability score.

l1 Use of the sum of the GRE quantitative, verbal, analytical scores as an indicator of institutional excellence and selectivity - rather than using each component separately - was motivated by the desire for parsimony. It is recognized that the use of such a combined score is a crude measure for this purpose. It is not recommended practice to use combined scores in admissions decisions.

l2 This lack of significance reflects in part the negative correlation between financial support and students/faculty. In the restricted specification, the coefficient for “Students/faculty” is negative for three of five fields. This is consistent with the Bowen and Rudenstein finding that students in smaller entering cohorts had higher completion rates.

l3 Including the interaction term “For_GRE verbal” is equivalent to allowing “GRE verbal” to have separate coefficients for domestic and international students. The coefficient for domestic students is simply the coefficient on “GRE verbal.” The coefficient for international students is the coefficient on “GRE verbal” plus the coefficient on “Foreign*GRE verbal.” The reason for making this specification is the possibility that the GRE verbal ability score may underestimate the verbal reasoning aptitude for nonnative English speakers.

l4 These findings are consistent, by and large, with those of Bowen and Rudenstein and Espenshade and Rodriguez.

I5 In contrast, Espenshade and Rodriguez found significantly higher completion rates for foreign students.

l6 Both the limited number of years (1989-1993) in the data set and the inability to determine whether a student graduated or dropped out prevents direct comparison with the results of Bowen and Rudenstein. When the data set is extended and information about degree completion is obtained, such comparisons will be possible.

” Evidence that the GRE lsubject tests have superior predictive power is provided in Willingham (1974).

Documents

Determinants of Persistence of Graduate Studentspersistence include student aptitude and achievement, financial support, and demographic characteristics, as well as characteristics