2
Current Approaches To The Measurement Of Graduate Attrition

The demand for accurate statistics about graduate attrition arises chiefly from the planning activities of research universities. A number of independent estimates have been generated to meet institutional needs for information. The cumulative effect of studies with different reference dates, different coverage, and different definitions has been to create data sets that generate incompatible statistical results (Duncan 1977).

Despite the limitations, recent studies of student attrition provide a useful basis for understanding the issues and developing future studies of graduate attrition. They do so by suggesting what to measure, how to measure it, and how to interpret results. The sections that follow summarize what is known about graduate attrition from available studies and surveys, beginning with a brief consideration of the concept of attrition itself.

The Concept Of "Attrition" At The Graduate Level

Education has traditionally proceeded at a predictable tempo in the United States, with students completing their high school (or secondary) education around 18 years of age and their baccalaureate (or tertiary) education five or six years later. The regularity of this pattern is broken, however, when doctoral education is examined. The age at which an individual will earn a Ph.D. or its equivalent varies widely, determined in part by the discipline of study6 and a number of other factors (see, for example, Tuckman, Coyle, and Bae 1990; Cheney 1988). For example, many graduate students have dependents or outside employment which may directly affect the time it takes to earn a doctorate. Whatever the reason, we do know that the time taken to complete a doctoral degree is considerably longer than the traditional period of four to five years.

Among 1994 doctoral recipients in the sciences and humanities, for example, the median number of years between receipt of the baccalaureate degree and receipt of the Ph.D. ("total time-to-degree") ranged from 8.5 years in the physical sciences to 12.0 years in the humanities (NRC 1995b) (see Figure 2-1). Clearly, some of this time may be accounted for by work or other activities before entering

6  

The median age of an individual who earned a doctorate in 1994 varied from 30.0 years for chemists, to 31.2 years for mathematicians, to 36.8 years for anthropologists and sociologists (combined), to 35.2 years for English language and literature majors (NRC 1995a).



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--> 2 Current Approaches To The Measurement Of Graduate Attrition The demand for accurate statistics about graduate attrition arises chiefly from the planning activities of research universities. A number of independent estimates have been generated to meet institutional needs for information. The cumulative effect of studies with different reference dates, different coverage, and different definitions has been to create data sets that generate incompatible statistical results (Duncan 1977). Despite the limitations, recent studies of student attrition provide a useful basis for understanding the issues and developing future studies of graduate attrition. They do so by suggesting what to measure, how to measure it, and how to interpret results. The sections that follow summarize what is known about graduate attrition from available studies and surveys, beginning with a brief consideration of the concept of attrition itself. The Concept Of "Attrition" At The Graduate Level Education has traditionally proceeded at a predictable tempo in the United States, with students completing their high school (or secondary) education around 18 years of age and their baccalaureate (or tertiary) education five or six years later. The regularity of this pattern is broken, however, when doctoral education is examined. The age at which an individual will earn a Ph.D. or its equivalent varies widely, determined in part by the discipline of study6 and a number of other factors (see, for example, Tuckman, Coyle, and Bae 1990; Cheney 1988). For example, many graduate students have dependents or outside employment which may directly affect the time it takes to earn a doctorate. Whatever the reason, we do know that the time taken to complete a doctoral degree is considerably longer than the traditional period of four to five years. Among 1994 doctoral recipients in the sciences and humanities, for example, the median number of years between receipt of the baccalaureate degree and receipt of the Ph.D. ("total time-to-degree") ranged from 8.5 years in the physical sciences to 12.0 years in the humanities (NRC 1995b) (see Figure 2-1). Clearly, some of this time may be accounted for by work or other activities before entering 6   The median age of an individual who earned a doctorate in 1994 varied from 30.0 years for chemists, to 31.2 years for mathematicians, to 36.8 years for anthropologists and sociologists (combined), to 35.2 years for English language and literature majors (NRC 1995a).

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--> FIGURE 2-1 Median years to doctorate from baccalaureate award, by broad field, 1994. graduate school, but that pattern is less common in the sciences and humanities than in engineering, education, and other professional areas. Once enrolled, the median time actually registered in graduate study ("registered time-to-degree") for 1994 graduates ranged from 6.7 years in the physical sciences to 8.5 years in the humanities (see Figure 2-2). This measure is not the same as years enrolled in a doctoral program, since students may enroll first in a master's or other post-baccalaureate program or may take time out for employment once enrolled. Although a longer time-to-degree (registered or not) does not necessarily lead to noncompletion for any individual student, the likelihood of not completing the degree increases with each additional year in doctoral study, based simply on the fact that each additional year of doctoral study carries with it a positive chance that a student will decide to drop out. Attrition from graduate study refers to a reduction in the number of individuals pursuing the Ph.D. The most accurate calculation of "attrition" depends on the specification of a group or cohort of students who begin doctoral study at the same time and then a later look at that cohort to determine the proportion of students having completed their degrees by a certain time (to derive a "completion rate") or the proportion of

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--> FIGURE 2-2 Median years to doctorate from first registration, by broad field, 1994. students who are no longer enrolled ("attrition rate").7 It is difficult to estimate a completion rate for doctoral study for several reasons. First, Ph.D. programs vary widely in their definition of when students begin doctoral study, even within the same university. A review of the literature on higher education suggests that there are essentially three models for pursuing the Ph.D. in the sciences and humanities at U.S. universities. The American Model treats the student who has entered the first post-baccalaureate year of study as a member of the Ph.D. program. The German Model, evident in many U.S. universities, considers an individual as a Ph.D. student only when that individual has been admitted to candidacy. The M.A.-First Model is apparent in certain professional fields such as engineering or education, whereby a student may enter a Ph.D. program only after receipt of the master's degree, with or without intervening work experience. Complicating this picture further are the students who enter a master's program and then switch to the Ph.D., and those who transfer from other graduate degree programs. 7   In addition to students no longer enrolled, there are two other groups of "noncompleters": individuals who are still enrolled in the program and those who have "stopped out." This latter group includes students who are not enrolled at a particular time but may return to the program in the future. Thus, at any given time, attrition equals the original cohort of students minus "completers" minus ''those still enrolled" minus those who have "stopped out."

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--> Second, there is no fixed time beyond which students can be considered no longer enrolled in doctoral study. Institutions vary widely in the maximum number of years permitted for students to complete the Ph.D., typically ranging from five to 10 years after entry into doctoral study. Even if graduate schools have a written policy, exceptions for individual students are often made. Many individuals start and stop their graduate study, taking leaves of absence for personal or professional reasons, sometimes returning years later to complete their degrees. The combination of these factors makes it impossible to determine decisively when students should no longer be considered in pursuit of the doctorate. Researchers interested in measuring attrition in the face of these enrollment irregularities have approached the definitional problem in a variety of ways. Most have established an "operational definition" of graduate attrition by setting arbitrary cutoff points for completion and a uniform starting point for entry. Many researchers use the American model to define the start of doctoral study, assuming that a student's first enrollment in graduate study after the baccalaureate constitutes entry into a doctoral program. Cutoff points for degree completion have been established variously at 6, 10, and sometimes 11 years after entry into graduate programs. The use of a cutoff point such as this has the advantage of treating all "non-enrolled" students as "noncompleters" but obviously cannot accurately account for those students who eventually return to the program and complete their degrees (see Text Box 3). Contemporary Estimates Of Attrition Studies of graduate attrition and degree attainment can range from theoretical studies that aim to build or test models of student persistence to empirical studies that rely on scientific samples from carefully framed populations. Although restricted to samples involving a single institution or smaller sets of institutions, recent studies have been more rigorously quantitative.8 A flurry of quantitative studies of attrition appeared in the 1980s, involving analysis of student records or the linkage of data sets from which estimates of attrition could be made. Selected examples of quantitative studies are presented below. Student records provide a rich data set that plots the career trajectory of the doctoral work force at a critical phase of its unfolding. With the advent of computerized data systems, there has been a small but increasing trend toward the analysis of student records for purposes of estimating graduate attrition. Three sets of studies in particular have achieved national attention for the quality of their analyses: (1) work by Nerad (1991) and Nerad and Cerny (1991) that focuses on graduate attrition at the University of California at Berkeley; (2) a study by Miselis, McManus, and Kraus (1991) that uses data from the University of Pennsylvania; and (3) a comprehensive assessment of graduate 8   Bowen and Rudenstine (1992) report that Tucker and his colleagues at Michigan State University attempted to analyze completion rates at 24 universities as early as 1964 using longitudinal student records in an attempt to give more precision to estimates of graduate attrition. However, they apparently restricted their analyses to students holding a master's degree, thereby removing early attrition from their estimates.

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--> TEXT BOX 3 The most recent notable attempt to generate a common definition of completion rates has been offered by Bowen and Rudenstine (1992): "The main complication in studying all aspects of the effectiveness of graduate education—and certainly in defining and measuring completion rates—is that students pursue doctorates, on and off, over many years. For a small number of students, pursuit of the Ph.D. becomes almost a lifelong endeavor. Since the percentage of each entering cohort who earn the doctorate rises as the number of years since entry increases, we have elected to work primarily with two kinds of completion rates: minimum completion rates (MCR) and truncated completion rates (TCR). "Perhaps the easiest way to define these rates is by using a set of hypothetical numbers. Suppose that: 100 students enter graduate study in English in 1972; By 1978, 50 have earned doctorates, 25 have ceased pursuing the doctorate, and 25 are still enrolled; By 1982, 60 have earned the doctorate, 32 have ceased pursuing the doctorate, and 8 are still enrolled. The minimum completion rate is the percentage of the entering cohort who have earned the doctorate by a specified year. In this example, the MCR was 50 percent in 1978 and 60 percent in 1982. Obviously, the MCR rises with the number of years that have elapsed between entry to graduate school and the year in which the measurement is made. Because of its simplicity and wide applicability, this is the completion rate that is used most frequently in this study, and whenever we refer simply to the completion rate (with no modifier), this is the concept that is being used. The MCR can be misleading, however, especially when time series comparisons are being made, and that is why we also use the concept of the truncated completion rate. "The truncated completion rate is the percentage of an entering cohort who earned the doctorate within a specified number of years from entry to graduate study. In this example, the TCR after six years was 50 percent in 1978, as well as in 1982 and all subsequent years, since it is impossible for more students to earn degrees within a time interval once the limit of that interval has been exceeded. If the cutoff number of years had been set at ten rather than at six, the TCR could not have been measured in 1978 and would have been 60 percent in 1982 and all subsequent years. Truncated completion rates are particularly useful when comparisons are being made between outcomes for recent cohorts (who will have had only a limited number of years in which to complete their studies) and outcomes for earlier cohorts. "A further complication in computing completion rates concerns transfers. The completion rates that we calculate on the basis of the Ten-University data set treat all students who have left each university as having dropped out, even though some may have completed a Ph.D. after transferring to another university. The National Fellowship data set, on the other hand, tracks individual students who have moved from one university to another, and the completion rates including transfers will, of course, be somewhat higher than the corresponding completion rates that do not allow for transfers" (pp. 106-107).

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--> education by Bowen and Rudenstine that uses a ten-university data set.9 University of California at Berkeley Maresi Nerad and Joseph Cerny have undertaken a number of special studies of graduate education at the University of California at Berkeley using the institution's administrative files. One study involved the analysis of completion patterns for cohorts who entered in 1978 and 1979 (see Text Box 4). Responding to concerns about anticipated shortages of skilled personnel, the Graduate Division broke from its "traditional role" and undertook research "to design and implement programs that encourage students to complete their degrees and to do so in a reasonable amount of time" (Nerad and Cerny 1991, 1). The Berkeley study proceeded in five steps. The first step involved developing a number of statistical analyses based on demographic data about the graduate students to determine such things as average time-to-degree and the points in the program at which students tended to leave. Only students who identified themselves as working toward the doctoral degree were included in the study. The analysis utilized cohorts entering in 1978 and 1979 and looked at completion rates as measured in November 1989 when "most of the students, by then, should have had sufficient time to complete their doctoral programs." As Figure 2-3 indicates (1) 24 percent left during their first three years of study,10 (2) 10 percent left after advancement to candidacy, (3) 58 percent completed doctoral degrees, and (4) another 8 percent were "pending." Doctoral completion rates varied significantly by field, as illustrated in Figure 2-4. The biological and physical sciences had the highest completion rates while the arts, languages, and literature had the lowest. The authors note that Berkeley may be fairly typical, "at least among public universities," citing as evidence Benkin's work (1984) at the University of California at Los Angeles (UCLA), which reveals that about 30 percent of UCLA students leave during the early period of doctoral study. University of Pennsylvania Concerned for some time that graduate students were taking too long to complete their doctorates, Karen Miselis, William McManus, and Eileen Kraus (1991) undertook a project in the School of Arts and Sciences at the University of Pennsylvania to conduct "a very thorough and informative attrition and time-to-degree study" (see Text Box 5). The authors spent over a year collecting, cleaning, and analyzing a wide variety of academic, demographic, and financial data for each student. There were several sources of information available in both electronic and paper form. The registrar had student activity tapes back to Fall 1973 and transcripts for all students who ever attended the University. Student Financial Aid had 9   The universities include Berkeley, Chicago, Columbia, Cornell, Harvard, Michigan, Princeton, Stanford, University of North Carolina, and Yale. 10   Most of these students (83 percent) earned a master's degree along the way.

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--> TEXT BOX 4: FROM FACTS TO ACTION Mounting concern over the "anticipated shortage of college teachers, scientists, and engineers" led Maresi Nerad and Joseph Cerny (1991) to analyze completion rates for students entering in 1978 and 1979, as measured in November 1989, and attrition patterns from Ph.D. programs at the University of California at Berkeley. Fifty-eight percent had completed doctoral degrees, with 72 percent doing so in the biological sciences, 69 percent in the physical sciences, 39 percent in the arts, and 37 percent in the languages and literature (the lowest). In addition, the authors arranged for the administrators in the Graduate Division to meet monthly with representatives of the Graduate Council to specify recommendations for action, such as "a new policy requiring students to meet annually with at least two members of their dissertation committee to review their progress on their dissertations and to map out a plan for the following year." Contrary to popular belief, the majority of graduate students who did not earn their doctorates left the program before advancement to candidacy for the Ph.D., not after. Through in-depth interviews, the authors asked 40 UC-Berkeley students from history, English, French, and sociology why they left doctoral studies. These students' answers were compared with students from psychology and biochemistry who had just completed their dissertations and who were asked how they moved from one stage of doctoral work to the next stage. Six similar patterns were found for students who had left doctoral studies in the humanities and social sciences: Students in departments that require a M.A. thesis spent an excessive amount of time polishing the thesis. Humanities and social science students over prepared for their orals. After having passed the qualifying exam, these students spent between one and two years searching for a dissertation topic and writing a dissertation prospectus. Humanities and social science students wrote their dissertations in total isolation. These students perceived the course work, orals, and prospectus-writing stages of their doctoral programs as hurdles that needed to be jumped, but not as steps leading to the completion of their dissertations. Many humanities and social science students complained that the department and faculty failed to assist them in preparing for orals, in applying for grants, and in the actual writing of their dissertations. Finally, Nerad and Cerny "developed recommendations and designed and implemented activities'' to work to decrease time-to-degree and lower attrition: Faculty. The Graduate Division initiated a monthly seminar involving faculty, department chairs, deans, and graduate students to "inform and sensitize a part of the campus community, particularly the faculty, about these particular issues of graduate education." Graduate Students. Meetings were initiated with interdepartmental student focus groups. Besides functioning as a "support group" for students, the focus groups gave students a chance to share problems and to understand what other departments were doing for their students. In addition, "the Graduate Division developed a better understanding about the specific needs of students" and gathered useful ideas for educational activities to meet their needs.

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--> FIGURE 2-3 University of California at Berkeley progression status of 1978-79 cohorts, as of November 1989. tapes going back to 1979, and Personnel/Payroll tapes were available back to 1974. The authors found that one of the factors making the study of graduate programs more difficult than studies of undergraduate programs is the fact that there is not "one" doctoral program, but "many": "Every Ph.D.-granting department can set its own policies and is quite distinct in its program from others within the University." Findings are presented in Figure 2-5 for three divisions at the University of Pennsylvania: the humanities, the social sciences, and the natural sciences. The authors observe major differences among divisions with regard to attrition: The Natural Sciences tend to lose their students early, while other divisions continue to lose students even after a decade of study. For instance, the Humanities department with the worst record on attrition after 6 years had lost 54 percent. After 10 years of study, that department had lost another 25 percent, to have a cumulative attrition rate of 79 percent. Within the Natural Sciences, however, the cumulative attrition rates at 6 years post-matriculation and 10 years post-matriculation are virtually identical. The study further noted that the humanities have consistently graduated less than 50 percent of their matriculants. For the natural sciences, from 60 to 75 percent typically finish successfully, while the social sciences reveal a range of graduation rates from 33 to 54 percent over a 10-year period.

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--> FIGURE 2-4 Doctoral completion rates for the 1978-79 cohort at the University of California at Berkeley, by field and gender, November 1989. The Ten-University Data Set In 1989 William Bowen and Neil Rudenstine undertook a project to "[p]lace doctoral programs in the arts and sciences within the larger context of doctoral education in all fields and examine trends in recipients of Ph.D.s over the last 35 years …" (Bowen and Rudenstine 1992, 8). The authors were interested in knowing, among other things, how the overall "system" of graduate education has been affected by the expansion of the 1960s and subsequent contraction in enrollments and degrees conferred. Noting that graduate education has many outcomes, Bowen and Rudenstine focus attention on completion rates and time-to-degree using data from a set of 10 institutions for entering cohorts in six specific fields: English, history, economics, political science, mathematics, and physics. The authors acknowledge that distinguishing Ph.D. candidates from students who entered graduate school only to earn a master's degree was "a particularly vexing problem." The solution was to ask the universities to send records only for those entering students who were regarded at the time of entry as interested in obtaining a Ph.D., even though it was understood that in certain programs students would formally become Ph.D. candidates only after completing certain requirements.

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--> TEXT BOX 5: ANALYSIS OF PH.D. STUDENT ATTRITION AT THE UNIVERSITY OF PENNSYLVANIA In 1991 Karen Miselis, William McManus, and Eileen Kraus presented a paper describing their experience in "collecting, cleaning, and analyzing data" about attrition and time-to-degree. The authors spent over a year on the project using data from five of the 36 separate graduate groups in the School of Arts and Sciences at the University of Pennsylvania. They gathered a wide variety of academic, demographic, and financial data for each student in order to "build the data base of graduate student information required for this study." Miselis and her colleagues described numerous issues involved in creating the computerized data system, noting two general problems they encountered: The first had to do with errors in the data, and the second with student characteristics. In addition to errors associated with miss-keying data and data redundancy, we encountered data errors that resulted from the way the data were created. Establishing the degree sought, Ph.D. or M.A., was extremely important and yet difficult to do. Our biggest data problem was with the financial aid data. The financial aid tapes supplied us with information on fellowship, teaching assistantship, and won support for 1979 through 1989 only and the tape for 1985 had been lost. The payroll tape supplied us with information on grant support for Fall 1974 through Spring 1989 but contained no information on loans. We decided not to use any of the financial aid data because of the analytic problems induced by the missing year's worth of data and because the breadth of the data was so short compared to payroll. The paper describes the final data set, findings, and proposed institutional reforms. Above all, the study demonstrates the feasibility and utility of creating institutional data sets that address graduate attrition and degree completion. Fortunately, this problem of distinguishing M.A.only candidates from likely Ph.D. candidates did not exist in the majority of programs included in this study, since most of these programs either admit only Ph.D. candidates or distinguish at admission those on the M.A. track from those on the Ph.D. track. Some ambiguities were never resolved satisfactorily, but most universities that had this problem seem to have been successful in segregating the records of those entering students who were interested from the beginning in obtaining the Ph.D. (p. 291). From this data set, Bowen and Rudenstine provide many types of analyses. In the area of "outcomes" they provide information about patterns of attrition from graduate study. As Figure 2-6 illustrates, the authors were able to calculate the stages at which individuals left graduate study at these 10 universities: (1) before starting the second year of study; (2) after starting the second year, but before completing all requirements for the Ph.D. other than the dissertation; and (3) after completing all requirements but the dissertation (ABD). For the 1972-1976 entering cohort, the probability of achieving second-year status was 87 percent; the probability of achieving ABD status given second-year status was about 80 percent; and the probability of achieving the Ph.D. given ABD status was 81 percent.

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--> FIGURE 2-5 Attrition patterns for the 1976-1978 cohort in three divisions at the University of Pennsylvania, high and low departments, after 6 and 10 years. The authors also report differences in attrition by major field, which are summarized in Figure 2-7. They note that the conditional probability of completing a dissertation in mathematics or physics once a student has achieved ABD status was about 90 percent for the two cohorts that were analyzed. Among English, history, and political science students the corresponding conditional probability was 79 percent for the 1967-1971 cohort and just 75 percent for the 1972-1976 cohort. Several explanations are offered for the differences across fields. Financial support continues to be an important factor in degree completion, and there is more support available in the natural sciences than in the humanities or social sciences and less reliance on teaching assistantships. However, even when financial support was not an issue (in the case of fellowship recipients), differences in completion rates persisted. Bowen and Rudenstine assert that the structure of the graduate programs themselves plays a large role in completion. Programs in the physical sciences are more structured, setting out more uniform degree requirements and providing closer faculty supervision. Programs in the humanities are usually less structured, providing multiple options for completing requirements and more independent study. At the dissertation level especially, students in the physical sciences doing their research in a laboratory have ready access to faculty help, are monitored, and interact regularly with

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--> FIGURE 2-6 Attrition by stage, six-field total, 1972-1976 entering cohorts. colleagues. Students in the humanities doing independent library research have to seek out faculty help, may not receive regular monitoring, and may work alone for long periods of time. Other Institutions A number of other studies provide us with some estimates of attrition, if only as a by-product of other analyses. These studies include work by Bodian at the University of Maryland (1987), Dolph at Georgia State (1983), Valentine at West Virginia University (1987), Zwick and Brown using data from Northwestern University (1990), and Ehrenberg and Mavros at Cornell (1992). Administrative records and statistical data sets thus offer an opportunity to monitor trends in attrition. They do not alone provide explanatory power often sought by educational planners and policy makers. More theoretically grounded studies are needed to probe relationships among variables (Bradburn and Gilford 1990), some of which are described in the next section.

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--> FIGURE 2-7 Attrition by stage and fields, 1967-1971 and 1972-1976 entering cohorts.

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--> References Benkin, Ellen M. 1984 "Where Have All the Doctoral Students Gone? A Study of Doctoral Students' Attrition at UCLA." Ph.D. diss., University of California, Los Angeles. Bodian, Lester Hal 1987 "Career Instrumentality of Degree Completion as a Factor in Doctoral Student Attrition." Ph.D. diss., University of Maryland. Bowen, William G., and Neil L. Rudenstine 1992 In Pursuit of the Ph.D. Princeton, NJ: Princeton University Press. Bradburn, N.M., and D. Gilford 1990 A Framework and Principles for International Comparative Studies in Education. Washington, DC: National Academy Press. Cheney, Lynne V. 1988 Humanities in America. Washington, DC: National Endowment for the Humanities. Dolph, Robert F. 1983 "Factors Relating to Success or Failure in Obtaining the Doctorate." Ph.D. diss., Georgia State University. Duncan, Joseph W. 1977 "Priority Setting in the Coming Decade." Statistical Reporter Series, No. 77-7. Washington, DC: Office of Management and Budget. Ehrenberg, R. G., and Mavros, P. G. 1995 "Do Doctoral Students' Financial Support Patterns Affect Their Times-To-Degree and Completion Probabilities?" Journal of Human Resources 30 (3):581-609. Miselis, Karen L., William McManus, and Eileen Kraus 1991 "We Can Improve Our Graduate Programs: Analysis of Ph.D. Student Attrition and Time-to-Degree at the University of Pennsylvania." Paper presented at the Annual Forum of the Association of Institutional Research, San Francisco, California, May 29. National Research Council (NRC) 1995a Summary Report 1994. Doctorate Recipients from United States Universities. Washington, DC: National Academy Press. 1995b 1994 Survey of Earned Doctorates, Special Tabulations. Washington, DC: NRC. Nerad, Maresi 1991 Doctoral Education at the University of California and Factors Affecting Time-To-Degree. Oakland, CA: Office of the President, University of California. Nerad, Maresi, and Joseph Cerny 1991 "From Facts to Action: Expanding the Educational Role of the Graduate Division." Communicator (May Special Edition). Washington, D.C.: Council of Graduate Schools. Tuckman, Howard P., Susan Coyle, and Yupin Bae 1989 "The Lengthening of Time to Completion of the Doctorate Degree." Research in Higher Education 30:503-16.

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--> Valentine, Nancy L. 1987 "Factors Related to Attrition from Doctor of Education Programs." Paper presented at annual meeting of the Association of Institutional Research, Kansas City, Missouri, May 3-6. Zwick, Rebecca, and Henry I. Braun 1988 Methods for Analyzing the Attainment of Graduate School Milestones: A Case Study. GRE Board Professional Report No. 86-3P. Princeton, NJ: Educational Testing Service.

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