**THE TOOLBOX REVISITED**

**Paths to Degree Completion From High School Through College**

**U.S. Department of Education**

**THE TOOLBOX REVISITED**

**Paths to Degree Completion from High School Through College**

Clifford Adelman

Senior Research Analyst

Policy, Research, and Evaluation Staff

Office of Vocational and Adult Education

U.S. Department of Education

**U.S. Department of Education**

Margaret Spellings

*Secretary*

**Office of Vocational and Adult Education**

Beto Gonzalez

*Acting Assistant Secretary*

**February 2006**

The views expressed herein are those of the author and do not
necessarily represent the positions or policies of the U.S. Department
of Education. No official endorsement by the U.S. Department of
Education of any product, commodity, service, or enterprise mentioned in
this publication is intended or should be inferred. This document is in
the public domain. Authorization to reproduce it in whole or in part is
granted. While permission to reprint this publication is not necessary,
the citation should be:

Adelman, C. *The Toolbox Revisited: Paths to Degree Completion From High
School Through College.* Washington, D.C.: U.S. Department of Education,
2006.

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(202) 260-0818.Organization of This Data Essay

The following is a brief outline of *The Toolbox Revisited* so the
reader knows what to expect.

**Part I: Background.** The introduction presents the basic question,
the data sets invoked, the purposes and statistics of the investigation,
and the demography of the subject universe.

**Part II: Variables Explored and Used in This Analysis**. This short
section of the study lists all the independent variables that were
considered and provides brief definitions and basic statistical
characteristics. A summary figure (pp. 20--21) indicates which of these
met the criteria for inclusion in the logistic narrative of Parts III
and IV. A more elaborate glossary

(pp.179--193) provides details on the construction of these variables,
allied data and commentary, and will be of particular interest to
researchers.

**Part III: What Is and What Happens Before Matriculation.** Here we
begin the chronological narrative, using both descriptive and
multivariate data, of what ultimately made a difference in bachelor's
degree attainment by December 2000 for 1992 12th-graders who attended a
four-year college at any time. Part III begins with background
demographic characteristics, then adds the critical components of high
school academic history.

**Part IV: Matriculation and Beyond.** This section continues the
cumulative steps of the logistic narrative, starting with the
characteristics of entry to the postsecondary world, and continuing with
first calendar year performance, financing considerations, attendance
patterns, and extended performance (that is, taking students' entire
undergraduate careers into account). It includes a special consideration
for the second calendar year of enrollment and concludes its logistic
narrative with attention to two very powerful variables: continuous
enrollment and the ratio of course withdrawals and repeats to the number
of all courses attempted.

**Part V: Closing the Gap**. Having demonstrated how the universe of
independent variables is related to degree completion, *The Toolbox
Revisited* then asks two questions: (1) To what extent do the major
national data sets agree on \"graduation rates\"? And (2) Given what we
have learned about what makes a difference in degree completion, what
variables provide the most promising guidance for closing the gap in
graduation rates, by race/ethnicity and socioeconomic status, for
students who attend a four-year college at any time?

**Part VI: The Missing Element of This Story**. A key missing part of
the story that is a by-product of the limited features of the
NELS:88/2000 is addressed in this section: the content standards of high
school and postsecondary course work. Other brief
\"excursions\"---timing and reasons for permanent (\"status\") drop out
from college, and time-to-degree---are placed in Appendices H and K
respectively.

**Part VII: Messages**. Finally, *The Toolbox Revisited* offers some
messages---to students and to those who engage in public discourse about
the issues we have covered---and highlights the major conclusions of the
study.

**Appendices**: With one exception, appendices are presented in the
order in which they are cited in the text. The exception is the last
appendix, Appendix L, that contains a variety of reference tables on
miscellaneous topics raised in the text.

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**Part I**

**Background**

This study explores the academic resources and momentum students build
through their high school and college careers, and analyzes the
relationships between those factors and degree completion rates. It
departs from most previous research on attainment by focusing on the
details of students' high school and college curricula and academic
performance that are available from transcript records. Its principal
data are drawn from the National Education Longitudinal Study of 1988
(hereafter referred to as the NELS:88/2000 or just NELS). This
longitudinal study followed a national sample of over 12,000 students
(representing a weighted 2.9 million students) from the time they were
in the eighth grade in 1988 to roughly age 26 or 27 in December 2000.

In round numbers, of the high school graduates in this cohort, 83
percent engaged in some form of postsecondary education by age 26, and
68 percent attended a four-year college at some time.

Of the group who attended four-year colleges at some time (which
includes a substantial proportion of students who began postsecondary
study in community colleges), 66 percent earned a bachelor's degree.

While the 66 percent completion rate sounds impressive for a mass system
of higher education, it masks an unhappy differential by race/ethnicity,
and more so by socioeconomic status. As we strive to improve high school
graduation rates, to invite greater numbers of high school graduates
into the postsecondary system, simply to maintain---let alone
improve---our completion rates will take a great deal of effort. We need
constructive guidance and benchmarks.

This study was designed as a follow-up and replication of a previous
attempt to provide that guidance*---Answers in the Tool Box: Academic
Intensity, Attendance Patterns, and Bachelor's Degree Attainment*
(hereafter referred to as the original *Tool Box*).[^1] Since its
publication in 1999, the original *Tool Box* has become one of the most
frequently cited works in public discussions about---and initiatives to
improve---the preparation of students for higher education. Its most
visible uses have included the presentations of the Texas "Master
Scholars" program (2002), the revisions in entrance requirements for the
University of North Carolina system (2000), standards goals set by the
Illinois Board of Higher Education (2001), and suggestions of the
Education Commission of the States for state high school graduation
policies (2001). It was summarized in major litigation addressed to
inequities in opportunity-to-learn in high schools (e.g., *Daniel v.
California* 1999), and in the research literature, its analyses of both
precollegiate preparation and post-matriculation attendance patterns and
performance have also been marked (e.g., Horn and Kojaku, 2001; Zucker &
Dawson, 2001; Cabrera and La Nasa, 2001) and improved on (DesJardins,
McCall, Ahlburg and Moye, 2002; Cabrera, Burkum, and LaNasa 2005).

The analyses in the original *Tool Box* were based on the High School &
Beyond/Sophomore cohort longitudinal study (hereafter occasionally
referred to as the HS&B/So), the second of the U.S. Department of
Education's national grade-cohort longitudinal studies,[^2] which
followed a national sample of 10th-graders from 1980 to1992 in surveys
and to September 1993 on postsecondary transcripts. As with all of the
grade cohort longitudinal studies carried out by the National Center for
Education Statistics,[^3] test scores are included in the database,
along with surveys of parents, school teachers, and school
administrators. The modal high school graduation year for the HS&B/So
was 1982, and student age at the conclusion of the study was 29 or 30.

The HS&B/So data, while compelling, are now somewhat dated. There were
considerable changes in both the demography and postsecondary entrance
behavior of high school seniors in the comparatively short span of the
decade between 1982 and 1992. Appendix A highlights contrasts in
selected background characteristics of all 12th-graders in the two
longitudinal studies cohorts. Some of these changes have been frequently
observed (higher proportion of minority students, westward and southward
movements of populations, higher proportion of high school seniors
entering higher education and planning to earn a bachelor's degree), and
some rarely observed (higher proportion who grew up in mixed-ethnicity
neighborhoods, and a higher proportion with parents who indicated some
postsecondary education). The question naturally arises as to whether
the hypotheses and analyses based on the history of the High School &
Beyond/Sophomore cohort would hold up in the story of the NELS:88/2000.
The NELS history offers a more contemporary account,[^4] one that, in
terms of secondary school records, may reflect the high school
curriculum reforms of the mid- and later-1980s[^5] that followed the
discussion of the report of the National Commission on Excellence in
Education, *A Nation at Risk* (1983). *The Toolbox Revisited* follows
the same path of analysis using the NELS:88/2000 as did its predecessor
with the HS&B/So. In that sense, it is a replication. It is a modified
replication, however, because it introduces new constructs based on
critiques of the original *Tool Box* and because it offers a more
refined chronology of steps from high school to the end of a student's
undergraduate education.

A substantial amount of the analyses and endorsements that followed the
original *Tool Box* revived the flagging \"seamless\" K--16 themes of
the 1980s post*-Nation at Risk* reform effort. In an October 2000 policy
brief that visited these issues, the Education Commission of the States
reminded people of what most of the 1980s reform reports did not
address: the fact that K-12 and postsecondary systems are governed in
very different ways, even in the public sector of postsecondary, and
that there is a consequent \"disconnect\" of substantial dimensions
(Education

Commission of the States 2000). The metaphor of bridges (Venezia, Kirst
and Antonio 2003) and the rhetoric of disconnect (e.g., Conley 2003)
created a more sophisticated focus of analysis than the reform reports
of the 1980s embraced. The major work that sought to build new bridges
and connect the disconnects underscored the obligation of the system not
merely to assure college \"access,\" but degree completion, with
curriculum playing the key role. While \"degree completion,\" in public
discourse, refers to the bachelor's degree, the same principles apply to
associate degrees granted principally by community colleges as well
(Adelman 2005a).

> **What Did the Original *Tool Box* Say?---And Based on What Kind of
> Evidence?**

In a nutshell, here are the major conclusions of the High School &
Beyond/Sophomore-based *Answers in theTool Box* analysis:

1\) Of three traditional measures of precollegiate educational
history---curriculum configuration, academic performance (on a scale
that combines class rank and GPA), and assessed general learned
abilities (a senior year mini-SAT)---the intensity and quality of one's
secondary school curriculum was the strongest influence not merely on
college entrance, but more importantly, on bachelor's degree completion
for students who attended a four-year college at any time. The highest
level of mathematics the student reached in high school played a
significant role in the strength of the curriculum configuration. One of
the major contributions of *Tool Box* not only to the literature, but to
practice as well, was to change what was understood by the "entry
characteristics" of students by digging out and demonstrating the power
of the academic intensity of secondary school curriculum over
combinations of standardized test scores and grades.

2\) By moving into the top two quintiles of the curriculum measure and
completing a high school mathematics course beyond Algebra 2,
African-American students who started out in a four-year college would
increase their bachelor's degree attainment rate from 45 percent to 73
percent; Latino students who did the same would increase their
bachelor's degree attainment rate from 61 percent to 79 percent.[^6]
These increases were significantly greater than those for white and
Asian students under this scenario, and, more importantly, were
considerably greater than the effect of moving into the top two
quintiles of either test scores or class rank/GPA. In other words,
curriculum counts, particularly for minority students.

3\) The three traditional precollegiate measures can be combined in a
composite measure of "Academic Resources." This measure had continuing,
statistically significant relationships with bachelor's degree
completion in both linear and (more appropriately and convincingly)
logistic regression sequences involving four post-matriculation steps
(blocks of variables for financial aid, attendance patterns, first-year
performance, and extended postsecondary performance).

4\) Post-matriculation behaviors and attendance patterns that were
strongly and positively associated with bachelor's degree attainment
were continuous enrollment, transfer from a community college to a
four-year institution after more than 10 credits earned at the community
college, and the *trend* in students' grades.

5\) Post-matriculation behaviors and attendance patterns that had a
strong negative influence on bachelor's degree attainment were the ratio
of courses from which the student withdrew or repeated to all courses
attempted, and earning less than 20 credits in the first calendar year
of postsecondary attendance.

6\) Socioeconomic status had a modest and diminishing association with
bachelor's degree attainment. Minority status had a modest negative
association until performance (first-year performance and continuing
performance) was taken into account, at which point it had no effect.
Gender had no effect at any stage of the model. The only demographic
variable to have a strong (and in this case, negative) association with
degree completion was becoming a parent by age 20.

The overall message was about academic momentum and what adds to that
momentum at each stage of a student's history from secondary school
onward. The evidence was archival, was treated in the tradition of
quantitative history (Elder, Pavalko, and Clipp 1993; Clubb, Austin and
Kirk 1989; Haskins and Jeffrey 1990), and like this essay, does not
claim causality.

**Why use these data sets?**

There are three types of national data sets available to construct
longitudinal analyses such as the original *Tool Box* and this
replication, but only one type of data set---the NCES transcript-based
grade-cohort study---is truly suited to the task. The other two are (1)
the Cooperative Institutional Research Project (CIRP) occasional
longitudinal follow-ups to its annual survey of entering college
freshmen, and (2) the NCES Beginning Postsecondary Students studies
(BPS). Each of these has its virtues, and will be revisited in Part V of
this study when we compare what three different longitudinal studies of
the 1990s say about degree-completion rates. The CIRP produces an
enormous amount of information on student attitudes, values, and college
experiences, and does so with large samples of (principally) entering
four-year college students. Its occasional longitudinal follow-ups
involve sufficient history (e.g., six or nine years) to track not only
long-term undergraduate completion rates, but also postbaccalaureate
education (Astin 1993). The BPS longitudinal studies are shorter (five
or six years), not dependent on institutional decisions to participate
(as is the CIRP), inclusive of students of all ages at entry, and, as
befits their principal population sample (a subset of the triennial
National Postsecondary Student Aid Study), contain very strong and
reliable financial aid data. The BPS study of 1995/96--2001 will be used
at a number of points in this study to expand the range of our
observations.

However, in both cases, all features of precollegiate history must be
rendered as exogenous variables. The high school histories provided by
students in CIRP are retrospective, and the precollegiate histories in
the Beginning Postsecondary Students studies derive from a

combination of retrospective offerings by students and accounts on the
student information questionnaires for those who took either the
Scholastic Assessment Test (SAT) or American College Test (ACT) within
the two years prior to the BPS start date (nearly half the students in
the BPS studies did *not* take either exam). As Kahn and Nauta (2001)
demonstrated, there is an inevitable loss of accuracy in the process of
these retrospections.

On the other hand, the very nature of a longitudinal study population
assembled in the 10th grade (High School & Beyond/Sophomore cohort) or
eighth grade (NELS:88/2000) renders precollegiate history endogenous to
analytic models. The transcript-base overrides student accounts and
provides far more detail than either paper-and-pencil surveys (used by
CIRP) or computer-assisted telephone interviews (used by the BPS
studies) can provide.

Every data set sacrifices something. No data set is constructed with the
questions a particular researcher may have a decade later, so variables
are derived and secondary. The High School & Beyond/Sophomore study and
the NELS:88/2000 are wanting in many ways where the other studies are
strong: financial aid (BPS), and changes in values and opinions (CIRP).
But as stories about the core activities we call education, they are
unsurpassed by the others.

# Purposes and Statistics of This Monograph

The primary purpose of this monograph is to trace the elements of
academic momentum as they played out in the secondary school and college
history of the High School Class of 1992 (through December 2000)
compared with the parallel history of the High School Class of 1982 that
was the foundation for the original *Tool Box* study. In the process,
the analysis is enriched by including variables we learned to construct
or modify on the basis of commentaries and critiques of *Tool Box*, and
by a more accurate chronological order in presentation of those
variables. The portrait of academic momentum that emerges is a framework
within which more sophisticated analyses can be pursued, and within
which ameliorative policies (the tools) can be advocated. This study
does not pretend to answer complex questions about indirect effects of
home, peer, school, and postsecondary institution interactions, but
rather trusts future research to deal with those issues.

A secondary task is to demonstrate the construction of a replication
when the two data sources, a decade apart, are presumably parallel**,**
but turn out to be something less (for a key example, see Appendix C).
The principal encouragement for the replication is that the bachelor's
degree attainment rate for students who attended a four-year college at
any time remained the same despite differences in the length of cohort
history: 65.6 percent for the HS&B/So over 11 years, and 66.5 percent
for the NELS:88/2000 cohort over 8.5 years (Adelman 2004a, table 2.2, p.
21). If the HS&Beyond/So history were truncated at 8.5 years, the
bachelor's degree attainment rate would have been 59.7 percent. From
this perspective there was a marked improvement in degree completion for
traditional age college students over the two decades in question. It is
natural to ask how this happened, and if the answers to that question
provide any guidance for the future.

In terms of statistical technique, both the original *Tool Box* and *The
Toolbox Revisited* use simple logistic regression, not structural
equations or other path models that are common to causal inquiries or
searches for indirect effects, e.g., of discrete aspects of school or
college environments (Dey and Astin 1993). A logistic regression is
focused on an event that either happens or it doesn't. The dependent
variable is dichotomous: yes or no. The independent variables are judged
within each model by the degree to which they contribute to what
happened in relation to or controlling for all other independent
variables in the model (Hair, Anderson, Tatham, and Black 1995).

There are a number of ways of expressing this "degree." One is by an
"odds ratio," which, expressed in a simple way, is a ratio of the odds
that X will happen given a unit of change in the independent variable to
the odds of X not happening, and ultimately shows the strength of
association between the independent and dependent variables---with the
closer the odds ratio

to 1, the less the strength of the association.[^7] This was the measure
used in the original *Tool Box*. Another way of expressing the value of
the contribution of an independent variable is by a "Delta-p" statistic
that says every unit change in the independent variable changes the
*probability* that X will happen by Y percent given the values of the
other variables in the model (Peterson 1985; Cabrera 1994). The
narrative of *The Toolbox Revisited* relies on Delta-p,[^8] and the
logistic model tables provide Delta-p statistics only for those
parameter estimates that are statistically significant since there is no
way to determine the statistical significance of the Delta-p itself
(Cabrera 1994).[^9]

But in this paper there is a major methodological departure from the
original *Tool Box* study: there are seven (and not five) steps in the
model employed, all driven by the empirical history of the NELS:88/2000
students. Following St. John, Paulsen, and Starkey (1996), the blocks of
variables in each step were entered \"in a sequence that parallels the
order in which students pass through well-established stages of
persistence behavior\" (p. 194) on their way toward bachelor's degree
completion (or not). Each of the seven steps, too, is cumulative. That
is, variables in one step that meet the statistical criteria for
remaining in the model are carried forward to the next step. This
extended accounting, which we will call a \"logistic narrative,\" allows
\"a meaningful examination of the direct effects of variables on
persistence, as well as their interactions with the variables entered in
successive steps\" (St. John, Paulsen, and Starkey 1996, p. 194).

The reader can already tell that there is a great deal of technical
material in this presentation, but it is presented in the spirit of the
U.S. Department of Education's goal of building a culture of evidence.
The author trusts that reports such as *The Toolbox Revisited* will
contribute to the attainment of that goal. Some of the technical
material is placed in appendices so that researchers have access to
documentation, and all readers have access to reference material.

**Who Are We Talking About? And Who Are We *NOT* Talking About?**

As was the case for the original *Tool Box*, the basic universe of
analysis in *The Toolbox Revisited* does *not* consist of everybody who
started out in the cohort. We have to be very clear about this. The
basic question of both studies is:

What demographic, high school performance, postsecondary entry, and

> postsecondary history (attendance patterns, academic performance)
> factors are convincingly associated with bachelor's degree attainment
> for 12th-graders who subsequently attended a four-year college at any
> time in their undergraduate careers?

This is not a question about completing high school, completing high
school on time, or completing high school on time with a standard
diploma (as opposed to a GED or certificate of attendance).[^10]

This is not a question about entering the postsecondary system. We are
not talking about \"access.\" Nor is it a question about \"persistence\"
to the second term or the second year following entry to postsecondary
education. It certainly is not about \"retention\" in the same
institution to the second term or the second year.

This is a question about *completion* of academic credentials---the
culmination of opportunity, advisement, choice, effort, and commitment.

The question is carefully worded. The universe does not include people
who never reached the 12th grade. In fact, as a consequence of the
sampling design and weighting of the two longitudinal studies, both
essays include only those students who were in the 12th grade *in the
same year,*[^11] along with those who graduated from high school. The
definition of the universe also requires that we have demographic
information, high school transcripts,[^12] test scores, and
postsecondary transcripts for everybody whose careers are subject to
analysis. Not everybody can present all this information, and, with rare
exceptions (involving some aspects of high school records, and as
explained in Appendix C) both the original *Tool Box* and *The Toolbox
Revisited* decline to impute any of this information.

There are two other notable features of the basic question. First, both
essays argue that, regardless of what students *say* on a survey about
their education expectations, it is what they actually *do* that counts.
So the only students we can talk about honestly with respect to
bachelor's degree attainment are those who set foot in a bachelor's
degree-granting institution at some time. This criterion obviously
includes students who started their postsecondary careers in community
colleges and other types of sub-baccalaureate institutions. Second, the
term used to describe the relationship between the dozens of independent
variables describing demography, high school performance, postsecondary
entry, and postsecondary history and the dependent variable of
bachelor's degree completion is \"convincingly associated.\" Neither
essay claims \"cause\" or \"prediction.\"

To illustrate how these conditions restrict the universe, let us start
with 2.93 million 1988 eighth-graders in the NELS:88/2000 cohort. Table
1 lays out the stages of contraction of the basic population until we
reach the subject universe of this study.

![](media/image1.wmf)

Looking more closely at our universe in terms of the types of schools
attended, we find that

20.2 percent (s.e. = 1.13) started in community colleges, and 41.0
percent (s.e. = 1.29) earned credits from community colleges, whether or
not they started at community colleges. While we will describe the
attendance patterns of the NELS:88/2000 cohort in more detail later, the
point is that the universe under analysis is not limited to those who
attended *only* four-year institutions, and that the community college
plays a significant role in the careers of the group of students under
consideration.

To repeat: Our subject universe consists of half the 1992 12th-grade
students in the NELS:88/2000 cohort. We are *not* talking about:

-   students who did not graduate from high school or those who
    graduated with something other than a standard diploma (G.E.D. or
    Certificate of Attendance);

-   students for whom we do not have full high school records
    (transcripts, grades, test scores);

-   students for whom socioeconomic status could not be determined;

-   students who did not enter any postsecondary institution by December
    2000, when they were 26 or 27 years old; and

-   students who entered the postsecondary system, but never set foot in
    a bachelor's degree-granting institution.

That is the other half. Some 22.2 per cent (s.e. = 1.05) of 1992
12th-graders who attended a four-year college at any time are in this
"other half" because they are missing key information that excludes them
from the universe under analysis. Readers interested in the demographic
differences between included and excluded students due to missing data
elements are referred to

Appendix E.

**Comparative demography of the subject universe**

Given the strong boundaries drawn around the subject universe, how does
its demography compare to less restrictive definitions? Table 2 sets out
the major demographic categories, and compares the target subject
universe with (a) all 1988 eighth-graders who participated in the last
survey of the NELS:88/2000 in 2000, (b) all participants in the 1992
survey, whether or not they were in school or in the 12th grade,[^13]
and (c) all 1992 12th-graders who attended *any* postsecondary
institution by December 2000.

As readers work from left to right across the columns of table 2, they
will notice that gender balances are even until the moment of entry to
postsecondary education, at which point women pull ahead of men. The
same type of observation applies to the race/ethnicity distribution: At
the point of entry to postsecondary education, the proportion of
African-Americans, Latinos, and American Indians declines, while that of
whites and Asians rises. In the universe for this study,

![](media/image2.wmf)

the proportion of whites rises even further, while that of Asians,
American Indians, and African-Americans[^14] holds steady, and that of
Latinos declines. There are no statistically significant differences in
the proportion of students who were nonnative speakers of English[^15]
until the final boundaries are drawn for the universe for this study.

The most dramatic and expected changes in the distributions of table 2
are by socioeconomic status quintile, with quantum leaps in the
proportion of students from the top two quintiles as soon as one crosses
the postsecondary line, and parallel declines in the proportion of
students from the bottom two quintiles. Only the third quintile (the
41st--60th percentile) remains stable until the final contraction of the
cohort for the universe used in this study.

What do these demographic changes within the universes of students who
might be the subjects for a study mean? *The Toolbox Revisited*---and
*Answers in the Tool Box* before it---is a study about students who
graduate from high school and go on to college. Given historical data,
it is not surprising that this group will evidence a higher SES profile
and a lower percentage of under-represented minorities than others in
the same grade cohort. Since the 1980s, women have been in the majority
in this group.[^16] Within our subject universe, demography is not
necessarily destiny, as the original *Tool Box* demonstrated. For the
comparison group---the other half that either does not graduate from
high school, graduates but doesn't continue its education, or graduates
and continues but never at a four-year college---*The Toolbox Revisited*
says: If we want more people to wind up with at least a bachelor's
degree in life, here are some guidelines based on the experience of
people who tried.

**Summary of Part I**

What do *Answers in the Tool Box* and *The Toolbox Revisited* do, and
what do they not do? Both studies use the histories of 12th-graders who
subsequently attended a four-year college at any time (entered in any
term and not just the fall term, entered as part-time as well as
full-time students, entered in community colleges as well as four-year
institutions) to indicate what factors in those histories are associated
with completing a bachelor's degree---not in four years, not in six
years, but whenever the longitudinal tracking ended (8.5 years from high
school graduation for the class of 1992; 11 years for the class of
1982). They do not ascribe cause or pretend to predict. They recognize
that what is associated with degree completion in one generation may not
be associated with it in the next, or that the strength of association
may change. Conditions and populations change, after all. Rigid
prediction is a risky call, and besides, that's not what the data and
statistical standards allow one to do.

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**Part II**

## Variables Explored and Used in This Analysis

The purpose of this section is to provide the reader with an advance
reference list of the variables considered and used in this analysis.
The reader should keep in mind that "variables" are *representations* of
realities (e.g., first-year college grades) or constructs (e.g.,
transfer). We use them as a shorthand.

The variables listed and described are presented in the order of the
steps of the logistic narrative for which they were considered. The
collection represents neither a \"fishing expedition\" nor a \"mind
dump,\" as a majority of the variables considered were determined by the
attempt to replicate the original *Tool Box* study with a more recent
parallel cohort. A quick summary of their properties can be found in
figure1.

**Demographic background variables defined**

1\) NNSE---Nonnative speaker of English. A dichotomous variable marking
those students whose first language was not English *and* who, in grade
12, reported that they conversed in that language with their mothers
most or all of the time.

2\) IMMIG---Parent immigrant status. A dichotomous variable indicating
whether the student's parents were immigrants to the United States
within the previous 10 years.

3\) BROSIS---Number of siblings. A dichotomous variable marking students
with three or more siblings, versus those with one, two, or none.

4\) FIRSTGEN---First generation postsecondary student. A dichotomous
variable indicating students whose parents had never attended a
postsecondary institution.

5\) FAMINC---Family income. This variable was first set in six bands,
then trichotomized to yield upper-, mid-range, and low-income
populations.

6\) URBAN---A dichotomous variable indicating whether the student's high
school was located in an urban area.

7\) NEWCHILD---A dichotomous variable to mark students, male or female,
who became parents by the time they were 20 years old.

8\) RACE---A dichotomous race/ethnicity variable, with minority
(African-American, Latino, and

American Indian) = 1 and White and Asian = 0.

9\) GENDER---A dichotomous variable in which male = 1 and female = 0.

10\) SESQUINT---Socioeconomic status quintile. See Glossary.

**High school background variables defined**

1\) EDUANTIC---Education anticipations. A three-level variable: (a)
consistently (in grades 10 and 12) expected to earn a bachelor's degree;
(b) raised expectations to the bachelor's degree between grades 10 and
12; and (c) either lowered expectations from the bachelor's level
between grades 10 and 12 or never expected to earn a bachelor's degree.

2\) CLSSRNKQ---High school class rank/GPA quintile. See Glossary and
Appendix C for accounts of construction and limited imputation,
respectively.

3\) SRTSQUIN---Senior year test score quintile. A test of general
learned abilities was administered to NELS high school seniors and the
results set out in percentiles. For those who did not take that test but
for whom SAT or ACT scores were available, those scores were substituted
using an equipercentile concordance methodology, weighted, and set out
in quintiles.

See Glossary for a more detailed account.

4\) HIGHMATH---Highest level of mathematics reached in high school. A
five-level variable with calculus and precalculus at the high end and
Algebra 1 and prealgebra at the low end. See Glossary.

5\) SCIMOM---High school momentum in science and mathematics. A
three-level variable combining highest level of mathematics with numbers
of credits earned in core laboratory science. See Glossary.

6\) FLAN---Number of units of foreign language in high school on a
five-level scale.

7\) ADVANCE---Number of Advanced Placement (AP) courses. Three values
based simply on the number of AP courses recorded: three or more, one or
two, and none. See Glossary for a full account of identifying AP course
work.

8\) HSCURRQ---Academic intensity of high school curriculum, in
quintiles. This variable is the core of the analysis of students'
precollegiate histories, and, hence, is described in detail in

Part III and Appendix F.

9\) ACRES---Academic Resources. A quintile index representing a
composite of students' pre-

collegiate attainment (curriculum plus class rank/GPA plus senior year
test score). ACRES is the dominant precollegiate variable in both the
original *Tool Box* and *The Toolbox Revisited.* The construction of
this variable is described in detail in Part III.

**Postsecondary entry variables defined**

1\) FIRST4---A dichotomous variable indicating whether the first
postsecondary institution attended by the student was a four-year
college.

2\) DOCT---Another dichotomous variable indicating whether the first
postsecondary institution attended was a doctoral degree-granting
institution.

3\) SELECT---A dichotomous variable indicating that the first
institution attended by the student was either highly selective or
selective.[^17] See Glossary for details on selectivity.

4\) NODELAY---A dichotomous variable marking students who entered
postsecondary education within seven months of high school graduation.

5\) ACCELCRD---Acceleration credits. A sum of all college credits earned
by both course work prior to high school graduation and by examination.
The values of this variable were set at three levels: more than 4
credits, 1--4, and zero.

**First-year performance variables defined**

1\) LOWCRED---A dichotomous variable marking students who earned less
than 20 additive credits earned in the first calendar year of
attendance. For descriptive data on the relationship between number of
credits earned in the first year and highest degree, see Appendix L,
table L4.

2\) FRSHGRAD---GPA in the first calendar year of attendance. Grade point
averages were determined for the first *full calendar year* of
postsecondary attendance and were then set out in quintiles. FRSHGRAD is
a dichotomous variable that divides the highest two quintiles from the
other three.

3\) FREM---A dichotomous variable indicating any remedial course work in
the first calendar year of attendance**.**

4\) FCOLMATH---Another dichotomous variable indicating whether the
student earned any credits in college-level mathematics during the
calendar year following first enrollment. \"College-level mathematics\"
was defined to include college algebra, finite math, statistics,
precalculus, calculus,[^18] and a category of \"liberal arts
mathematics\" courses that require the equivalent of high school Algebra
2 as a prerequisite, and include such topics as game theory, basic
combinatorics, and foundations of numerical methods.

**Financing postsecondary schooling variables**

There are three dichotomous financing variables in both *Answers in the
Tool Box* and *The*

*Toolbox Revisited*: GRANTS, LOANS, and STUWORK. Each indicates only
whether the

student used that form of financing during his/her early postsecondary
career. The reader is

referred to the text of Part IV for elaboration.

**Attendance pattern variables defined**

1\) TRANSFER---community college to four-year. With students going back
and forth between community colleges and four-year colleges, it is
important to mark transfer as a permanent change of venue, a migration
that is formally recognized by system rules. A transfer student is one
who (a) started in a community college, (b) earned more than 10 credits
from the community college before (c) enrolling in a four-year college
and (d) earning more than 10 credits from the four-year college. The
only time limit set for these changes of venue and credit accumulation
is the length of the longitudinal study. In the case of the
NELS:88/2000, that means 8.5 years from the modal high school graduation
data of June 1992. This is a dichotomous variable.

2\) FOURTRAN---A dichotomous variable indicating transfer from one
four-year college to another**.** The algorithm for classic transfer
from a community college to a four-year college was fairly easy to
construct. But to distinguish a true four-year-to-four-year college
transfer required an indirect route. See Glossary for details.

3\) MULTINS---A dichotomous variable indicating that the student
attended more than one institution. This is a macro-vision of otherwise
multidirectional student behavior.

4\) SUMMER---Number of credits earned during summer terms, set in three
bands: more than 4,

1--4, and none.

5\) PARTTIME---A dichotomous variable tagging students whose enrollment
intensity was *ever* part-time**.** The construction of this variable
involves complex algorithms, and the reader is referred to the Glossary
for details. (For an account of enrollment intensity in both the
NELS:88/2000 and the Beginning Postsecondary Students longitudinal study
of 1995/96--2001, see Appendix L, table L5).

**Extended postsecondary performance variables defined**

1\) TREND---Trend in student's GPA: rising, flat, or falling. Cumulative
undergraduate GPA was measured at three points in time---at the end of
the first calendar year following initial enrollment, at the end of the
first two calendar years following initial enrollment, and at the end of
the student's undergraduate career, no matter when that occurred. See
Glossary for further elaboration.

2\) CUMMATH---Number of credits earned in college-level mathematics**:**
more than 4, 1--4,

and 0.

3\) CHANMAJ---A dichotomous change-of-major variable. See Glossary for a
full description.

**Final factors variables defined**

1\) NOSTOP---In all three NCES postsecondary transcript-based
grade-cohort studies, noncontinuous enrollment was defined as *more
than* a one semester (or its equivalent, e.g., two quarters) stop-out
period. In the dichotomous variable, NOSTOP, the student is considered
continuously enrolled even with one semester (or two quarters) off.

2\) WRPT Ratio---A dichotomous variable. On one side of the dividing
line are students who withdrew from or repeated 20 percent or more of
all courses in which they enrolled (ratio of non-penalty withdrawal and
no-credit repeat grades to all grades received).

**Summary: Locus of Responsibility**

Figure 1 presents the basic statistical characteristics for 39 of the
major variables described above that were either tested, used in trials,
and/or employed in the final logistic narrative of *The*

*Tool box Revisited.* Seven of these variables describe demographic
characteristics, and another three label types of financial aid that
ultimately are offshoots of demography. Of the remaining 29 variables,
14 are principally matters of student choice (e.g., changed major), five
are indicators of student academic effort (e.g., first-year grades),
seven reflect interactions of student choice plus student effort plus
opportunity to learn (e.g., highest high school math), two mark
interactions of student effort and institutional judgment or guidance
(e.g., first-year remediation), and one (education anticipations)
reflects student experience, attainment, and self-assessment, along with
the encouragement of family and peers. The student is at the center of
all these representations. The locus of responsibility for the way each
of these variables will tilt lies as much with the student as with
external forces. *The Toolbox Revisited* is optimistic that most
students can make it all come out right. We will return to this optimism
in Part VII.

![](media/image3.wmf)

![](media/image4.wmf)

**\[THIS PAGE INTENTIONALLY LEFT BLANK\]**

**Part III**

**What Is and What Happens Before Matriculation**

There are at least three distinct ways of setting up Step 1 in the
progression of multivariate analyses that lead us to appreciate what
makes a difference (and how much of a difference) in completing a
bachelor's degree for students who attended a four-year college at any
time. The first step covers both student demographics and high school
performance. Let us cover the demographics first because they do not
present complex analytic choices.

**What If We Knew Nothing Except Demography?**

The demographic background of students is marked as of a set moment in
time (in our case, in grade 12). It is what students look like, where
they are living, their parents' education(s), occupation(s), and
income(s), and other features of the student's family. Demographic
characteristics may be subject to special attention in education policy
from local to national levels, but, with the exception of the student's
marital and parental status, are not subject to change.

Demographic variables are normally considered in the context of other
aspects of student experience, behaviors, and attitudes when attainment
of any kind (e.g., high school graduation, test scores, grades, college
degree) is the dependent variable. Indeed, that is the way this analysis
treats demographic characteristics. But to demonstrate what happens to
the demographic variables in the analysis, this section opens with a
stark presentation. If someone asked us to explain bachelor's degree
completion for 1992 12th-graders who subsequently attended a four-year
college at any time, and all we knew about them were demographics, what
would the various associations of demography with degree attainment look
like?

Table 3 presents a logistic exploration that started with nine
demographic variables described in Part II above. The socioeconomic
status quintile variable is not included, but two of its components
(family income and parents' highest level of education) are present to
serve as proxies for SES. Two of the nine demographic
variables---whether the student was a nonnative speaker of English and
family immigrant status---were not accepted into the logistic equation.

Whether there were nine variables or seven, however, this logistic model
fails to reach significance as a *model,* regardless of whether
independent variables within the model turn out to be significant. The
*t* value for the intercept falls far below the threshold of 0.765 this
study uses for keeping independent variables under consideration, and
the proportion of concordant probabilities predicted at 63 percent is
the lowest of any logistic model in this study.

Of the independent variables within the model, four are significant,
even though that significance is undercut by the statistical
characteristics of the model as a whole. The most significant

(*p* \< 0.01) is first generation college status, with a Delta-p
statistic that says the probability of completing a bachelor's degree is
reduced by roughly 21 percent for first generation students.

Race/ethnicity and gender are significant at *p* \<. 05, with the
messages of the Delta-p that minority status reduces the probability of
earning a bachelor's degree by 17 percent, and being male reduces that
probability by 11 percent. Falling in the highest third of family income
is marginally significant.

  -------------------- --------------- --------------------- ------------------ ---------- ---------- -------------
  **Table 3.**         **Logistic                                                                     
                       account of the                                                                 
                       relationships                                                                  
                       among major                                                                    
                       demographic                                                                    
                       variables and                                                                  
                       bachelor\'s                                                                    
                       degree                                                                         
                       attainment for                                                                 
                       1992                                                                           
                       12th-graders                                                                   
                       who attended a                                                                 
                       four-year                                                                      
                       college at any                                                                 
                       time**                                                                         

                                                                                                      

  **Variable**                         **Parameter           **Adjusted         ***t***    ***p***    **Delta-p**
                                       estimate**            standard error**                         

  Intercept                            0.2250                0.1869             0.69                   

  **Race/ethnicity**                   **-0.7257**           **0.1434**         **2.90**   **0.05**   **-0.1660**

  **Gender**                           **-0.4760**           **0.1072**         **2.54**   **0.05**   **-0.1089**

  Parenthood                           -1.6285               0.5255             1.77       †          †

  Siblings                             -0.3619               0.1109             1.87       †          †

  **Family Income**                    **0.3870**            **0.1111**         **2.00**   **0.10**   **0.0885**

  **First generation**                 **-0.9137**           **0.1420**         **3.69**   **0.01**   **-0.2089**

  Urban high school                    0.1839                0.1217             **0.87**   †          †

  † Variable did not                                                                                  
  reach the minimum                                                                                   
  level of                                                                                            
  significance                                                                                        
  (p\<.10) in                                                                                         
  two-tailed test.                                                                                    

  **NOTES**:                                                                                          
  Statistically                                                                                       
  significant variable                                                                                
  are in bold. G^2^ =                                                                                 
  6288.09; *df* =5144                                                                                 
  G^2.^df =1.222;                                                                                     
  X^2^(df) =                                                                                          
  413.76(7); pseudo                                                                                   
  R^2^ = .077.                                                                                        
  Proportion of                                                                                       
  concordant                                                                                          
  probabilities                                                                                       
  predicted = 63.0.                                                                                   
  Root design effect =                                                                                
  1.75                                                                                                

  **SOURCE:**                                                                                         
  NELS:88/2000                                                                                        
  Postsecondary                                                                                       
  Transcript Files                                                                                    
  (NCES 2003-402 and                                                                                  
  Supplement).                                                                                        
  -------------------- --------------- --------------------- ------------------ ---------- ---------- -------------

But the most important message is the failure of the purely demographic
analysis itself. If the statistical model does not reach a convincing
level of significance, and all the variables inside the model are
basically cut from the same cloth, then even if some of those variables
are significant within the model, the cloth is frayed. That failure sets
up a hypothesis that will unravel in the course of subsequent steps of
the logistic narrative: Among students who attended a four-year college
at any time, student demographics and family demographics may have, at
best, indirect connections with degree completion. In fact, at the
moment high school academic history is included in the multivariate
account, demography plays a considerably reduced role at the same time
that the logistic model becomes more persuasive.

**High School Background and History**

This is where the academic momentum story begins, where the major
contributions of the original *Tool Box* were most prominent, and where
the story continues to be of considerable importance.

There were four core high school background and performance variables in
the first step of the logistic inquiry in the original *Tool Box*:
senior year test score, a combined index of class rank and GPA, academic
curriculum intensity, and the student's education "anticipations." The
first three of these variables were combined in a composite index of
"Academic Resources" that proved to have lasting positive repercussions
through students' postsecondary histories.

Before we examine the results of the Step 1 logistic model, we should
(a) revisit education \"anticipations,\" and (b) provide a detailed
account of how *The Toolbox Revisited* deals with high school
curriculum.

**\"Anticipations\" versus \"aspirations\"**

Both the original *Tool Box* and this study employ a variable that some
people will interpret as indicating students' education \"aspirations.\"
But this construct is carefully labeled \"anticipations,\" and is *not*
based on the student's answer to a question asked only once (for
example, in a 12th-grade survey or in a freshman registration line).
Rather, \"anticipations\" is built from sets of questions asked in both
the 10th grade and the 12th grade, and describes the *consistency* and
*level* of the student's abstract expectations and concrete plans.

Perhaps as a by-product of the national visibility of discussions on
secondary-to-postsecondary transitions that followed the release of *A
Nation at Risk* in 1983, along with a burst in recruitment of minority
students by both colleges and professionally-oriented organizations such
as the National Action Committee for Minorities in Engineering, the
proportion of 12th-graders who *consistently* expected to earn at least
a bachelor's degree more than doubled from 22.5 percent (s.e. = 0.58)
among 1982 12th-graders to 59.4 percent (s.e. = 1.02) among 1992
12th-graders.. Continuing one's education after high school, at some
point and \"in some form of postsecondary education\" is now a norm of
expectations among high school graduates: 92.6 percent (s.e. = 0.54) of
NELS:88/2000 students who graduated from high school with any kind of
diploma, whether \"on-time\" in 1992 or later, expected to continue
their education in a postsecondary setting. That which is a norm of
behavior is like breathing in and breathing out. When virtually everyone
expects to continue, the serious curricular "disconnect" between K-12
and postsecondary systems eloquently dissected by Venezia, Kirst, and
Antonio (2003) is even more fraught with hazards and ironies.
\"Anticipations,\" one can surmise, will not play as significant a role
in a logistic account of bachelor's degree completion as it did in the
original *Tool Box.*[^19]

To aspire is an active concept. In our ordinary usage, it means to hope,
seek, wish, or yearn. When Kao and Tienda (1998) describe
\"aspirations\" as \"a realistic evaluation of likely out-comes\" (p.
352), they are not describing \"aspirations\" as we normally understand
the term. Qian and Blair (1999), too, indicate that they use the
\"aspirations\" to describe expectations or plans \"rather than a wish\"
(p. 622). And that's just the point: With these rare exceptions, the
literature

on education \"aspirations\" consistently confounds an emotively-laden
term applied to motivation, desire, or drive with an assessment of
possibility based in experience (Mezias 1988). Underneath the
consistency-by-level construct of the educational \"anticipations\"
variable used in both the original *Tool Box* and in this study is what
Kao and Tienda (1998) document as a growth from abstract attitudes about
a very distant possibility when students are in junior high school to a
rational judgment based on both school experience and input from parents
and peers as the time draws closer to high school graduation. There is
no doubt that the consistency-by-level formulation of our anticipations
variable is influenced by what happens to students between grades 10 and
12.

A different interpretation of expectations is implicit in Venezia,
Kirst, and Antonio (2003): Expectations become assumptions, more passive
than "aspirations." Their principal thesis---that students falsely
assume that the momentum inherent in a high school diploma is sufficient
not merely to enter a postsecondary environment (\"the easy part,\" in
their words) but to complete a credential---is all the more powerful
when these assumptions end in less than completion. The principal
culprit lies in poorly articulated (secondary-to-postsecondary)
curricula (Conley 2005), a topic addressed in Part VI of this essay.

# Academic Intensity of Secondary School Curriculum

Think of a series of moving walkways in an airport. Passengers expect
that one leads to the next, and don't think too much about what's
happening along the way. What the most perceptive of contemporary
analysts of the curriculum paths from high schools into colleges of any
kind have observed (Venezia, Kirst and Antonio; and Conley) might be
described as a disconnect in both the location and speed of these
successive moving walkways, so that the passengers stepping mindlessly
off the first and heading to the second trip, stumble into the moving
hand rail, and desperately grasp at their luggage so that it doesn't get
stuck in the space between the two segments. This issue was imperfectly
highlighted in the original *Tool Box* and is worth extended preliminary
attention here.

The "differential course work" hypothesis, originating in the work of
Pallas and Alexander (1983) and Alexander and Pallas (1984) in relation
to high school test scores, and validated by *Answers in the Tool Box*
with a longer time frame and a bachelor's degree attainment dependent
variable, remains the core of the presentation in *The Toolbox
Revisited* as well. With these forebears as guidance, we are going to
look at the components of the curriculum variable, alternative
presentations of those components for multivariate analyses, and some
critiques of the measure. In the past decade, a number of short-hand
representations of the high school curriculum, e.g., the New Basics as
advocated in *A Nation at Risk* (1983), \"minimum college-qualified
(Berkner and Chavez 1997), and \"track location\" (Lucas 1999; Lucas and
Berends 2002) have become common in both the research literature and the
general press. The New Basics are the best known of these heuristics.
The highest level of these \"new basics\"

---which simply counted Carnegie units[^20] (four of English, three each
of mathematics, science, and social studies, and two of foreign
language)---has been labeled \"rigorous\" (McCormick 1999), even though
three units of mathematics could amount to no more than plane geometry
and the science in question could lack any laboratory components. After
the publication of the original *Tool Box*, the literature added
criteria for highest level of math, core laboratory science, and
Advanced Placement course work to the judgment of \"rigor,\" and sought
a trichotomous presentation with labels such as \"core curriculum or
less,\" \"mid-level,\" and \"rigorous\" (Horn and Kojaku 2001).

Quite frankly, the word \"rigorous\" is somewhat of a misnomer since a
course requiring a high concentration of intellectual effort can be
presented in a relaxed manner with comparatively low standards for
success. Put another way, calculus or laboratory chemistry, for example,
can be taught in a very laid-back fashion, while an otherwise
\"ordinary\" survey of U.S. history can require the search for,
discovery, and cataloguing of original source material, readings in
archival methods, and frequent examinations and project presentations
with criterion-referenced grading standards. Both the original *Tool
Box* and *The Toolbox Revisited* prefer the term, \"academic
intensity,\" defend the continuous variable of academic curriculum
intensity as a more flexible language of accounting, and decline to
invoke labels of "college qualified," "at risk," and others.

The academic curriculum intensity variable is called HSCURRQ. It takes a
weighted distribution of NELS:88/2000 students across 31 levels of
academic curriculum intensity and quality (there were 40 levels in the
records of the High School Class of 1982, the subjects of the original
*Tool Box*), and divides the distribution by quintile. Each level of
academic curriculum intensity is a distinct configuration of numbers of
Carnegie units[^21] earned in core academic areas and other distinct
notations about students' course of study. For example, in both data
sets, at the highest level, one finds students who, between grades 9 and
12, accumulated.[^22]

3.75 or more Carnegie units of English;

3.75 or more Carnegie units of mathematics;

highest mathematics of either calculus, precalculus, or trigonometry;

2.5 or more Carnegie units of science *or* more than 2.0 Carnegie units
of core

laboratory science (biology, chemistry, and physics);

more than 2.0 Carnegie units of foreign languages;

more than 2.0 Carnegie units of history and/or social studies;

more than 1 Advanced Placement course; and

no remedial English; no remedial mathematics.

These are minimums. In fact, at the highest level of academic curricular
intensity, students had accumulated an average of 4.30 Carnegie units of
English, 4.34 units of mathematics (94 percent having reached
precalculus or calculus), 3.63 units of core laboratory science, 3.76
units of foreign languages, and 3.79 units of history and other social
studies, along with an average of three AP courses. That is an
impressive portfolio.

To this particular configuration, the NELS:88/2000 version of the
highest level of academic curriculum intensity adds any Carnegie units
in \"computer science,\" a far more frequent and integrated elective in
the high school curriculum by 1990, when the NELS students were in the
10th grade, as opposed to 1980, when the High School & Beyond/So
students were in the 10th grade (the mass availability and marketing of
PCs began in 1984).

Each subsequent level in a descending logical cascade subtracts
something from this configuration (see Appendix F) until a relatively
smooth distribution is achieved. Nothing is perfect in these algorithmic
adjustments; and whatever lumpiness in distribution remains is assuaged
in the quintile version.

In light of recent literature on the effects of AP course-taking versus
scores on AP examinations (e.g., Geiser and Santelices 2004;
Klopfenstein and Thomas 2005), it is important to note that in both the
original *Tool Box* and in this study, AP course work is *not* treated
as a discrete variable, rather as *part* of the overall index of
academic curricular intensity. However, in a moment we will demonstrate
what happens when AP is invoked as a distinct independent variable in
alternative constructions of the first step of our core logistic model.

The basic critique of this account of high school curriculum has much
merit: Numbers of courses (expressed in Carnegie units) in specific
subject areas are not equivalent to high content standards or
performance standards in those courses (Barth and Haycock 2004). In the
cascading curriculum levels of the Academic Intensity variable, a
student could accumulate three units of watered down history and social
studies and still have three units. A national transcript accounting has
no way of knowing what is demanded in thousands of history and social
studies courses offered in 1100 high schools, a point made in the staff
research for *A Nation at Risk* (see Adelman 1983). The only domestic
examples available for those who argue for test-driven high content
standards in individual high school subjects such as U.S. history or
chemistry or

Algebra 2 are the College Board achievement tests (now called SAT II)
and the New York State Regents. Some other states (e.g., Michigan) have
tests in place for merit-based scholarships that cover broad areas of
the curriculum (e.g., math, science) and language skills (reading,
writing) but not specific subjects. In this respect, they are closer to
the ACT examination, though at a less demanding level (Bishop 2004). The
high school transcripts that serve as our evidence are very inconsistent
in entering SAT II subject exam scores, so we have nothing on which to
rely for an external validation of content. Getting beyond course titles
to content standards is addressed in Part VI of this study.

Altonji's work (1996) offers a second important critique. He would have
us control high school curriculum variables for school effects and
\"quality of courses,\" but admits that whatever one tries for proxy
measures, the results would be \"imperfect.\" Altonji draws our
attention to the fact that more than half the variance in the mean
number of Carnegie units earned in academic subjects by the NLS-72
cohort[^23] was across schools, indicating disparities in opportunity to
learn, teacher quality, and student talents and proclivities. One might
put Altonji's conclusion more baldly: Students from higher SES
backgrounds attend high schools that serve similar students, schools in
which parental expectations and involvement are high, and schools in
which curriculum offerings and teacher quality follow SES demands and
can afford to do so because the tax base is higher. These students tend
to enter college and earn degrees at higher rates than students from
\"lesser\" backgrounds and from schools that accompany those
backgrounds, therefore, the influence of the academic intensity of high
school curriculum will be overstated.

The implicit response of the original *Tool Box* made explicit in *The
Toolbox Revisited* is that there are inequities in opportunity to learn
and proclivity to learn that are reflected in the geo-demography of
schools, but in a logistic account of bachelor's degree attainment in
which the results are reported with the Delta-p statistic, socioeconomic
status will modulate some of the effects of curriculum. The message
encourages all high schools to offer the requisite curricula, to make
sure they have teachers who can deliver that curricula, to believe that
their students can all reach higher levels of academic intensity in
preparation, and to encourage their students to do so---no matter what
their intentions for subsequent education or work may be. As the
principles of the *No Child Left Behind* legislation are applied in high
schools, this is a large part of what they mean.

**Highest level of mathematics and changes in high school
course-taking**

In comparing the high school records of the HS&B/So (High School Class
of 1982) with those of the NELS:88/200 (High School Class of 1992), and
looking only at earned Carnegie units, what we principally witness is an
improvement of precollegiate preparation of students in mathematics and
science, a change that affects the amount of remediation necessary in
four-year colleges, as well as mathematics course-taking at the
college-level (Adelman, Daniel, and Berkovits 2003). We also note an
unsettling increase in the percentage of students taking a maximum of
one year of foreign language course work (though that percentage spread
might be mitigated somewhat if we accounted for the increase in
bilingual heritage language users between the two cohorts). Table 4 sets
forth some basic threshold markers in these curricular areas.

![](media/image5.wmf)Thresholds are suggestive, but not conclusive, of
the shape of change in curricular preparation.

By reverse logic, table 4 says only that X percent of students are
getting beyond point Q in secondary school study. It does not say how
far beyond, and that may make more of a difference in academic momentum.
The mathematics analysis in the original *Tool Box* was a proxy for the
general metaphor of momentum, and it may be instructive to compare the
results of those calculations---a distribution and a logistic---to what
emerges from the NELS:88/2000 involving all the rungs on the "math
ladder." Tables 5, 6, and 7 do so, confining their universes only to
students who were in the 12th grade in the year they were scheduled to
be in the 12th grade. They do not restrict the universes to those who
entered postsecondary education, let alone to those attended four-year
colleges at some time. These are very inclusive groups.

Table 5 confirms other observations in these data sets: The efforts
following *A Nation at Risk* to move students further ahead in high
school mathematics had positive results. Higher proportions of students
were reaching Algebra 2 and higher levels. Bachelor's degree attainment
rates for those who moved at least one step beyond Algebra 2 in high
school were stable, but declined at every level at or below Algebra 2.
Table 5 provides a framework that needs to be validated in a more
convincing way, and that is the purpose of table 7. Table 7 presents the
results of logistic analyses and does so in odds ratios (departing from
the presentation of other logistics in *The*

*Toolbox Revisited*) to match the way in which this table was presented
in the original *Tool Box* study.[^24]

From the write-ups and presentations of the original *Tool Box* study a
principle for high school curriculum guidance arose: \"One step beyond
Algebra 2 doubles the odds that you will earn a bachelor's degree.\"
What does that mean, i.e., how does one read table 7? An odds ratio
indicates that every unit of change in an independent variable (in this
case, each step up the math ladder) increases the odds of X happening
(in this case, earning a bachelor's degree) by Y (the odds ratio). For
table 7, the data for the full model---using only highest mathematics
and socioeconomic status quintile---are presented first, in bold. In
both cohorts, the odds ratio says that every step up the math ladder
multiplies the odds of earning a bachelor's degree by roughly 2.5 versus
an odds ratio for each step up the socioeconomic status quintile measure
of 1.68

(for the class of 1982) and 1.78 (for the class of 1992). These data are
statistically significant

(*p* \<.05 or better).

![](media/image6.wmf)

The balance of the table takes each level of high school mathematics,
and runs a logistic regression *for that level*, with bachelor's degree
completion as the dependent variable, and SES quintile as the sole
control. For the class of 1982, reaching calculus in high school
increased the odds of earning a bachelor's degree by a very impressive
8.18 to 1. For the class of 1992, the odds ratio for calculus was still
in the same range at 7.52 to 1. The parameter estimates for the calculus
line are almost identical (2.102 versus 2.018). These are consistent
results.

When one looks at the columns in table 7 for the class of 1982, one
notices that the sign of the parameter estimate moves from negative to
positive territory between geometry and Algebra 2, and the value of the
parameter estimate rises above 1.0 between Algebra 2 and trigonometry.
The odds ratio more than doubles in each of those steps, but only in the
step between Algebra 2 and trigonometry (the \"one step beyond\") is the
parameter also positive. For the class of 1992, all those relationships
move up one rung on the \"math ladder,\" principally because a higher
percentage of this group (than the percentage for the class of 1982)
reached precalculus or calculus while a lower percentage failed to get
as far as Algebra 2. The critical boundary for math momentum now lies
firmly beyond Algebra 2.

But therein lies the rub, for not everyone has the chance to reach
beyond Algebra 2. Differential lack of opportunity-to-learn was a major
theme in the original *Tool Box* and is just as prominent a theme in
this study of a cohort a decade later. Table 6 illustrates this unhappy
situation. It asks what proportion of students---by race/ethnicity and
socioeconomic status quintile---attended high schools that offered key
math courses beyond Algebra 2.

If mathematics momentum is as important as we contend it to be, one can
see the ripples of opportunity---or lack of opportunity---that start in
high school offerings. In the matter of calculus, Latino students and
those from any socioeconomic status quintile other than the highest are
at a distinct disadvantage with respect to the opportunity even to
confront the subject. African-American students join the other groups in
less access to both trigonometry and statistics. While this issue will
be revisited, it deserves underscoring here: The task of providing
quality secondary school curricula to *everybody*, the *paths* to AP,
the *paths* to the kind of learning challenges students will face in
higher education, is enormous. If the promise of *No Child Left Behind*
is to be realized at the secondary school level, it is first and
foremost through the equitable provision of opportunity-to-learn.

![](media/image7.wmf)

Since "highest high school mathematics" is a critical sorting component
in the construction of the composite variable describing the academic
intensity of a student's secondary school curriculum, the ramifications
of more students completing courses beyond Algebra 2, it is
hypothesized, will ironically diminish (however modestly) the
explanatory power of curriculum and raise the power of academic
performance (class rank/GPA). To illustrate with a metaphor: If it was
said that a student who reaches precalculus in high school and earns a C
has a better chance of finishing a bachelor's degree than a student who
gets only as far as Algebra 2 with an A-, we now have to raise the bar
for performance in precalculus to at least a B- in order for the
prediction to hold.

![](media/image8.wmf)

The general improvement in the high school curriculum profile of the
NELS:88/2000 cohort is reflected, at least among students who
subsequently attended a four-year college at any time,

in diminished postsecondary remediation for that population. Table 8
sets out the distribution of what in the *original Tool Box* study was
called the "remedial problem," a logical cascade that distinguishes not
only the amount of remediation a student takes in college, but also the
kind of remediation at issue. The logical cascade begins with remedial
reading, then sorts out those students whose only remediation consists
of one or two courses in mathematics, then divides the balance of the
remedial population between those who required more than two remedial
courses and those who required only one. The type of remediation at
issue for both these residual populations is usually writing, but also
includes courses devoted to basic study skills and general developmental
work. If the population included students who never attended a four-year
college, this distribution would look very different.[^25]

![](media/image9.wmf)

**Summary of high school curriculum and performance variables**

To remind the reader of our tools before heading into Step 1 of the
logistic narrative: For the high school curriculum components of the
analysis we have a composite variable called HSCURRQ, and four variables
set forth in Part II above describing discrete components of HSCURRQ
that we can test as proxy measures for the composite---highest level of
mathematics, science momentum (a combination of highest math and core
laboratory science credits), foreign language credits, and number of
Advanced Placement courses. In a moment all these will appear in a
correlation matrix that will provide a preview of how they might play
out in multivariate analyses.

For our other performance measures, we bring forward from Part II a
quintile presentation of the student's high school class rank/GPA, and a
quintile presentation of senior year test score.

**Academic Resources**

The original *Tool Box* advanced a notion explored and developed by Karl
Alexander of Johns Hopkins and his associates in numerous exemplary
contributions to the research literature: A student's academic
background was far more important than demographic variables such as
gender, race/ethnicity, family composition, and socioeconomic status in
relation to test performance (Alexander and Pallas 1984), entering
higher education (Thomas, Alexander, and Eckland 1979), and, in one
study, degree completion (Alexander, Riordan, Fennessey and Pallas
1982). How does one reflect a composite idea of \"academic background\"
of students coming out of high school and into postsecondary education?
The key measure of Academic Resources (or ACRES, as the original *Tool
Box* variable was called in order to elicit the idea of academic
cultivation), combined curricular record, academic performance (class
rank/GPA) as an indicator of student effort, and an external measure in
the form of performance on tests of general learned abilities. These
three components, as we have seen, are set out in quintiles. To get a
preliminary idea of their relative strength in relation to bachelor's
degree completion, table 9 takes all on-time high school graduates in
1992 and indicates the percentage who completed a bachelor's degree by
December 2000 by quintile of each of the three components. To be
included in table 9, the student's record had to contain positive values
for all three components.

Table 9 offers some hints of what multivariate analysis will confirm.
The universe consists of all on-time high school graduates, as opposed
to 1992 12th-graders, in order to equalize the condi- tions of judging
degree-completion rates by performance quintiles. Compared to the
distribu-tions for academic curriculum intensity and class rank/GPA, the
test score quintile variable yields weaker degree completion rates in
its highest quintile. Comparing second quintile distri- butions, test
scores are weaker than academic curriculum. These are signs that the
test score quintile will not have as strong an association with degree
completion as the other two factors. On the surface, it looks as if
class rank/GPA will be fairly dependable, but it has one minor bump. The
reader is directed in table 9 to the percentage of eventual bachelor's
recipients from the lowest quintile of class rank/GPA (13 percent)
compared to the percent of bachelor's degree

![](media/image10.wmf)completers in the lowest quintile of test scores
and academic curriculum (about 9 percent in both cases). The differences
are statistically significant in a descriptive account such as that of
table 9, but how meaningful they turn out to be must await a
multivariate context. In the meantime, one would posit that the class
rank/GPA measure will not prove as strong as the curriculum measure.

A multivariate analysis involving these variables, in fact, confirms our
suspicions, and its results are presented in table 10. The model is the
foundation for construction of the composite variable, Academic
Resources, and is derived from ratios of the standardized beta estimates
of the three high school performance indicators produced by a logistic
regression with bachelor's degree attainment as the dependent variable
and no controls (the logistic regression itself can be found in Appendix
L, table L7). The change in these ratios between those for the High
School Class of 1982 and those for the High School Class of 1992, while
still leaving academic curriculum with the highest weight, narrows the
gap between curriculum and performance, and lowers the strength of test
scores as a component of Academic Resources. Given the differences in
overall participation in the variable, i.e., the proportion of
12th-graders for whom all three components have positive values, some of
the change may be an artifice of the NELS:88/2000 data set. But the
principal message is one observed when commenting on the change in the
distribution of students by highest level of mathematics studied in high
school: The higher the average level of mathematics attainment, the more
student effort, reflected in grades, will count. This theme will
continue to play out when our story crosses the matriculation line into
postsecondary education; and it was one of the principal points made by
DesJardins, McCall, Ahlburg and Moye (2002) in their critique of the
original *Tool Box* study.

When using all three measures---curriculum, class rank, and ACT test
score---in a traditional linear analysis predicting first-year college
grades, Pike and Saupe (2002) found curriculum to be

![](media/image11.wmf)the strongest, though their curriculum variable
was dichotomous (students either meeting or not meeting the entrance
specifications for a selective state university), which would naturally
increase its power. Even when they introduced indirect effects of high
school characteristics ---control (private/public), size, mean ACT score
of students, and mean proportion of students who attended the
university---the parameter estimates for this curriculum variable were
significantly greater than those for test scores or class rank. While
*The Toolbox Revisited* is not in the business of predicting first-year
grades, it is gratifying to note research that has similar respect for
the propulsive power of course of study.

A second message bears repeating from its formulation in the original
*Tool Box*: Student effort in curriculum participation and performance
over the three *years* of high school (grades 10 to 12) reflected in the
transcript data is worth considerably more than performance on a
three-*hour* test on a Saturday morning. Test scores are a natural
consequence of the academic intensity of curriculum and quality of
student effort reflected in grades, and the weakening position of the
test score variable in the ACRES configuration for the NELS:88/2000
cohort is a natural outcome of improvements in academic curriculum
participation of the post-*A Nation at Risk* era.

**Correlations**

Now that we have all the precollegiate variables explained and in place,
the process of bringing zoom and macro lenses of multivariate analysis
to bear begins. The first stage sets forth a correlation matrix of
precollegiate academic variables including three outcomes: on-time high
school graduation, basic postsecondary "access," and bachelor's degree
completion. Table 11 presents the Pearson's *r* results. Some of these
correlations are weak, suggesting that one or both of the variables in
question will not add to the explanatory power of a logistic regression.
On-time high school graduation, for the most noted example, is not
related to anything (this was also true in the parallel correlation
matrix in the original *Tool Box*). Other relationships are not
surprising, e.g., Advanced Placement has almost no bearing on entering
postsecondary education (96.7 percent \[s.e. = 1.48\] of NELS
12th-graders with any AP courses entered the postsecondary sphere,
versus 75.9 percent \[s.e. = 1.01\] of those with no AP course work).

  --------------- ---------------- --------- --------- ---------- ---------- ---------- ---------- ---------- ----------------
  **Table 11.**   **Correlations                                                                              
                  of major                                                                                    
                  precollege                                                                                  
                  Academic                                                                                    
                  Resources                                                                                   
                  variables and                                                                               
                  high school                                                                                 
                  graduation                                                                                  
                  status, college                                                                             
                  entry, and                                                                                  
                  bachelor\'s                                                                                 
                  degree                                                                                      
                  attainment by                                                                               
                  December 2000                                                                               
                  for 1992                                                                                    
                  12th-graders**                                                                              

                                                                                                              

                                                                                                              

                  Curriculum       AP        Highest   Science    Foreign    Class rank Senior     On-time HS Post-secondary
                  Intensity        Courses   math (5th momentum   Language   / GPA      test       grad,      entry (PSENT)
                  Quintile (CURRQ) (APCRS)   levels)   (3 levels) (3 levels) quintile   quintile   standard   
                                             (HMATH)   (SCIMOM)   (FLAN)     (RANK)     (TEST)     diploma    
                                                                                                   (ONTIME)   

  CURRQ           \-\-\--          0.368     0.777     0.774      0.645      0.572      0.581      0.167\*    0.352

  APCRS                            \-\-\--   0.438     0.366      0.270      0.326      0.317      0.050\*    0.111\*

  HMATH                                      \-\-\--   0.869      0.519      0.618      0.634      0.124\*    0.301

  SCIMOM                                               \-\-\--    0.489      0.590      0.578      0.118\*    0.279

  FLAN                                                            \-\-\--    0.430      0.510      0.146\*    0.338

  RANK                                                                       \-\-\--    0.566      0.185\*    0.298

  TEST                                                                                  \-\-\--    0.138\*    0.313

  ONTIME                                                                                           \-\-\--    0.168\*

  PSENT                                                                                                       \-\-\--

  BACHELOR\'S     0.524            0.319     0.538     0.530      0.451      0.493      0.469      0.129\*    0.332

  **NOTE:** All                                                                                               
  estimates                                                                                                   
  except those                                                                                                
  noted with an                                                                                               
  asterisk are                                                                                                
  statistically                                                                                               
  significant at                                                                                              
  p\<..05 or                                                                                                  
  better.                                                                                                     

  **SOURCE:**                                                                                                 
  National Center                                                                                             
  for Education                                                                                               
  Statistics:                                                                                                 
  NELS:88/2000                                                                                                
  Postsecondary                                                                                               
  Transcript                                                                                                  
  Files (NCES                                                                                                 
  2003-402 and                                                                                                
  Supplement).                                                                                                
  --------------- ---------------- --------- --------- ---------- ---------- ---------- ---------- ---------- ----------------

True to its position in the construction of the composite academic
curriculum intensity variable (abbreviated here as CURRQ), in fact,
Advanced Placement does not exhibit as strong a correlation with the
composite as do the mathematics, science momentum, and foreign language
components. Why? Because it is invoked as a sorting criterion in only
six of those 31 levels of academic curriculum intensity (see Appendix
F), while highest mathematics is invoked in 25 levels, foreign languages
in 18, and core laboratory science or all science in 30. Common sense
says that we will find higher correlations of these other components
with the composite curriculum variable.

But among those other components, the correlation between the highest
level of mathematics and science momentum (which includes highest math
in its definition) is so strong (0.869) as to set off collinearity
bells. The clear message is to use only one of them in any multivariate
analysis. The highest level of mathematics was dropped because the
variable represents only one curricular area, whereas SCIMOM carries
two. Likewise, following Pedhazur's (1982) rules of thumb for
identifying potential collinearity problems from correlations, table 11
advises that if we use the high school academic curriculum index, we
should not invoke either highest level of math or science momentum in
the same multivariate model.

The only other observations of the correlation matrix of table 11 worth
special attention are:

-   When bachelor's degree completion is the reference point, the
    relative correlations of the curriculum, class rank/GPA, and test
    score variables are in roughly the same relationship observed in the
    more complex construction of the composite Academic Resources
    variable: Curriculum exhibits the strongest correlation, followed by
    class rank/GPA, followed by test score.

-   However, when the referent variable is simply entering postsecondary
    education, (a) the correlation coefficients are much lower, and (b)
    the test score variable is slightly stronger than class rank/GPA.

The bottom line of these two conclusions: What counts for completion
will be more potent than what counts for mere entrance (the \"easy
part,\" in the words of Venezia, Kirst, and Antonio, 2003).

# Step 1: The First Logistics

In the commentaries and critiques of these aspects of the original *Tool
Box*, two potent questions were raised:

1\) Is a composite variable such as Academic Resources, a variable that
yokes together

> very different types of measures (a basically qualitative curriculum
> index, class rank and GPA, test score), as convincing as these
> measures taken separately in any multivariate account of degree
> completion (DesJardins, McCall, Ahlburg, and Moye 2002)?
>
> 2\) Unlike class rank/GPA and senior test score, the academic
> curriculum intensity variable is built from components, some of which
> are high profile in their own right, e.g.,
>
> Advanced Placement and highest level of mathematics reached in high
> school. If we substitute the major components for the composite in an
> account of degree completion, will they be as convincing?

In light of these questions, three distinct ways of setting up the first
step in the progression of logistic analyses that lead us to appreciate
what makes a difference (and how much of a difference) in completing a
bachelor's degree for students who attended a four-year college at any
time were explored. The first step covers both student demographics and
high school performance.

What happens to all those demographic variables in the \"demography
only\" logistic of table 3 when these three competing approaches were
tried out? With the exception of gender, race/ethnicity, and becoming a
parent by age 20, the minute the high school performance variables
enter, the demographic variables disappear. Taken individually, none of
them---first postsecondary generation status, second language dominant,
recent immigrant status, family income, number of siblings, and
urbanicity of community in which the student's high school was
located---meet the statistical criteria for either entering or staying
in the logistic models employed in this study. But two of these
variables, family income and level of parents' education, play dominant
roles in the construct of socioeconomic status, which itself more than
qualifies for the logistic treatment.

Repetition of a special note on the components of the high school
academic curriculum intensity variable is necessary in the context of
this first step in the logistic narrative. With the exception of
Klopfenstein and Thomas (2005), a spate of recent reports and
commentaries on the Advanced Placement program (e.g., College Board
2005) claim that the original *Tool Box* demonstrated the unique power
of AP course work in explaining bachelor's degree completion. To put it
gently, this is a misreading. AP is only a *component* of the academic
curriculum intensity in both the original *Tool Box* and this
replication. But to test the misreadings, AP was tried out as one of
three variables that might serve as proxies for curriculum intensity.
The other two variables tested as substitutes were a measure of momentum
in science (SCIMOM) which includes elements of HIGHMATH and Carnegie
units earned in both core laboratory science and all science courses,
and number of Carnegie units earned in foreign languages.

So, three distinct approaches to logistic regression models were tried
out for Step 1. The first, table 12, keeps the composite variable
Academic Resources, and includes nothing else. The second divided
Academic Resources into its three components. And the third dropped the
high school academic curriculum intensity variable and replaced it with
its three proxy components: science momentum, foreign language study,
and AP.

Which one of these three versions should be carried forward in the
stepwise analysis? In the first version (table 12), maintaining the
composite of Academic Resources, only Academic Resources and
socioeconomic status quintile are statistically significant (though with
a *p* value of \<0.10, SES is a barely influential presence) The Delta-p
statistic says that each step up the five-quintile ladder of Academic
Resources improves the probability of degree completion by about 15
percent. The Delta-p applied to socioeconomic status quintile says that
for each step the probability of degree completion increases by about 7
percent. Expectations do not make a difference, and the demographic
variables, while all carrying negative parameter estimates, do not meet
the criteria for statistical significance either. Message: At this
stage, and in this formulation, the composite representation of student
learning in high school, Academic Resources, is a very persuasive
construct.

The second and third versions of the Step 1 logistic can be found in
Appendix G, and both are far less convincing. In the second version,
Academic Resources was divided into its three components: curriculum,
performance (class rank/GPA), and test score. The test score component,
with a *t* statistic of 0.35 (far below the threshold requirement of
0.765), disqualifies this version from the logistic narrative. This
result also reinforces our previous observation that when both academic
curriculum participation and the quality of student effort within that
curriculum (grades) improve, test scores will automatically rise and
paradoxically become less important with reference to the dependent
variable of degree completion.

In the third version of Step 1, of the three proxy variables for high
school academic curriculum intensity, only science momentum (that
combination of highest level of math and number of Carnegie units in
core laboratory science) emerged as statistically significant. Neither
Advanced Placement nor foreign language study reached the threshold
level of significance, and, with a *t* statistic of 0.75, foreign
language study was on the borderline of disqualification in terms of
further consideration. The senior test score quintile variable did not
even meet the minimum statistical criterion for entrance. Had we taken
this version forward into subsequent stages of student history we would
have only one proxy for high school curriculum (science momentum), and
no traces of the external measurement of general learned abilities that
the senior year test

score quintile conveys. At least the composite index of high school
performance, Academic Resources, includes a trace of external
assessment.

![](media/image12.wmf)

**Summary decision: The composite variable, Academic Resources, stays in
the logistic narrative; other versions of representing high school
performance fail.**

**THIS PAGE INTENTIONALLY LEFT BLANK**

**Part IV**

**Matriculation and Beyond: The Features of Postsecondary History**

On reflection, the original *Tool Box* made a mistake in the order and
boundaries of the blocks of variables entered in its analysis. Following
high school background, and tracking students who ultimately attended a
four-year college at any time, it jumped first to financial aid, for
which the High School & Beyond/Sophomore data set contained detailed
information (including unobtrusive Pell Grant files) covering the first
four years of a student's postsecondary history. It then considered a
configuration of attendance patterns that covered everything from the
timing of entry to postsecondary education to extended aspects of
attendance such as whether the student *ever* left his or her first
institution of enrollment and *never* returned to that institution.
Thirdly, it followed this mixture of time periods with a block of
first-year performance indicators. The order and content of these three
blocks of variables scrambled time and student history.

*The Toolbox Revisited* unscrambles that sequence so that momentum can
be more clearly observed. We begin with the transition from secondary
school to postsecondary matriculation, and focus on timing of entry and
type of first institution. We then move on to first-year performance,
the importance of which is fully justified by the research literature.
Only after accounting for the first year do we confront financial aid
(which, in the NELS:88/2000 data set, covers only the first two years of
post-high school history, and is the weakest section of the study, by
far).[^26] Longer-term attendance patterns and extended performance
(curriculum and trends in grades) come later, as they should.

In shaping the universe for analysis so that a full history is visible,
one minor change to the boundaries will be exercised. The NELS:88/2000
cohort was scheduled to graduate from high school in the spring of 1992.
Not all of them did, so the upper boundary for high school graduation
will now be set at December 1996. Very few cases are affected,[^27] but,
as the NELS history ends in December 2000, the point of changing the
upper boundary is to allow enough time for late high school graduates to
build a postsecondary history.

In entering this sequence, the reader should note that the master
program generating the mass of student-level variables included on the
restricted NCES data sets of transcript-based files for both the HS&
B/So cohort and the NELS:88/2000 was basically the same, hence, there
were no

algorithmic differences that would account for change in student
behaviors such as attendance patterns and academic performance. There
are minor exceptions, and these will be noted in the narrative.

# Step 2: Matriculation

The research literature has long held that where one starts out in
higher education has enormous

consequences, particularly with reference to completing degrees (Velez
1985). The vast majority (78.7 percent; s.e. = 1.15) of the universe
under study here started out in a four-year college. Do any
characteristics of that first institution stand out in multivariate
analysis?

Only selectivity of the first institution was admitted to the Step 2
logistic model (the fact that the institution was a four-year college
was not admitted). To be sure, there are other characteristics of the
first institution of attendance. But if the dichotomous "selective"
variable turns out to have but modest, if any, significance in the
account, it is unlikely that other stock institutional
characteristics---size, control, residential/commuter ratio---will have
any influence, either. The best of the institutional characteristics
variables in the literature is probably Stoecker, Pascarella and
Wolfle's (1988) "size." This is not a simple measure, rather a factorial
scale that includes total enrollment, student/faculty ratio, and public
control. However attractive the concept, institutional size rarely
breaks through as a stand-alone factor in literature with large national
samples because of student taste---some like it large, some like it
small---and taste is too variant. All this does not mean that where one
starts out is irrelevant to completion, rather it directs our attention
to other features of student academic history. More to the point, with
64.8 percent (s.e. = 1.06) of NELS:88/2000 students who attended a
four-year college at some time attending more than one institution, and
26 percent (s.e. = 1.01) attending more than two, the task of ascribing
influence to institutional characteristics is daunting (for a discussion
of this issue, see pp. 81--84).

In addition to the selectivity variable (SELECT), Step 2 includes
NODELAY, a marker for direct entry to postsecondary education following
high school graduation. It also includes a new variable, ACCELCRD, made
possible by the construction of the NELS:88/2000 postsecondary
transcript file to reflect the practice of dual-enrollment that expanded
during the period the High School Class of 1992 was attending high
school and that has become much more visible since then. ACCELCRD sums
all college credits earned by course work prior to high school
graduation, along with credits earned by examination---including AP, the
College Level Examination Program (CLEP), and institutional challenge
exams. Most of these credits were earned either prior to matriculation
or during the first term of enrollment, though some were earned at later
points in the student's undergraduate career. A previous brief analysis
of this phenomenon (Adelman 2004a, pp. 55--56) suggested that
acceleration might have a bearing on degree completion since the
descriptive data indicated a positive relationship between the number of
\"acceleration\" credits earned and both (a) high school academic
curriculum intensity quintile and (b) selectivity of the first
institution attended.

Table 13 sets forth the relationships of the variables in play at the
postsecondary matriculation stage to bachelor's degree completion for
students who attended a four-year college at any time.

Academic Resources is still in a commanding position, and the Delta-p
statistic indicates that with each step up the quintiles of Academic
Resources the probability of completion increases by 12.8 percent.
Socioeconomic status quintile is still significant, though again,
marginally so. Of all the new variables, no delay of entry alone is
statistically significant, and its Delta-p says that students who enter
college directly from high school increase the probability of bachelor's
degree attainment by 21.2 percent, a very persuasive marker.

![](media/image13.wmf)

The selectivity of the first institution of attendance, while yielding a
positive parameter estimate, does not reach the threshold of
significance, and the *t* value for acceleration credits, at 0.73, falls
just below the threshold for retention in the overall statistical model.
The case of acceleration credits is one for which the author hoped for a
better outcome, but once a rule is set, it is observed: The variable is
dropped from subsequent steps. The demographic variables are retained,
but don't tell us much. And education expectations barely stays under
consideration with a *t* value of 0.78. Beattie's human capital analysis
(2002) downplayed education expectations as a central feature of
explaining outcomes, particularly in consideration of group differences.
It turns out that, even with a more sophisticated variable (our
"anticipations") than the customary way of marking "aspirations,"
Beattie is right.

**Step 3: First-Year Performance**

Now that we have our universe of 1992 12th-graders in college, no matter
where they started out, the most prominent initial marker of progress is
a configuration of first-year academic performance indicators---and by
\"first year\" is meant the *first calendar year* following the month in
which the student first enrolled in their \"true\" first postsecondary
institution after high school graduation.[^28]

Most research on the critical first year of postsecondary education
takes as its subjects students who start out in the fall term, and, by
custom-and-usage, measures of retention (whether term-to-term or
year-to-year) begin with fall enrollments. The transcript data, however,
teach us that not all students commence postsecondary study in the fall
term, and that there is a modest bias in drawing a universe based on
fall term beginners only. For all 1992 12th-graders who entered
postsecondary education at any time, 82.1 percent (s.e. = 0.83) started
in the fall term, 5.8 percent (s.e. = 0.46) started in the summer term,
and 12.1 percent (s.e. = 0.71) began in the winter or spring terms
(depending on local academic calendars). While the full data on first
term of entrance are presented in Appendix L, tables L8a and L8b, it is
important to note here that Latino and African-American students are
less likely than white students to commence postsecondary study in the
fall term, and the same is true when students from lower socioeconomic
status quintiles are compared with students from the highest
socioeconomic status quintile. Any measure of retention or completion
that confines its universe to students who began their postsecondary
careers in the fall term is, to put it gently, grossly incomplete.

The cumulative number of variables qualifying for the logistic narrative
increases by 50 percent when our field of vision opens out to first-year
performance. The logistic model of the original *Tool Box* included
three first-year performance variables, two of which were major
contributors to understanding degree completion, and are carried
forward: a marker for earning less than 20 credits in the first calendar
year and a tag for students whose first calendar year GPA fell in the
top 40 percent of the GPA distribution for that period. *The Toolbox
Revisited* adds dichotomous variables indicating whether the student
took any remedial courses in the first calendar year, and

whether the student earned any credits in college-level mathematics
during that period. The mathematics variable, identified as potentially
potent by Astin and Astin (1993), represents a major departure in the
way *The Toolbox Revisited* approaches its subject, for it introduces
the potential association of *postsecondary* curriculum with degree
completion (the original *Tool Box* did not raise this issue).

The first calendar year of attendance is the year in which students'
preparation for postsecondary education is most sorely tested
(Pascarella and Terenzini 1991), and in which both remediation and
college-level mathematics study serve as indicators of that preparation.
The lower division curriculum sets out course \"gateways\" through which
students must pass in both universities (Hanson 1998) and community
colleges (Boughan 2001). Every school can identify its list from high
enrollment courses[^29] and there is no question that most of these
gateways require a direct connection to the content of high school
curricula that define \"readiness.\" Remediation stalls student momentum
toward those gateways; college-level mathematics itself is a gateway.

In a different approach, American College Testing (2004) defines
"college readiness" as a remediation-free postsecondary experience, and
sets its benchmarks for "readiness" as

. . . The level of achievement \[based on ACT test scores\] for students
to have a

high probability of success (a 75 percent chance of earning a course
grade of C

or better, a 50 percent chance of earning a B or better) in such
credit-bearing

college courses as English Composition, \[College\] Algebra, and
Biology. . . (p. 1).

With all due respect to ACT, earning a C---or even a B---in college
algebra is not why most students go to school. There are better ways to
benchmark, starting with the Academic Resources index of total high
school performance in which curriculum (including highest level of
mathematics reached in secondary school) dominates and test scores do
not. Instead of a grade in a single course, we then acknowledge the
proportion of students who completed credits in *any* of five core
college-level math courses during the first year of attendance, and,
among those who became non-incidental students (i.e., earned at least an
adjusted semester's worth of credits), the proportion who *ever*
completed credits in those courses. In table 14, one notes right away
that among those who start in community colleges and complete
college-level math courses in the first year, college algebra is the
dominant math course. Among those who start in four-year colleges, it is
not the dominant math course, even though it ranks at the top in terms
of student participation.[^30]

Ironically, the ACT study helps explain why curriculum quality emerges
as more influential than test scores in building the Academic Resources
composite, and justifies continuing to track curriculum (in this case,
using mathematics momentum) across the matriculation line. The test
scores are dependent variables that respond directly to increases in the
concentration and level of study in each of the major secondary school
content areas (see, e.g., Florida Department of Education 2005). The ACT
study sees value-added in each step up the math curriculum ladder in
terms of scores on the ACT math test. So when the dependent variable is
degree completion, it is this curriculum---more than the test
score---that sets the value-added tone.

![](media/image14.wmf)

But does that mean that curriculum continues to have the same influence
in a postsecondary setting? The issue comes up twice in the sequence of
logistic models, first in table 15, which presents the results of the
Step 3 logistic: first-year performance variables. What do we see?

-   Earning less than 20 credits in the first calendar year following
    postsecondary entry is a distinct drag on degree completion. The
    Delta-p says that falling below the 20-credit threshold lessens the
    probability of completing a bachelor's degree by a *third*!

-   First-year grades, a proxy for both student effort and acclimation
    to the academic demands of a new environment (Pascarella and
    Terenzini 1991), move in the opposite direction from low credits: If
    one's first-year GPA falls in the top two quintiles, the probability
    of earning a degree increases by nearly 22 percent.

![](media/image15.wmf)

-   Academic Resources and socioeconomic status are the only other
    statistically significant variables. The Delta-p story for
    socioeconomic status quintile remains at roughly the same level:
    Each step up the SES ladder increases the probability of degree
    completion for this population by 6 percent or so. The Delta-p
    strength for Academic Resources, however, falls from 12.8 percent in
    the postsecondary entry model to 7.5 percent here, a natural
    consequence of the introduction of other competing curricular and
    grade-based variables.

-   The two new curricular variables for remediation and college-level
    mathematics produce *t* statistics that justify carrying them
    forward, but do not reach even a threshold statistical significance
    level of *p*\<0.10.

In the last observation there is a surprise that calls out for
explanation. The parameter estimate for remediation in the first year is
positive, not negative as conventional wisdom would assume. Students in
this group who took any remedial courses in the first year earned
bachelor's degrees at a 48.7 percent rate (s.e. = 2.70) compared to 69.9
percent (s.e. = 1.26) of those who did not take remedial courses in the
first year (not in table). That is a significant and meaningful
difference from which, one might assume, remediation would be a
negative. But there are other variables in this model that determine the
sign and strength of the parameter estimate and its statistical
significance. In a study of the academic careers of traditional-age
community college students, the author found that remediation (one
dichotomous variable marking any remedial reading, and one multi-level
variable based on type and number of remedial courses) did not affect
either transfer or (for students who did not transfer) completion of an
associate degree (Adelman 2005a). Other recent research, using a very
sophisticated targeting of students whose need for remediation may
differ according to the school they enter, goes beyond the finding that
remediation is not a drag on degree completion to demonstrate that, in
terms of persistence, remediation yields decidedly positive results
(Bettinger and Long 2005). Two studies do not make for a definitive
conclusion, but the evidence that students who successfully pass through
remedial course work gain momentum toward degrees is beginning to build.

As for the other variables in the Step 3 model, we note that NODELAY
drops out of the statistically significant range with an indirect
message of "once a student is in college, their performance counts more
than when they arrived." In other words, the ramifications of delayed
entry can be overcome, but only with the kind of considerable effort
reflected in first-year credit accumulation and first-year grades. The
reader will note of table 16, however, that when financial aid variables
are part of the logistic model, NODELAY rises back above the
significance threshold.

# Step 4. Adding Financial Aid to the Equation

There is a major difference between the High School & Beyond/So and
NELS:88/2000 data sets in the nature and temporal coverage of financial
aid information. For the HS&B/So, an unobtrusive Pell Grant file
provided data on at least one type of grant-in-aid. Student reports
covered four years (1982--86) of other types of grants-in-aid, loans,
and work (including, but not confined to, college work-study from all
sources) while enrolled. Three dichotomous variables resulted: GRANT,
LOAN, and STUWORK. In the original *Tool Box* study, based on the
HS&B/So data, GRANTS and STUWORK were modestly significant contributors
to the explanation of bachelor's degree completion in both the financial
aid and attendance pattern steps of the model, but fell below the
threshold of statistical significance as soon as first-year and extended
performance factors were taken into consideration.

The NELS:88/2000 financial aid information covered the period 1992--94
only, i.e., the first two years following the modal high school
graduation date for the cohort. In the initial input versions of the
data in 1994 (the third NELS follow-up survey), the information was
provided by students for each institution attended, and in answer to the
question, simply phrased, "besides your previous savings, how are you
paying for this?" The options were grants, loans, work, parents, and
other forms of aid. For students who attended more than one institution
during the 1992--94 period, it is thus possible for different
combinations of financial aid types to be attached to the

discrete attendance cases. For our purposes, if a student reported using
any one form of financial aid or support (grants, loans, work-study or
campus job) at *any* institution attended, a positive entry was recorded
for that *type* of financial aid or support for that student.

![](media/image16.wmf)

For those who ask about the importance of initial financial aid package
offerings to students' choice of where to enter the postsecondary
system, the NELS:88/2000 is of little help. The Beginning Postsecondary
Students longitudinal study of 1995/96--2001, on the other hand, has the
data elements but does not provide convincing guidance: For
traditional-age students (i.e., those who began at age 20 or younger) in
the BPS95/96--2001,7 percent (s.e. = 0.7) of those who

started at four-year colleges and had applied to more than one school
and 3.4 percent (s.e. = 1.6) of those who started at community colleges
and had applied to more than one school said the financial aid package
was the principal reason for their selection.[^31] Such percentages do
not merit further inquiry.

We come to Step 4 of the logistic model, then, with a weak collection of
dichotomous financial aid variables, and the results must be judged in
that light. As table 16 reveals, only the variable indicating whether
the student received College Work-Study funds from any source or held a
campus job was even admitted to the *Toolbox Revisited* model, and even
then, produced a *t* statistic of 0.66, below the 0.765 required for
carrying forward to the next step. Before that next step is taken,
though, this narrative needs an important pause.

**A Critical Pause for the Second Calendar Year**

The literature on postsecondary persistence, retention, and attrition
has historically taken its pauses and measures at the end of the
student's first academic year. A more constructive notion for plotting
the path of academic momentum on the far side of the postsecondary
matriculation line may be to give students two full calendar years
following the initial date of enrollment before taking their progress
pulses, yet the research on this possibility has been surprisingly
limited to date (see Smith 1995, and Nora, Barlow and Crisp 2005).[^32]
Looking backwards from the final degree completion status of our
NELS:88/2000 universe to mark cumulative change to the end of the second
calendar year following entry on key indicators provides a richer
framework for advisement.

**\"Retention\" and its paradoxes**

No national database will support the assertion that a quarter of
four-year college entrants and half of community college entrants \"do
not return for their second year\" (Kazis 2004, p. 4). Contrary to this
negative conventional wisdom, the proportion of students in the universe
for this study who \"persisted\" to the second postsecondary year is
substantial. The definition of \"persistence\" is active and
student-centered, marks a calendar academic year as July 1 through the
following June 30, and runs as follows:

> Whenever the student first enrolls and earns credits in postsecondary
> education (summer, fall, winter, spring) marks the first academic
> calendar year of their postsecondary history.
>
> If the student enrolls and earns credits at *any* time and at *any*
> institution during the next academic calendar year, that student has
> \"persisted.\"

\"Retention,\" which puts the student in a passive role vis-a-vis a
specific institution, is not the right word to describe this sequence:
It's \"persistence.\" There are two important points to underscore: (1)
This definition reveals an extremely high rate of persistence, but (2)
whether we talk about institutional "retention" or student
"persistence," the true measure is not the fact of the event, rather the
*quality* of the student's record going forward. The second academic
calendar year offers students the opportunity to recapture any lack of
momentum of the first. In that respect, the second year may be even more
important than the first.

The unhappy paradoxes of retention rates and retention quality[^33] are
revealed in table 17. The universe for the table is confined to students
with complete records. The proportion of

students who enrolled sometime, somewhere in the second academic
calendar year following

entrance to postsecondary education is about 90 percent for all
NELS:88/2000 postsecondary students and 96 percent for those with
standard high school diplomas who subsequently attended a four-year
college at some time (and in this group, just about everybody who
started in community colleges). These data ought to destroy the
mythologies of low first-to-second year retention (which, by the
formulas most commonly applied, include only students who started
full-time and in the fall semester and returned to the same school the
following fall semester). This account gives students credit for
persisting, and gives students who started in sub-baccalaureate trade
schools credit for earning a certificate in their first year and then
going on their way.[^34]

However, this account also shows that, even when one confines the
universe to the group being followed in *The Toolbox Revisited*, roughly
one out of five entered the second year with low credit momentum, and
roughly one out of six carried low first year GPAs. The overlap, too, is
considerable: 40 percent of those coming out of their first year with
fewer than 20 credits were also in the bottom quintile of first year GPA
(not in table). Low credit momentum is also due to the number of courses
taken in the first year, with 41.7 percent (s.e. = 2.46) of those who
earned less than 20 credits attempting seven or fewer courses---a proxy
for part-time status---versus 2 percent (s.e. = 0.27) of those who
emerged with 20 or more credits. The reason for counting

course attempts and not credit attempts is a by-product of the volume of
remedial courses (which do not carry additive credits). Half of the low
first-year credit group were tied up in remediation, versus 17 percent
of those who reached or exceeded the 20-credit threshold.

![](media/image17.wmf)

**Momentum at the end of the second calendar year**

First-year background certainly helps explain some of what transpires in
student histories by the end of the second year. Tables 18 and 19 offer
a skeleton of two-year performance so that future research on the
momentum hypothesis can become more sophisticated than this outing. The
information is presented in two separate tables to make sure the
messages are clear. The most overwhelming phenomenon to note in table 18
is that by the end of the second calendar year, those who never earned
their bachelor's degree were already 25 credits behind those who did
(57.4 credits earned by those who eventually received a bachelor's
degree versus 31.6 for those who did not earn the degree), and for those
who were behind, there was no difference between starting in a four-year
college and starting in a community college. One set of \"culprits\" was
attendance pattern related: lower percentage full time, lower percentage
continuously enrolled, lower percentage getting to and beyond 20 credits
in the first calendar year. All these factors decrease the probability
of completion.

Credit momentum is clearly in play. For the universe of this study, the
mean number of credits earned within two calendar years of the date of
entry was 49.5 (s.e. = 0.51). It takes a lot of work in the second
calendar year for those whose additive credit totals in the first year
were less than 20 to reach that mean, and only 3.6 percent (s.e. = 1.03)
did, compared with 77.6 percent

(s.e. = 1.02) for those who earned 20 or more credits in the first year.

But a second set of negative vectors is clearly that of academic
performance. In table 18 the spread in mean grade point average between
those who eventually earned the degree and those who did not is
substantial by the end of the second year, and it is not surprising that
nearly one in five of those who never earned any credential had already
become status dropouts (see table 19). The data remind us of a common
sense fact that few analysts or commentators ever acknowledge when
writing about student academic careers after high school: A measurable
proportion of postsecondary students will not perform well (for GPAs of
status dropouts, by timing of permanent departure from postsecondary
education, see Appendix H, table H4). Higher education has standards,
and some students will, in fact, be placed on academic probation or be
formally dismissed for academic reasons, i.e., flunk out. These
compressed signals are not as likely to be entered on official records
as graduation with honors (*cum laude*, etc.). [^35]

![](media/image18.wmf)

Table 19 serves another function in the narrative, namely, to look back
from the end of the longitudinal study in December 2000, and ask what
percentage of postsecondary students were no longer enrolled and had not
earned a credential of any kind, by timing of the gap between their
first month and last month of enrollment? These students are called
\"status dropouts\" (though they may return to postsecondary education
at a later date). While the general subject of timing and reasons for
departure is elaborated in Appendix H, table 19 looks at the eventual
dropout population only by their status end of the second year of
attendance. It says, very simply that:

\(a\) of those who never earned a credential, 23 percent became status
dropouts by the end of the second year;

\(b\) of all those who ultimately became status dropouts over an 8.5
year period, roughly a third did so by the end of the second year;

\(c\) for those who dropped out in either the first or second year, GPAs
were decidedly below thresholds required for degrees, but

\(d\) when asked why they left without a degree, less than 6 percent
cited academic reasons (also see Appendix H, table H2).

Yes, the status dropout rate proves higher during the first year than
the second, but by the end of the second year, the loss of academic
momentum is very evident.

![](media/image19.wmf)

**Curriculum gateways**

As significant in the panorama of student performance through the end of
the second calendar year are rates of participation in specific courses
identified as curricular gateways in four-year colleges by Hanson (1998)
and in community colleges by Boughan (2001). The taxonomy of
postsecondary courses used to code the transcripts for both the High
School & Beyond/ Sophomore cohort and the NELS:88/2000 data files
includes over 1100 discrete course categories[^36] of which 645 were
used to answer the following question: \"What percentage of students in
the *Toolbox Revisited* universe successfully completed credits in each
course category between the month they first entered postsecondary
education to a point two calendar years later?\" Table 20 presents the
25 academic course categories[^37] in which the highest percentage of
those who eventually earned bachelor's degrees garnered credits during
that time span, and for each course category, also presents matching
percentages for students who attended a four-year college at any time
but who did not complete a bachelor's degree.

![](media/image20.wmf)

This is a story that moves the curriculum theme forward from high
school. It is empirically-driven, which is to say that the volume of
course participation identifies the gateways for both community college
transfer students and those who started in four-year colleges in the
NELS:88/2000 cohort. Given the disparity in the number of credits
accumulated by the end of the second academic calendar year between
those who eventually earned the bachelor's degree and those who did not,
the spreads in participation rates in these 25 course categories are not
surprising. The ratios of these percentage participation rate contrasts
are 7:1 in calculus,

6:1 in American literature, 5:1 in general physics, 4:1 in general
chemistry, and more than 3:1 in precalculus, micro/macroeconomics,
introduction to philosophy, general literature surveys, statistics,
history/criticism of drama, and world civilization. These courses cover
the full range of traditional lower-division distribution requirements
(akin to pick one from bin A, two from bin C, etc.) in four-year
colleges and general studies associate degree requirements (the bulk of
the transfer curriculum) in community colleges, with the standard
non-remedial English composition and college algebra the most visible
gateways for the community college group (Boughan 2001).

The list of 25 discrete categories in table 20 invites aggregation and,
with aggregation, the inclusion of other lower division courses that
serve gateway roles. For example, there are four college-level
mathematics courses among the 25, and they certainly can be aggregated
as we have already done in our assessment of first-year performance.
General biology is not the only introductory biology course category in
the taxonomy used. Some institutions still use a zoology-botany
sequence; others open the study of life forms with cellular biology;
others, still, offer the option of human biology as a starting point.
All of these course categories are in the taxonomy, and joining them
with general biology in an aggregate allows a broader and more accurate
coverage of participation in gateways to upper division course work
requiring a grounding in the biological sciences.

Table 21 takes this alternative approach to describing the curricular
participation of students who earned bachelor's degrees and those who
did not. Table 21 uses 14 aggregate gateways, two of which are
single-course categories repeated from table 20 (general psychology and
micro/macroeconomics). While Appendix I provides a listing of all course
categories under each aggregate, a few notes are necessary in the text:

-   Humanities other than literature covers multidisciplinary
    introductions to the humanities, introduction to philosophy, ethics,
    and introduction to religious studies (usually a comparative
    religions survey). It does not include foreign languages.

-   \"Foundation business\" is included for two reasons. First, business
    fields have historically claimed the largest percentage of majors
    among traditional-age bachelor's degree completers and a substantial
    proportion of associate degrees awarded to traditional-age students
    by community colleges (Adelman 2004a, tables 5.1, p. 61 and 5.4, p.
    65). Secondly, prospective business majors appear to take at least
    one introductory gateway course in the area during their first two
    years (introduction to business, business law or business legal
    environment, and/or introductory accounting).

Table 21 displays not only the percentage of students in the bachelor's
and no-bachelor's groups who earned credits in each of the 14
aggregates, but also, for those who earned any credits in the
aggregates, the average number of credits earned. The reader will notice
first, that the use of aggregates narrows the difference in
participation rates between the two groups. For example, in the category
of standard English composition, the difference in participation rates
between those who eventually earned a bachelor's degree and those who
didn't is 82.3 percent to 53.4 percent (table 20); but when the category
becomes \"college-level writing,\" and includes technical writing,
creative writing, and advanced essay, the participation difference
narrows to 84.5 percent to 68.6 percent. That is still a significant
gap, though not as severe as others in table 21. For the record, the
credits earned in the aggregates of table 21 account for 59 percent of
all credits earned by students in this study during their first two
years of postsecondary education.

![](media/image21.wmf)

At the same time---and with few exceptions---the differences in average
credits earned in the 14 aggregates are negligible, statistically
insignificant, or meaningless---or all three of the above. In other
words, when students who did *not* earn a degree took courses in these
aggregates, they earned credits at the same rate as those who *did* earn
the degree. The problem is still that a much lower percentage of those
who did not earn degrees even pass through these gateways.

**What does this account of the second calendar year mean?**

The sequence of steps of the logistic narrative of what matters in
degree completion in *The Tool- box Revisited* moves from first-year
performance (with an apostrophe of financial aid considerations) to
longer-term vistas of attendance patterns and extended performance. It
does not make a distinct stop at the end of the second year. And yet by
the end of students' second year, a significant spread in credit
generation, academic performance, and curricular participation has
opened up between those who eventually completed bachelor's degrees and
those who did not. An event history account appropriate to the analysis
of withdrawal (e.g., DesJardins, Ahlburg, and McCall 1999) would include
a measurement at this point. So as the logistic narrative heads into
consideration of attendance patterns (Step 5), the reader might ask what
would happen if we took first year-credits and first-year GPA and
replaced those variables with *second*-year cumulative measures.

An experimental logistic was constructed in response to that
hypothetical question (see Appendix L, table L10). What happened? The
Delta-p statistic for the credits variable barely budged and the Delta-p
for GPA declined but slightly, i.e., at first glance, it doesn't make a
difference whether one uses first- or cumulative second-year measures.
At the same time, though, the strength of that cumulative second-year
credits substitute[^38] wreaked havoc on critical variables that would
otherwise be highlighted under attendance patterns, e.g., community
college transfer and four-year-to-four-year transfer. As we will note in
a moment, disentangling the consequences of different kinds of
multi-institutional attendance is more critical to the analysis of
degree completion than status at the end of the second year.

What about the gateway lower-division courses taken by the end of the
second calendar year? Are any of them key portals to degrees? Beyond
college-level writing (a requirement) and college-level mathematics,
this is not a fair question, for the answer depends on a student's major
and the requirements of the degree-granting department. Consider an
English major who took general physics, the introductory
micro/macroeconomics sequence, and introduction to design to satisfy
distribution requirements. None of these courses (which are gateways to
upper-division offerings in other fields) is a portal to completing a
degree in English, though one could argue that they provide literature
majors with analytic tools, reference points and contexts that can only

enrich their interpretive powers. In fact, it could also be argued that
the distribution courses gathered in the 14 aggregates of table 21 are
secondary in propulsive power to the second level of course work in
specific fields. For example, \"everybody\" takes general psychology,
but those who log experimental psychology and developmental psychology
are establishing a beachhead in the field, and those courses become the
real portals to the degree.

One might use the number of curricular \"gateways\" through which
students had passed by the end of their second calendar academic year as
an independent variable, but the national samples with which we work in
grade-cohort longitudinal studies would require consensus of academic
administrators as to the curricular locations and expected threshold
numbers of these gateways, and that consensus is simply not available.
In fact, given the variety of presentations of postsecondary curricula
across over 3,000 degree-granting institutions, that consensus may be
impossible. This is ultimately a matter for local configuration and
analysis (for a course cluster approach, see Zhai, Ronco, Feng, and
Feiner 2001) as well for future research that would

revisit the differential course work hypothesis in *postsecondary*
contexts that appeared in the literature a decade ago (e.g., Ratcliff et
al. 1995; Kroc, Howard, Hull, and Woodard 1997). As this pause in the
narrative of *The Toolbox Revisited* demonstrates, though, those
analyses cannot be profitably engaged on the basis of the student's
first-year work alone. The second year is just as important.

**Step 5: Postsecondary Attendance Patterns**

One of the principal contributions of *Answers in the Tool Box* was to
document, on a national scale, what college and community college
registrars, institutional research officers, and enrollment managers had
known for some time: the increasingly complex enrollment patterns of
postsecondary students (Hearn 1992; Kearney, Townsend, and Kearney
1995). This complexity has steadily accelerated since the 1970s, when
the first high school cohort tracked by the National Center for
Education Statistics attended college (for historical comparisons of
multi-institutional attendance patterns, see Appendix L, table L11). It
is not merely a case of the proportion of non-incidental[^39]
undergraduates attending more than one school increasing from 47 to 57
percent;[^40] it is more a question of *how* they attended more than one
school, and in what combinations and order (Adelman 2004a, pp. 45--50).

The most critical distinction on this dynamic landscape is between
transfer and multi-institution- al attendance. Transfer is a migration
that is formally recognized by system rules, a sequential movement from
a *de jure* status in one institution to a *de jure* status at a second
institution (or third, or fourth). Furthermore, the student's stay at
the second institution is not a short visit. So, for example, the
beginning community college student who earns 46 credits at the first
school and 5 credits at the second is a multi-institutional student not
a transfer student. In the context of

a four-year student's history, earning 102 credits at the first school
(ultimately, the degree-granting school), 21 credits at a different
four-year college and 9 credits at a community college along the way,
involves a situation in which *credits* are transferred, not the
student. But the student who begins at a community college and earns 44
credits at the community college before attending a four-year college,
then earns 55 credits from the four-year college and is still enrolled
at the four-year college at the end of our tracking period is a transfer
student.

Whether and how students attend more than one school may also depend on
student performance in the first calendar year of enrollment. Using the
five-year Beginning Postsecondary Students longitudinal study of
1989--94, McCormick (2003) demonstrated that for students who started in
four-year institutions, the higher the first-year self-reported GPA, the
more likely the student would stay put, whereas for students who started
in two-year colleges, a higher GPA was associated with transfer, hence,
with multi-institutional attendance. Do these findings hold up in a
transcript-based longitudinal study such as the NELS:88/2000? Table 22
outlines the corroboration: For four-year college students, McCormick's
observation is unconditionally

seconded; for community college students, the difference between
attending one school and two schools strongly supports the argument.

![](media/image22.wmf)

The students in the subject universe of this study were even more mobile
than the NELS:88/2000 cohort as a whole: 35.9 percent (s.e. = 1.17)
attended only one institution, compared with 46.2 percent (s.e. =1.04)
of all NELS students who earned any postsecondary credits. And our
subjects were more likely to attend *more than two* institutions than
the larger universe (25.3 percent (s.e. = 1.15) versus 20 percent (s.e.
= 0.81). This higher degree of

mobility invites us to identify the deeper structures of attendance so
that we can better sort the relationships between starting point,
performance, migration, and degree completion.

For those students who attended more than one school, table 23 lays out
some basic patterns. One should be very careful in reading them. The
universe consists of the 64 percent of 1992 12th-graders who not only
attended a four-year school at any time *but also* attended more than
one institution as undergraduates. Institutional mobility is built into
the definition. It is not surprising (in fact, it is outrightly
redundant) that reverse transfers do not earn bachelor's degrees and
that classic community college transfers who earn bachelor's degrees
receive them from an institution other than the one first entered.

Those obvious observations aside, the most intriguing students in this
configuration are what

de los Santos and Wright (1990), Borden (2004), and others have called
"swirlers." The basic definition of "swirling" follows a pattern first
observed in the High School & Beyond/ Sophomore cohort data and was
labeled "alternating sectoral enrollment." In this pattern, the student
starts in either a four-year college or a community college, and moves
back and forth between them for at least one cycle, accumulating more
than 10 credits from both sectors in the process. In the sample isolated
in table 23, 63 percent of these cycles began in four-year colleges

![](media/image23.wmf)

and 37 percent in community colleges (s. e. = 3.98; not in table).
Furthermore, 57.6 percent of the students engaged in just one cycle of
alternating enrollment while 42.4 percent rotated through two or more
alternating cycles of attendance (s.e. = 4.05; not in table). Among the
major categories of students who attended more than one school in table
23 there is a broad range of bachelor's degree completion rates (39 to
86 percent), and the "swirlers" are at the low end of that range.

What's the point? Attendance patterns, as accounted for in the history
of the High School Class of 1982 (the HS&B/So), presented paradoxes. As
a dichotomous variable in the original *Tool Box*, multi-institutional
attendance evidenced no association with bachelor's degree attainment;
classic community college transfer bore strong and positive fruit; but
the more general phenomenon of attending more than one institution and
not returning to the first institution of enrollment evidenced a strong
negative relationship to degree completion. These paradoxes are unwound
in table 24, the logistic account of the associations between the
increasingly complex postsecondary attendance patterns of the 1990s and
degree completion.

As befits the topic of attendance patterns, the variables considered and
admitted to the Step 5 logistic model are those of time and place:

Ever part-time: flagging those students who, at some time in their
undergraduate

careers, enrolled part-time in an academic term other than a

summer term;

Summer: number of credits earned during summer terms in three bands:
none, 1--4, and more than 4;

Classic transfer: community college to four-year after earning more than
10

credits from the community college;

Four-to-four: four-year college to four-year college transfer; and

Multiple schools: marking students who attended more than one
institution, whether

they formally transferred or not.

Actually, one major time-related attendance pattern variable is
purposefully left out of the equation, continuous enrollment---or
NOSTOP, as it is abbreviated. NOSTOP was one of the most powerful of the
postsecondary history variables in the original *Tool Box*. Given the
length of the grade-cohort postsecondary histories in the longitudinal
studies,[^41] a student was allowed a one-semester (or its equivalent,
and exclusive of summer terms) stop-out period and still considered
continuously enrolled. When this variable is entered into the logistic
model, its

positive value and extraordinary statistical significance do not permit
us to ascertain fully how

![](media/image24.wmf)

the other variables in the model are interacting. Its strength deflates
the associative contribution of other factors in student performance
that might better illuminate the dynamics of degree completion. Hence,
in *The Toolbox Revisited*, we set aside NOSTOP until the last possible
moment, the final Step 7.

All five attendance pattern variables introduced in table 24 break the
barriers of significance at this stage of model-building:

-   Ever part-time: Whether the student was ever part-time, a decidedly
    negative influence on degree completion. The Delta-p statistic tells
    us that part-time status reduces the probability of completion by
    over 35 percent. While previous research has documented the extent
    to which part-time enrollment pulls students off the \"persistence
    track\" (Carroll 1989), the 35 percent reduction in probability
    seems high given the fact that nearly half of the NELS:88/2000
    postsecondary students were part-time at some time. Students are
    inconsistent in their understanding of what part-time means, and
    under a more generous definition of the concept, the reduction in
    probability dropped to 30 percent---still an puzzlingly high number
    (see definition of PARTTIME in the Glossary).

-   Summer-term credits: The more, the better. That is, each step up the
    short ladder of summer-term credits increases the probability of
    completion by 14.4 percent.

-   Classic community college transfer: The significance of transfer is
    solid at *p* \< .05, and the Delta-p says that the probability of
    completion for a transfer student increases by 21 percent. At one
    point in the construction of this variable for the NELS:88/2000
    cohort, a flag was added to indicate whether the student's first
    enrollment at the four-year college occurred within four years of
    entry to the community college. This attempted refinement of a
    time-sensitive variable did not change its position in the Step 5
    logistic model. Given the fact that many students who ultimately
    transfer move back and forth between community colleges and
    four-year institutions, it is very difficult to determine the
    precise moment of transfer, i.e., the moment on the academic clock
    at which both institutions recognize a permanent change in status
    for the student. A flag for first date of attendance at the
    four-year school does not help.

-   Four-year to four-year transfer: This variable is not as strong as
    community college transfer. Its statistical significance is marginal
    at *p* \< .10. The Delta-p says that those who started in a
    four-year college and transferred to another four-year college
    increased the probability of earning a bachelor's degree by 15
    percent. Some 18.5 percent (s.e. = 0.86) of those who started in
    four-year colleges transferred to another four-year college. In
    comparing those who transferred to those who didn't, one could say
    only that the more selective the first institution attended, the
    less likely the student would transfer.[^42]

-   Multi-institutional attendance: In the steps of the logistic model
    of the original *Tool Box*[^43] in which it appeared, the parameter
    estimates for this variable were

> -0.009, 0.015, and -0.077, and with odds ratios ranging from 0.93 to
> 1.02. All these data are basically flat and inconsequential. The
> situation in *The Toolbox Revisited* is different. In light of the two
> transfer variables and the ostensive intersection of
> multi-institutional attendance with transfer, what does this variable
> say by coming out of a logistic model with a Delta-p indicating that
> attendance at more than one school reduces the probability of earning
> a bachelor's degree by about 16.5 percent? While further probing of
> the issue is advised, it appears that the message of the three
> variables (community college transfer, four-year to four-year
> transfer, and multi-institutional attendance) is that formal transfer
> is more effective than broader patterns of multi-institutional
> attendance, including simultaneous enrollment and "swirling." This
> common sense encourages institutions to track and guide apparent
> nomads toward formal transfer.

Of the other statistically significant variables in this step, even
though Academic Resources and socioeconomic status quintile are receding
in time, they are not so receding in strength, and are very much with
the explanation of degree completion. In this new configuration, no
delay of entry to postsecondary education and first-year grades are
actually stronger than they were in Step 4 in their positive parameter
estimates and Delta-p statistics. The negative consequences of earning
fewer than 20 credits in the first calendar year following initial
enrollment is also among the continuing statistically significant
variables, though with a lower parameter estimate and Delta-p statistic
than observed in tables 15 (first-year performance logistic) and 16
(financing logistic). What counts continues to count.

And what counts less but remains statistically acceptable for
presentation includes: (a) the set of basic demographic variables that
has been in the logistic narrative from the beginning,

\(b\) education expectations (which are proving far weaker for the High
School Class of 1992 than they were for the High School Class of 1982),
and (c) two curricular features of the first year of postsecondary
attendance (remedial course work and credits in college-level
mathematics) that will be reconstructed in Step 6, when we extend the
temporal scope of curricular experience to a student's entire
undergraduate career.

**Step 6: Extended Postsecondary Performance**

Both the attendance pattern variables and those covered in this step
(and the next) are distinguished from first-year performance
considerations (Step 3) by the temporal reach of the observed behaviors.
All the variables from Step 5 are carried forward. We then ask what
additional key academic measures span the full range of a student's
undergraduate history---from entrance through the first calendar year of
attendance, and beyond.

As previously noted, consideration of continuous enrollment has been set
aside for the last step in the logistic model sequence. Of other
extended performance variables, what was called the "DWI Index" in the
original *Tool Box* and is described more prosaically here as the ratio
of courses from which the student withdrew or repeated to all courses
for which the student

enrolled, also is set aside for the last step, as it is another case of
a very strong variable that would overwhelm other extended performance
measures that the reader should see play out.

The block of variables entered for the first time in Step 6 includes two
reconstructions of curriculum-related factors originally presented
within the confines of the first calendar year of attendance: type and
extent of remedial problems (replacing first-year remediation), and
cumulative credits in college-level mathematics (replacing first-year
credits). "Remedial Problem" (see page 34 and table 8 above and
description in the Glossary, p. 190) was not admitted to the model,
while cumulative mathematics credits was easily admitted.

The variable marking the *trend* in cumulative student grade point
averages at three points in time is an improvement over its predecessor
in the original *Tool Box* (which offered only two points of reference).
Event-history analysts would no doubt want to see more points than
three, but more points than three would result in the loss of more
students than the 22 percent already lost by insisting on three (due
principally to cases in which the true date of first attendance could
not be determined).

Table 25 offers a descriptive account of the three trend populations
(rising, flat, and declining) in terms of average cumulative GPAs at
each measurement point, the average elapsed under- graduate time period
(in years) that is covered by those three markers, and the proportion of
each group that earned a bachelor's degree. The purpose of presenting
table 25 is to demonstrate

that the permutations of relationships between GPAs at the three moments
of measurement work, and the results evidence *prima facie* sense.
Students with rising GPAs are more likely to earn bachelor's degrees
than those in the other two groups, and students with falling GPAs seem
more likely to spend more time as undergraduates (though the differences
here are not great). The reader will also note that for the plurality of
students, grades were flat over an average undergraduate stay of roughly
four and three-quarter calendar years.

![](media/image25.wmf)

**Changing majors: Not a rare phenomenon**

St. John et al. (2004) complained that research on persistence pays
inadequate attention to college major. Agreed. There are a number of
problems with the extant research when major is an issue, not the least
of which is the definition of "persistence" as within-year, i.e., fall
to spring, and no attention to *change*-of-major. Stoecker, Pascarella
and Wolfle (1988) paid considerable heed to major field, found some
race-by-field interactions in a structural equation model, and did so
within the context of a nine-year longitudinal study with degree
completion as the dependent variable (a better framework than that used
by others). But they faced problems of tracking change of major, moment
of decision on major, the problem of students who drop out without a
major, and the exclusion of community college transfers.

In response to these difficulties, the Step 6 extended postsecondary
performance model tried out a variable that marks change of major. This
variable was not accepted into the model, principally as a by-product of
overlapping characteristics with the community college transfer
variable, as virtually all community college transfers "change major"
from general studies to a specific field on entrance to a four-year
college (see Glossary, p. 191). But it is worth noting that 50 percent
(s.e. = 1.26) of NELS:88/2000 bachelor's degree recipients changed
majors at least once, and that this estimate comes very close to
Simpson's (1987) estimate of 48 percent for a 1976--84 cohort. The 50
percent mark thus appears to be a strong reference point.

All the elements are now in place for the stage of analysis that
examines student histories through the end of their undergraduate
careers (with the exception of continuous enrollment and the ratio of
withdrawals and repeats to all courses). The logistic for Step 6 is
presented in table 26. There are three major observations:

1)  Race/ethnicity, never statistically significant in steps 1 through
    5, does not even qualify for entry under extended postsecondary
    performance. Performance variables overwhelm demography. At this key
    inflection point in the analysis of degree completion, it appears
    race/ethnicity doesn't matter (Light and Strayer 2002), though it
    may be operating as an indirect effect through other variables. But
    to test what happens in a different way, the Step 6 logistic model
    was run defining \"minority\" separately for each of the four major
    race/ethnicity groups. This test was run at this point in the
    logistic narrative because Step 7 introduces two very powerful
    variables that would bury race /ethnicity indicators. The model
    itself emerged significant for white students, but not for
    African-American, Latino, or Asian students. For white students, all
    the significant variables in table 26 were the same except for
    four-year to four-year transfer, which dropped below the threshold
    of significance. For Latino students, the only statistically
    significant variable within a nonsignificant model (*t* = 1.37 with
    10 degrees of freedom) was whether the student had ever been
    part-time. For African-American students, the only statistically
    significant variables within a nonsignificant model (*t* =1.70 with
    13 degrees of freedom) were summer-term credits and whether the
    student had ever enrolled part-time. For Asian students, nothing was
    significant within a nonsignificant model (*t* = 0.34 with 13
    degrees of freedom).

    ![](media/image26.wmf)

> 2\) The new cumulative college-level math credits variable proves its
> worth, with a
>
> Delta-p statistic that says for every move up the credit-range the
> probability of earning a bachelor's degree increases by 11.8 percent,
> putting it in the same range of influence as summer-term credits and
> trend in grades.
>
> 3\) When trend in grades is added to the variable block, the influence
> of first-year grades increases, in part because, by definition, a
> rising GPA trend requires a lower starting point. In fact, the
> first-year GPA quintile factor is twice as strong, measured in
> Delta-p, than the trend.

We also note variables carried forward and remaining statistically
significant in the model:

-   As predicted, Academic Resources continues to lose some of its power
    as students move further away in time from high school performance.
    There are too many intervening experiences. In Step 1, the Delta-p
    said that for each rung up the quintile Academic Resources scale,
    the probability of earning a bachelor's degree increased by nearly
    15 percent (see table 12 above). At this point, that increase in
    probability is 6.6 percent. Tested separately (see Appendix J), the
    tolerance collinearity statistic for Academic Resources dipped close
    to a 0.50 mark that was set for a caution light. While still
    acceptable, the tolerance statistic indicates that, at this point in
    a stepwise logistic with 17 other variables, a Venn diagram would
    show the circle for Academic Resources overlapping (but not
    eclipsing) many of the other variables in the model.

-   Socioeconomic status quintile continues to evidence some explanatory
    power, and with a Delta-p that basically doesn't change from model
    to model. In this model, moving up each step of the SES quintile
    ladder increases the probability of earning a bachelor's degree by
    6.5 percent. SES would assume a more significant dynamic, as
    Cabrera, Burkum, and LaNasa (2005) have demonstrated with the
    HS&B/So cohort, if one entered the entire logistic narrative by SES
    quintile, and the elaboration of that dynamic will be left to future
    research.

-   The echoes of first-year credit generation are still noteworthy. The
    Delta-p says that dropping below 20 credits will decrease the
    probability of bachelor's degree attainment by 22.4 percent.

-   Whether the student was ever part-time remains a very strong
    negative, with a Delta-p unchanged from its first appearance in the
    attendance pattern model.

-   Earning credits during summer terms is still good advice, though
    each step of that variable now adds 11.2 percent to the probability
    of earning a bachelor's degree, as opposed to 14.4 percent when it
    was first introduced under attendance patterns.

-   Both the classic community college transfer variable and the
    four-year-to-four- year transfer variable stay in the model with
    positive contributions to the

> probability of degree completion of 18 percent and 15 percent
> respectively, even as the multi-institutional variable strengthens
> with a negative parameter estimate and a restraining influence of 22
> percent on the probability of degree completion. This tension
> continues to challenge analysis.

The only other variable carried forward, but losing statistical
significance is that indicating no delay of entry. No delay, which has
bounced above and below the line of statistical significance, now drops
below.

Lastly, what has not counted in previous steps of the model still does
not count: education anticipations, selectivity of first institution,
first year remediation, gender, and parenthood.

Three major themes emerge in this penultimate step of logistic analysis:

-   The combination of the strength of Academic Resources (composite
    high school performance, dominated by academic curriculum intensity)
    and cumulative college-level math credits underscores the power of
    curricular momentum on both sides of the matriculation line.

-   A group of attendance and performance factors, including part-time
    status at some point, low credit momentum coming out of the first
    calendar year of enrollment, and multi-institutional attendance
    apparently colored by \"swirling\" and not formal transfer, are
    strong restraints on academic momentum.

-   Validating the event history critique of the original *Tool Box*
    offered by DesJardins, McCall, Ahlburg, and Moye (2002), two
    measures of GPA---first-year and trend---reflecting the quality of
    student effort, are very positive contributors to degree completion.
    The stronger position of the class rank/GPA quintile variable within
    Academic Resources reinforces this message. Grades count; and yes,
    there is a competitive message here, since our GPA scales and
    quintile breaks are relative, not absolute.

# Step 7: Final Factors

The very last step in the logistic narrative takes all 17 variables from
the extended postsecondary performance model of table 26, and adds the
two strongest variables from the original *Tool Box* analysis. One of
these, a dichotomous variable for continuous enrollment called NOSTOP,
is a staple of analyses of postsecondary careers (e.g., Carroll 1989;
Astin 1993; Horn 1998; Berkner, He, and Cataldi 2002).

The second of these notable variables is not such a staple of analysis.
It is the ratio of courses from which the student withdrew *without
penalty* and those the student repeated to all courses in which the
student enrolled. This is a rare topic in the higher education
literature, and was last

seen in the major journals in Adams and Becker (1990), though the number
of course withdrawals appears on the check list of elements in analyses
of time-to-degree (Knight 2002, 2004b). The ratio counts course
attempts, not credits. Withdrawals without penalty are not the same as
courses "dropped" within set periods most colleges and community
colleges mark for "drop-and-add," and dropped courses are not included
in the ratio. As for no-credit repeats: Less than 4 percent of
respondents to the 2002 survey of grading practices conducted by the
American Association of Collegiate Registrars and Admissions Officers
indicated their institutions did *not* allow repeats; fully 55 percent
indicated that a student could repeat *any* course for a better grade;
and 55 percent indicated that students could repeat a course as often as
they liked (AACRAO 2002). These proportions suggest a very lenient
environment. Nothing here involves penalty grades. These are all cases
of noncredit grades. The variable WRPT Ratio is dichotomous: On one side
of the dividing line are students who withdrew from or repeated 20
percent or more of all courses for which they enrolled.

Table 27 presents the final step of the logistic model for *The Toolbox
Revisited*. The power of the last two variables entered is instantly
obvious:

-   Withdrawing from or repeating 20 percent or more of courses
    decreases the probability of earning a bachelor's degree by nearly
    half!!!

-   Remaining continuously enrolled increases the probability of degree
    completion by 43.4 percent.

As a consequence of the introduction of NOSTOP and the WRPT Ratio,
remediation in the first calendar year, a weakening variable from the
point of its introduction, is forced out of the model. Its attempted
replacement, the more elaborate description of type and intensity of
undergraduate remedial problems (REMPROB, described in the Glossary),
did not even qualify to enter the model. The marker for earning less
than 20 credits in the first year of attendance, previously a strong
contributor to the model, is turned on its head in the final step, and
drops below the threshold of significance. Why? Principally because, as
table 28 demonstrates, nearly 60 percent of those who wound up
withdrawing from or repeating 20 percent or more of the courses for
which they registered were *already withdrawing from and repeating 20
percent or more of their courses in the first year.* When one withdraws
without penalty, one earns zero credits. When one repeats a course, one
earns credits only once (assuming one passes, of course). What the
relationships in table 28 strongly suggest is that low credit production
in the first year is a logical consequence of withdrawal and repeat
behavior. If we allow negative momentum to start early, the consequences
will snowball. The phenomenon argues for more intense academic advising
and monitoring, more accurate placement, and (in some cases) more
sensible credit loads in the first calendar year of enrollment.

![](media/image27.wmf)

Lastly, the variable marking swirling multi-institutional attendance
continues to be negative ---though marginally significant with *p* \<.
10---in table 30 at the same time that both community college transfer
and four-year-to-four-year transfer variables fall out of significance
altogether. In this final accounting, then, all three type of
multi-institutional accounts fade in associative power in the face of
behaviors that transcend institutional effects: continuous enrollment
and academic performance reflected in grades.

![](media/image28.wmf)

# Summing Up the Logistic Narrative

Parts III and IV of *The Toolbox Revisited* have walked the reader,
sometimes painstakingly, through the consideration of independent
variables for each of the seven roughly chronological steps from high
school background to extended postsecondary performance. At the end of
each step, a logistic account of what was associated with completion of
bachelor's degrees for 1992 12th-graders who attended a four-year
college at any time was offered. The logistic account applied to
students' histories as of that particular moment only. Step 7, of
course, offered the concluding account.

But to judge the full sweep of these seven steps, we ought to see them
together in the same table.

Table 29 allows summative statements about the changing strength of
independent variables, the continuity of what counts, and required
goodness-of-fit statistics for the whole model. Let's start with the
goodness-of-fit statistics because they validate the model. The reader
can find them at the bottom of the second page of the table. Everything
that is supposed to happen in a stepwise logistic model (Cabrera 1994;
Menard 1995) happens. The G^2^ (also called the \"maximum likelihood
function\") falls with each step; G^2^/df (degrees of freedom in this
calculation is the product of the unweighted number of students in the
model minus the number of variables

in the model) also falls with each step, though perhaps too much in Step
7. The chi square statistic is a little more erratic, but rises as it is
supposed to. So do the pseudo R^2^ and the percent of concordant
probabilities predicted at each step. These results are a relief to any
analyst .

Table 29 includes all the variables that were entered at any of the
seven steps of the logistic account, even if they were not carried
forward to subsequent steps because they did not meet the

*t* statistic threshold criterion that was set at 0.765. In this manner,
we can see where these variables were introduced and where they fell out
of the model (the first \"X\" in the table marks the spot).
Race/ethnicity is the most noted example because it was present from the
beginning, and even though it was never statistically significant, it
qualified to be retained until extended postsecondary performance
variables were introduced. At that point---and again for Step 7---and
because race/ethnicity is a sensitive factor in public discourse on
education---an alternative approach was tried out whereby each of the
four major race/ethnicity groups was treated as an independent variable
in the model. Only the Asian student variable qualified for entry, but
wound up with a *t* statistic less than 0.50 on both attempts (Step 6
and Step 7).

Another \"casualty\"---though for a very different reason---is the
variable describing credits in college-level mathematics in the first
calendar year. This variable was purposefully replaced in Step 6
(extended postsecondary performance) by cumulative credits in
college-level mathematics across the student's entire undergraduate
career because it was appropriate to the temporal

framework. First-year college-level math was never significant, but its
more expansive replacement was, as might be expected from comparative
participation rates in college-level mathematics by the end of the
*second* calendar year of enrollment (table 21).

Another virtue of the presentation in table 29 is that because all
statistically significant variables are highlighted in bold, the reader
can swiftly identify what was consistently meaningful among the
potential associations with bachelor's degree completion for this group
of students. From the moment of their introduction, the following
factors met the criteria:

1.  Academic Resources quintile

2.  Socioeconomic status quintile

3.  Low (less than 20) credits in the first calendar year of attendance

4.  First calendar year GPA

5.  Summer-term credits

6.  Ever part-time

7.  Trend in GPA

8.  Cumulative \"career\" credits in college-level mathematics

And no delay of entry to postsecondary education from high school
evidenced positive and significant association with degree completion in
half the stages of the logistic narrative in which it was in play.

![](media/image29.wmf)

![](media/image30.wmf)

When one adds the withdrawal/repeat ratio and continuous enrollment
(which appear only in the last step of model-building), some rough
themes emerge. Of the ten independent variables, three involve **uses of
time** (continuous enrollment, ever part-time, summer-term credits); and
four clearly reflect different aspects of **academic performance** (high
school Academic Resources, first-year GPA, trend in grades, low-credits
in the first year, and the withdrawal/repeat ratio).

Under the temporal theme, no delay of entry floats in and out of
statistical significance. Some might say, e.g., of no delay of entry,
that the fact a variable is significant in one step of the logistic and
not in another \"does not always mean that different effects are
operating\" (Anaya 1999, p. 507). One of the reasons that this
presentation of logistic regressions provides collinearity statistics
(see Appendix J) is to reassure the reader that, for whatever reason a
variable ducks in and out of significance, it is not because it is
excessively tangled up with other variables.

# Summary of Parts III and IV: Investment Behaviors

When we look across the series of ingredients that rise to the top of
strength of association with degree completion, we can interpret them in
terms of what Noxel and Katunich (1998) called an \"investment model,\"
though this author prefers \"investment behaviors,\" a microscale
version of human capital. Once the modest consequences of socioeconomic
status are accounted for, each step offers students a set of decisions
that require the commitment of time and effort likely to yield a future
benefit. These decisions move students, sometimes smoothly and sometimes
less so, toward the degree. The choices made, beginning with high school
curriculum (from the available curriculum---which is an
opportunity-to-learn issue) and quality of effort in high school
(reflected in class rank/GPA), allow subsequent leverage. Entering a
postsecondary institution directly from high school, earning 20 or more
credits in the first calendar year of enrollment, and performing well
enough in that first calendar year to fall in the top 40 percent of a
GPA distribution build on previous investment, and are all signs of
commitment. Subsequent choices that may not be reflected in a bounded
period of time, such as excessive course withdrawals, prove to be poor
decisions with negative returns, breaking accumulated momentum. Other
configurations of choice, including summer-term credit generation,
meeting the challenge of college-level mathematics, effort that yields a
rising GPA, and most of all, remaining continuously enrolled, all
reflect continuing leverage of attainment. This is what academic
momentum is all about.

Tinto's (1987) approach is just as direct: Students have
responsibilities, and are expected to invest time on behalf of their own
learning. Yes, in his words, students have the right "to refuse
education" (p. 135), but since the primary commerce of the institution
is education, those who refuse should not be surprised if (in his very
delicate phrasing) the institution exercises its "right . . . to be
selective in its judgments as to who should be further educated" (p.
135). One begins to see why student choice (and the responsibility
inherent in student choice) emerges not only as a dominant theme of *The
Toolbox Revisited* as well, but as the principal challenge to academic
advising and counseling from secondary through postsecondary education.

One grants that a great deal more is going on in the lives of
traditional-age students at the same time. They are not bloodless. The
literature on persistence has included not only a mass of psychological
and social considerations (Harmston 2004; Hu and St. John 2001; Kahn and
Nauta 2001; Robbins et al. 2004), but also basic aspects of maturation
such as physical fitness (Zhang and Richards 1998), nutrition, roommate
conflicts, dating problems, time management (Purcell and Clark 2002),
and personality-environment congruences and dissonances (Feldman, Smart,
and Ethington 2004). Studies such as Stage's investigation of
"motivational orientation" (1989) are also valuable in that they
override stock demographic explanations and identify "subsets of college
students who might react similarly to college experiences" and, hence,
assist advisors and student service personnel. Our data sources do not
include these factors.

**What the Literature Calls "Institutional Effects"**

A major strand of the literature on postsecondary retention derives from
Tinto's (1987) constructs of academic and social integration, constructs
that contributed to the emergence of the National Survey of Student
Engagement (Kuh 2001) and its use by hundreds of institutions in
assessing the effects of environments on student behaviors. The reason
Tinto's work generated such a continuing elaboration and response is a
combination of its elegance and *prima facie* common sense. At whatever
age they start out, entering postsecondary students are not empty
vessels; they come with demographic characteristics and high school
experiences (and, if there is a gap of years between high school
graduation and postsecondary entry, work experiences and family
formation as well) that condition and shade where and how they enter the
postsecondary system. Once at an institution, these background
characteristics interact with the academic processes and social
environment of that institution to yield varying degrees of
determination to persist and complete credentials. Institutional
culture, including habits of faculty interactions with students outside
of the formal classroom and opportunities for a variety of peer group
interactions, plays a significant role in Tinto's models of academic and
social integration.

It is not surprising that the mass of studies drawing on Tinto's work
are institution-specific or use institutional characteristics as
independent variables. To attain enough depth on all these features of
student lives so that direct and indirect influences can be mapped
through path analysis requires extraordinary probing, which is best
carried out in institutional contexts where adequate samples can be
assembled. Even if we employed hierarchical linear models to illuminate
the relationships between nested characteristics of individuals within
institutions and outcomes such as GPA, we would need much larger samples
of students within each institution than the NELS:88/2000 provides.[^44]

With the student as the unit of analysis, and 25 percent of the students
in the universe we are examining attending *more than two* institutions
as undergraduates, the calculation of institutional effects becomes
problematic. For the students who attended only one four-year college,
the weighting of institutional characteristics such as those Titus
(2004) admits into his analysis of three-year persistence at the same
institution (e.g., control, size, selectivity, degree of residentiality,
and percent female, etc.) are fairly easy to plot. But for those who
attended more than one institution, a weighting scheme for the influence
of each institutional characteristic based on the proportion of
undergraduate time each student spent in different institutions would be
necessary. For a student who earned 26 credits at a community college,
30 credits at a four-year baccalaureate residential college, and 75
credits at an urban university, the ratios would dilute the very
meaning---let alone effect---of any single institutional characteristic.
This example is not a fantasy. Consider, for example, the credit
accumulation at each school attended by two sets of students from the
NELS:88/2000 who attended three institutions as undergrad- uates (fig.
2).

![](media/image31.wmf)

How does one evaluate indirect effects of institutional characteristics
and experiences (class size, contact with faculty, peer group
interactions, etc.) for these students? Does one weight each potential
effect by the percentage of credits earned at each school in relation to
all creditsearned? Can one somehow arrive at a consolidated index for
each effect across schools? How would one compare these indices to those
for students who attended only two institutions? To those for students
who attended only one? All six of the students in figure 2 above earned
bachelor's degrees. For students who did *not* earn bachelor's degrees
but who attended three institutions, what is the minimum threshold of
credits one would set at each institution attended before trying to
determine the range of institutional characteristics and student
experiences that might have some degree of association with the
dependent variable? Across all patterns of inter-institutional
\"traffic\" (Astin and Astin 1993), is there a common effects metric
that encompasses mere excursions (incidental attendance at second or
third institutions), true migration (formal transfer), and the nomadic
behavior described as \"swirling\"? The author tried to develop a
descriptive framework of excursion, migration, fragmentation, and
discovery for this task, but with less than satisfactory results
(Adelman 2004b). Certainly, there are more sophisticated models that can
address the rhetorical questions above, but they risk both neglect or
devaluation of life-changing experiences at institutions where a student
spent comparatively little time and earned few credits, and false
identification of effects that can be very fleeting.

Postsecondary student attendance patterns have rendered consolidated
institutional-effects analyses moot. For that reason, these analyses are
best carried out within the context of individual institutions (no
matter where else the student goes to school). This study does not
belittle the constructs of institutional effects and assessment efforts
such as those of the National Survey of Student Engagement (NSSE) at
all. For college and community college administrators, these assessments
count a great deal in determining the kinds of environmental adjustments
likely to intensify student involvement with institutional services as
well as to heighten student satisfaction with instruction, even if the
student is present for only 24 credits.

Even so, many of the variables of institutional effects analyses (and
that includes high schools as well as colleges and community colleges)
are sufficiently beyond the control of administrators so that the
practical implications of whatever paths one delineates as productive
are limited. Yes, high schools can change the structure of
opportunity-to-learn, e.g., by not even offering arithmetic or
watered-down pre-algebra and simultaneously conveying a clear message to
students that they can meet the challenge of higher level math (Lee,
Croninger, and Smith 1997). And the postsecondary level can follow suit,
e.g., community colleges can refuse to teach arithmetic or basic
algebra. Neither of these strategies is micromanagement, and, however
some may wish otherwise, neither is likely to be implemented on a large
scale. At the postsecondary level, the very conditions of control shift:
An administrator cannot change the fact that the institution was not the
student's first choice and that he or she is determined to transfer from
the moment of first registration; there is no drug to prescribe for a
student with severe homesickness; one cannot---and should not---prevent
the student from changing majors for the second time; no college
authority has any influence on the romantic life and angst of 20
year-olds that may affect their involvement with academic pursuits
(Okun, Taub, and Witter 1986); administrators can't sand down every
potentially hard edge of their schools. Furthermore, there is a natural
capacity limit to truly meaningful contact with faculty outside the
classroom. To use examples from the National Survey of Student
Experience, how many faculty can deans deploy for student participation
in faculty research projects or for students to work with faculty on
committees and student life programs?[^45] The larger and/or less
residential the institution, the less the opportunity for
student-faculty interaction in other than casual or ritualistic
activities (Hu and Kuh 2002).

To repeat: The NELS:88/2000 does not reach the details of student
development or institution-specific student experiences accounted for in
other research lines. The elaborate connections between student
background characteristics, social and psychological predispositions,
initial perceptions and responses to a particular postsecondary
environment, strength of goal commitments, etc. in relation to not only
the fact but also the pace of student progress toward a credential---all
of which have been explored and documented by the touchstone giants of
postsecondary student outcomes research (Astin, Pascarella and
Terenzini, Cabrera, Tinto)---lie beyond the scope of national
longitudinal studies. That is not an excuse for the \"economic\"
reading, broadly construed, of academic momentum. We all know that the
many investment decisions made by students along their paths through
postsecondary education do not occur in social and psychological
vacuums. But the archival data on which this study draws isolate moments
in which student choice intersects the structures of opportunity offered
by institutions whose first order of business---and first order reason
for existing in our society and economy---is the generation,
preservation, and distribution of knowledge. This is a story about
taking advantage of that mission; it is not a story about growing up,
although that happens along the way.

Part V

**Closing the Gap**

One of the principal objectives of the *No Child Left Behind*
legislation as it works its way through grades K--8 is to close the gaps
in achievement between minority and majority students. When that
objective is extended to high schools, as this essay underscores in Part
III above, we have no adolescent left behind. And when extended to
postsecondary schooling, as the logistic narrative has done, our
objective is to leave no young adult behind, either. While
race/ethnicity itself was not a significant variable in that narrative,
the fact of an unhappy gap remains in degree completion---which means
that there are residual echoes of experience by race/ethnicity that
affect education outcomes. It is not the intention of this monograph to
explore these echoes (there are far more sophisticated techniques and
far more knowledgeable researchers than the author to engage in that
task). But if we focus on the academic story line, we can at least draw
some parameters of possibility for assisting minority students.

Two issues attendant on this observation are now addressed: our
confidence in degree completion rates, and what it would take to close
the gap between majority and minority populations in degree completion.

**Bachelor's completion rates: Some remarkable agreements**

The most prescient and eloquent statement of the problems attendant on
our romance with graduation rates was offered a decade ago by Ronco
(1996):

Performance, even in relatively straightforward terms like graduation
and retention,

> eludes our attempts to measure it. Students no longer march lockstep
> through four years of college to graduation. The educational model of
> the new millennium will likely be

characterized more by lifelong learning, where students move among
various kinds of

higher education institutions, stopping in and out as their lifestyles
and educational needs

dictate. Enrollment patterns like these make indicators like four- or
even six-year

graduation rates for first-time, full-time freshmen largely irrelevant.
Transfer students

deprive both the sending and receiving institution of retention and
graduation credit.

(p. 1).

But accepting the object of policy affections for a moment, the most
enduring context for the analyses of *The Toolbox Revisited* involves
what its predecessor called the Dow Jones Industrial Average
accountability measure of U.S. higher education: the proportion of
entering undergraduates who earn a bachelor's degree. There are very few
truly reliable national portraits of degree completion because there are
very few data sources of convincing scope and magnitude. The task
requires a longitudinal study with a tested sampling design and matching
weights. The technology for a full census of completion does not yet
exist.

Ewell (2004) has reminded us that a *student-based* indicator of
completion leads to assessments of the benefits of higher education to
the entire society and economy. An *institution-based* indicator does
none of that, though there is no question that the institution is
responsible for contributing to the student's discovery and path to
attainment. While the student is obviously more important, institutions
are partners.

There are three recent national accounts of bachelor's degree completion
for students who started out in postsecondary education together that
can demonstrate how these two indicators, student and institutional,
play out.[^46] Each account comes from a different data set:

1.  The NELS:88/2000 that is the subject of *The Toolbox Revisited*. To
    repeat its major characteristics: The temporal term is a maximum of
    8.5 years (1992--2000) from the month of entrance, no matter when
    that happens and at what enrollment intensity (full-time or
    part-time). This is a grade cohort, with all students roughly the
    same age.

2.  A six-year longitudinal study, based on the Cooperative
    Institutional Research Project's (CIRP) data, that followed 1994
    entering college freshmen to 2000 (Astin and Oseguera 2002). While
    dominated by traditional-age students, this cohort is not wholly
    homogenous in terms of age at entrance, but is confined to those who
    started out, full-time, at 262 four-year colleges, weighted to
    represent beginning full-time freshmen at all public and
    not-for-profit private four-year colleges (for-profit four-year
    colleges are not included).

3.  Another 6-year longitudinal study, 1995/6 through 2001, conducted by
    NCES as a spin-off from the massive Congressionally-mandated
    National Postsecondary Student Aid Study. We have used this data
    set, the Beginning Postsecondary Students longitudinal study,
    previously. Beginning students of all ages and enrollment
    intensities (full-time, part-time, and mixed) are included.

Let us set these three data sets side-by-side, adjust the two NCES
databases to match both each other and the CIRP database, and then
assess how much they disagree with each other. We will confine both the
NELS:88/2000 and the BPS 95/96--2001 to those who started out in
four-year

colleges, limit the dates of entry of the NELS:88/2000 cohort to the
same year (1992) and, most importantly, put an upper bound on age at
date of entry in the Beginning Postsecondary Students of 20. Table 30
offers these comparisons.

Given the conditions under which degree completion is judged, the
conclusions of these three data sets do not differ that much from each
other. We can say that roughly a third of traditional-age students who
start in a four-year college will earn a bachelor's degree from the
*same* school in the traditional four-year period, and that between 54
and 58 percent will earn the degree from the same school in which they
began within six years of entry. When the option of earning a degree
from a *different* four-year college than the one in which these
students commenced study is included (in the NELS:88/2000 and BPS
95/96--2001), six-year degree completion rates for traditional-age
students are in the 62--67 percent range. Only when the temporal
boundaries are extended to 8.5 years in the NELS:88/2000 does degree
attainment for those who started in four-year colleges approach 70
percent, and Florida state longitudinal studies show a similar rate
(Johnson, Coles, and Thomas 2004).

![](media/image32.wmf)

**Degree Completion: How High Can It Go?**

If roughly seven out of ten traditional-age students who start in a
four-year college---and roughly two out of three who ever attend a
four-year college---graduate within eight and one-half years**,** how
likely is it that the rate will improve, by how much, and among what
groups? When looking back at the factors consistently contributing to
bachelor's degree completion in table 29 and asking which are most
subject to change by external parties with little to modest, but
creative, effort, a few stand out, and encourage speculation. All depend
on student response. In the words of Tinto's (1987) astute guidance:

Though . . . institutions owe each admitted student an equal degree of
attention, it

does not follow that institutions should be held accountable for the
equal education

of all admitted students. To absolve . . . \[students\] of at least
partial responsibility

for their own education is to make a serious error. (p. 135)

Let's look at each of the more promising levers, and then explore what
the configuration of change in behaviors and policy might suggest for
upper boundaries of degree completion and the closing of the gap in
completion among race/ethnicity groups.

> 1\) **Less than 20 credits in the first calendar year of enrollment**:
> Approximately nine percent of those who entered four-year colleges at
> any time earned between 15 and 19 credits in their first calendar
> year, with African-Americans and Latinos overrepresented.[^47] Within
> this group, only 35 percent (s.e. = 3.05) earned bachelor's degrees
> compared with 77.7 percent (s.e. = 0.99) of those who earned 20 or
> more credits. Fifteen to nineteen credits is close enough to 20 to be
> optimistic: If we know more about who students are and where they come
> from, colleges and community colleges can target dual enrollment
> efforts to yield at least six additive credits for these students,
> thus pushing them across the 20-credit line. But we do know something
> about these students, and our optimism must be tempered by the facts
> that 15.3 percent (s.e. = 2.49) of them were assigned to remedial
> reading in their first postsecondary year, an overlapping 34.5 percent
> (s.e. = 3.93) never reached Algebra 2 in high school, and only 27.9
> percent (s.e. = 2.96) earned any college-level mathematics credits in
> that first year. For the residual group (about six percent of those
> who enrolled in a four-year colleges at any time), suburban high
> school students from the Pacific and Southwest Central census
> divisions[^48] are overrepresented, and provide some geo-direction for
> dual-enrollment policy targeting.
>
> 2\) **Ratio of non-penalty withdrawals and no-credit repeat courses to
> all courses attempted**: For about 10 percent of the NELS:88/2000
> cohort who attended a four-year college at any time, this ratio was 20
> percent or higher. That is, this group of students withdrew from or
> repeated at least one out of every five courses in which they
> enrolled, behavior negatively associated with degree completion.
> Compared with white students, all minority groups are
> overrepresented.[^49](s.e. = 3.56) of Latinos. What would happen if
> institutions limited the number of no-penalty withdrawals and
> no-credit repeats students were allowed to accumulate, converting
> these cases above a given threshold to penalty grades? This is a risky
> proposition and difficult to model because we do not always know why
> students withdraw from courses after the customary drop/add periods
> (Adams and Becker 1990). Students repeat courses to earn better or
> passing grades. In the case of remedial work, the repeat is required,
> and the list of courses with the highest ratios of withdrawal and
> repeat grades is dominated by remedial offerings (Adelman 2004a, table
> 6.6, p. 84). In other cases, repeats are a luxury. Since no-penalty
> course withdrawals and no-credit repeats increase time-to-degree
> measurably for those who earn degrees (Adelman 2004a, table 6.2b, p.
> 79; Knight 2004b; Noxel and Katunich 1998), and since these behaviors
> have a rippling effect by blocking other students from seats, often in
> high demand courses, it is in institutions' self-interest to limit the
> practice. Intensified advisory care to student credit loads (Szafran
> 2001) and more precise placement criteria should help.
>
> A good example of the way this might work is provided by Eno,
> McLaughlin, Brozovsky, and Sheldon (1998), who predicted difficulty
> ratings for specific courses likely to be taken by entering freshmen
> in their institution on the basis of both overall high school GPA and,
> more importantly, grades in specific high school courses. The
> hypotheses for each student within each course were then set against
> the empirical record of students' actual performance in the college
> course at issue. The information assists students' advisors with
> indications of which courses a student might find particularly
> difficult. The likelihood of no-penalty withdrawals or no-credit
> repeat grades is attenuated by delaying students' engagement with
> those courses until they have gathered the requisite momentum
> elsewhere in the college curriculum.
>
> 3\) **Use of summer terms**: As table 31 suggests, earning more than
> four credits during summer terms may have a considerable influence on
> the degree completion rates of African-American students in
> particular. That is, 78.2 percent (s.e. = 4.12) of those who started
> in four-year colleges and exceeded this threshold earned bachelor's
> degrees, compared with 21.2 percent (s.e. = 4.59) of those who did not
> earn summer-term credits at all. The difference was also significant
> for white students, but not to the same degree. Parallel comparisons
> for Latinos and Asians were not statistically significant.

![](media/image33.wmf)

Summer-term enrollment that results in more than four additive credits
works for just about everybody (we saw that in the multivariate
analyses). While it surprisingly does not shorten time-to-degree for
those who earn degrees (see Appendix K), summer credits are associated
with higher graduation rates for everyone except Latino students. It is
thus in an institution's self-interest to encourage the use of
summer-term work, either at the institution itself or at another school.
Ways of approaching this goal shy of tuition discounting include moving
some of the offerings of high demand courses from the traditional
academic-year terms into the summer term, offering summative course work
in the major in the summer term, and recruiting students for
credit-bearing internships and cooperative education placements in the
summer terms. Academic administrators in cooperation with strategic
enrollment managers can be very creative.

> 4\) **The high school curriculum component of Academic Resources:**
> One of the more dramatic illustrations of the potential influence of
> high school performance on bachelor's degree attainment in the
> original *Tool Box* isolated four major race/ethnicity groups,
> confined each to those who entered a four-year college directly from
> on-time high school graduation, and compared two estimates: the
> bachelor's degree attainment rate for everyone versus the bachelor's
> degree attainment rate for those who were in the top 40 percent on
> each of the three component measures of Academic Resources
> (curriculum, class rank/GPA, and senior year test score). Though
> undercut by the fact that, in multivariate analyses, race/ethnicity
> does not play much of a role in bachelor's degree completion, the
> cross-tabulation of these estimates suggested that the
> criterion-referenced curriculum variable had the potential to boost
> African-American degree completion by 28 percent and Latino degree
> completion by 18 percent (though that datum was statistically shaky)
> and white students' degree completion by 10 percent. For Asian
> students of the period, test scores made more of a difference than
> either curriculum or class rank/GPA.
>
> Class rank/GPA and senior year test score are not criterion
> referenced, and while performing better in high school in terms of
> grades and tests improved degree completion in the original *Tool
> Box*, it was by lesser magnitudes. It was observed that "in a happy
> paradox, *everybody* can be in the 'highest 40 percent' on the
> \[criterion-referenced\] curriculum measure," whereas that is not true
> for test scores or class rank (Adelman 1999, p. 85). Content counts,
> particularly for minority students, and the effect of special
> preparation programs supports that conclusion (Ishitani and Snider
> 2004)
>
> Does this analysis still hold, particularly as we have already
> observed improvements in academic curriculum participation by the High
> School Class of 1992 compared with the High School Class of 1982 (see
> tables 5 and 6 above)? That depends on what else is in the mix of
> factors associated with degree completion, and unlike the original
> analysis of this feature in *Answers in the Tool Box*, the other
> factors are matters of *postsecondary* entry and *postsecondary*
> academic behavior.

How might the four factors just highlighted, along with direct entry to
higher education following high school graduation, cumulatively
influence bachelor's degree completion for the core universe of this
study, the subjects of table 29? To remind the reader just who these
students are:

-   they were 12th-graders in 1992;

-   they earned a standard high school diploma (not a GED) by
    December1996 (as the NELS transcript records conclude in December
    2000, an honest account of degree completion should allow the
    student at least four years to reach that mark);

-   they attended a four-year college at any time (20 percent started in
    community colleges, and those who started in community colleges
    earned an average of 52 credits \[s.e. = 1.58\] from community
    colleges and 59.5 credits \[s.e. = 1.92\] from four-year colleges);
    and

-   their postsecondary records were complete, i.e., no transcripts were
    missing.

Table 32 takes this group, and first sets down a base bachelor's degree
completion rate for the entire cohort by four major race-ethnicity
groups.[^50] The table then enters five key conditions influencing
degree attainment that are subject to the initiatives and control of
second parties, and marks the *potential* bachelor's degree completion
rate for students meeting the thresholds of those cumulative conditions.
As each condition is added to the cumulation, the universe narrows for
the NELS:88/2000 cohort, and as it narrows, hypothetical degree
completion rates rise. One could choose a different sequence of these
conditions, but the bottom line would be the same.

![](media/image34.wmf)

These are statistical coincidences, not causes. The subjunctive is very
strong in this presentation. The standard errors indicate that not all
these changes would be statistically significant, particularly for
minority students, but that phenomenon, too, is a consequence of a
shrinking population at each step. No delay of entry is invoked as the
first condition because it results in the least shrinkage, leaving a
larger population with which to assess the other four factors.

All five conditions of table 32 are criterion-referenced. That is,
everyone can meet those conditions; everyone can cross those thresholds.
The populations could be much larger. Does that mean that future degree
completion rates will look like those in this table if everyone meets
the criteria on all five counts? No: We know that not everybody will
make it. We have already marked and acknowledged that some students will
flunk out or become status dropouts for other reasons. But the table
suggests just where the improvements are likely to be dramatic---and for
whom. Some examples, by race/ethnicity, would be instructive.

For **Latino** students, high school academic curriculum attainment
provides the greatest leap in degree completion, narrowing the gap with
white students from 22.2 percent in the base rate to 16.4 percent. But
nothing else narrows the gap any further. Postsecondary summer-term
participation, for an obvious case, yields something of a zero, and
getting across the 20-credit line in the first year of attendance
appears to do little for Latino graduation rates. So if we are looking
carefully at this fastest growing population in the United States, we
pour our efforts into high school preparation above everything else. A
decade from now, we will be able to assess better whether postsecondary
behaviors are more impressive contributors.

For **white** and **Asian** students, moving into the top 40 percent of
the high school academic curriculum intensity index and completing high
school mathematics beyond Algebra 2 also is the strongest engine among
these variables for boosting college graduation rates. Earning more than
four summer-term credits adds something for white students, but nothing
to speak of for Asian students. The other factors may contribute minor
momentum, but once one reaches a hypothetical 90 percent completion
rate, subsequent improvements are not meaningful.

For **African-American** students, who start out at a higher bachelor's
degree completion rate than do Latinos, the high school academic
curriculum factor does not improve degree completion by a statistically
significant amount, but earning more than four credits in summer terms
offers a stunning boost, narrowing the degree completion gap with white
students from 15.5 percent to 6 percent. The momentum provided by this
high-octane persistence behavior continues through the first calendar
year credits criterion and avoidance of no-penalty withdrawals and
no-credit repeat grades until, at the bottom line of the hypothetical
rates set forth in table 32, African-American degree completion rates
are no different from those of whites and Asians.

What did African-American students in the NELS:88/2000 cohort universe
who attended a four-year college at any time study during summer terms?
A transcript-based account can be very revealing---and in this case,
positively so. Using 110 aggregate course categories, table 33 displays
the 15 categories accounting for the highest percentages of summer-term
credits earned.

![](media/image35.wmf)

This is a very respectable list for anyone. It advises advisors: Point
out to African-American students that their peers have proved (a)
summer-term credit production is a benefit, and (b) the student can
concentrate in the summer terms on the kind of critically demanding and
critical gateway courses that might not otherwise be in as intense focus
during an academic year term. The learning goes deeper under
single-subject concentration. Examples include organic chemistry,
calculus, and experimental psychology. To repeat: There are values in
summer-term credit production for everybody, but if summer-term credit
production looks like it benefits a particular group more than others,
that needs to be said. If we don't know why the impact looks more
significant for African-American students, let us submit the issue to
future research.

**Is the story for low-SES students the same?**

Reviewers of drafts of this document asked whether the same type of
analysis could be performed by socioeconomic status, since we know that
the gap in degree completion between the highest and lowest SES
quintiles is far wider than any pair of race/ethnicity comparisons
(Adelman 2004a, table 3.1, p.34). The lowest SES quintile group is
small: only 6 percent of the

![](media/image36.wmf)1.43 million 1992 12th-graders who graduated from
high school by December 1996 with a regular diploma and who attended a
four-year college at some time. These students completed bachelor's
degrees at a rate of 35.9 percent, compared with 55.4 percent for
students in the middle (3rd) SES quintile, and 79.7 percent for students
in the highest SES quintile. Perhaps the best illustration of what might
close the gap for them is to compare their hypothetical rates of
completion with students from the middle and highest quintiles, and
table 34 does so. We use the same levers as variables because they are
subject to second-party action. But we have to stop after the step where
summer-term credits are added in because (a) in extending the data
beyond the boundaries of table 34, subsequent variables in the
cumulative sequence (first-year credit threshold and withdrawal/repeat
limits) do not add anything to the degree completion rates of low-SES
students, and (b) the standard errors of the estimates have risen to the
point at which comparisons between the lowest SES quintile group and the
middle group are not statistically significant. The data of table 34,
though, send clear messages: Despite obviously great limitations
inherent in low socioeconomic status, the most promising engine of
momentum for

these students is a strengthened high school curricular background, and
achieving that objective requires greater attention to the provision of
curriculum and the quality of learning environments in schools attended
by these students, no matter where those schools are located. Even then,
the degree completion gap between the lowest and highest SES quintile
would be 32 percent.

**The bottom line on degree completion**

In reporting the proportion of college students who complete bachelor's
degrees, there seem to be as many answers as there are observers. A
number of rules are recommended:

1\. Use transcript-based data sources. They do not lie; they do not
exclude.

> 2\. Follow the student, not the institution. Community college
> transfer students are
>
> followed to determine degree completion. Do it for everybody! And if
> one insists on institutional graduation rates, give the institution
> credit for students who transfer in. We don't do that now.

3\. Do not restrict the universe to students who entered higher
education only in the

> fall term and only full-time (otherwise one excludes half of an
> entering cohort).

4\. Do not mix your 18 year-old daughter and your 34 year-old
brother-in-law in the same

> analytic of degree completion. They are on completely different life
> trajectories. In
>
> other words, institutions should consider ledgers indicating degree
> completion rates
>
> separately by age bracket at the point of entry, and national accounts
> should follow
>
> suit.

5\. The only people for whom bachelor's degree completion rates should
be calculated are

those who actually enrolled at a bachelor's degree-granting institution
at some time.

All these common sense rules, respectful of students and their families,
were observed in *The Toolbox Revisited*---and in *Answers in the Tool
Box* before it.

The elaborate multivariate analyses of Parts III and IV of this essay
provided a framework within which academic momentum toward bachelor's
degree completion (not toward something else such as first-year GPA or
second-year retention) could be tracked and judged, but without
race/ethnicity as a vector. When we extract from this framework the most
tractable variables and examine their potential repercussions in terms
of closing degree completion gaps by race/ethnicity, there is no
question that the academic intensity of secondary school curriculum
continues to serve as the engine of subsequent academic momentum, and
that the use of summer terms for substantive, highly focused
postsecondary coursework is an effective booster to that engine. Both
these variables are mixtures of the student's use of time and the
mastery of content.

But what does "academic intensity" or "an academically 'rigorous'
curriculum" really mean? What content, postsecondary as well as
secondary, could be labeled as "challenging," that is, the knowledge
toward which students eagerly reach as opposed to unenthusiastically
slog through? These questions are part of a large missing component in
this study. Part VI of this essay will reflect on that component with
the greater care it deserves.

# Part VI

**The Missing Element of This Story**

There is (at least) one major missing element of the story line in both
the original *Tool Box* and *The Toolbox Revisited*, and some important
questions readers might have asked in the course of the logistic
narrative that should be addressed. The missing element, a by-product of
the limitations of the NCES grade-cohort longitudinal studies database,
is content standards in high school curricula. Postsecondary curricula,
which are far more complex in organization, offer a different framework
for assessing potential student learning.

**Beyond Course Titles to Content Standards**

In the years following the release of *A Nation at Risk* (1983), a
standing one-liner on the lecture and conference circuit ran something
like "we've changed the marquée on the theater, but the show inside is
still the same." The marquée carried the course titles, and for better
or worse, that is what our grade-cohort longitudinal studies transcript
files rely on. As Shireman (2004) has concisely put it, \"If schools
just change the names of the courses . . .students will not have learned
anything more\" (p. 4). In building the NELS:88/2000 data files, we
discovered that in some high schools, "precalculus" on a transcript
could mean any mathematics prior to calculus, including Algebra 1. On
the postsecondary transcripts we often ran across cases of professorial
marketing with course titles such as "Tooth Brush," "Dots to Dinosaurs,"
"Time After Time," and (yes) "Good Books" that even online catalogues
could not explain. The postsecondary transcripts also carried 3-credit
courses in topics such as social event planning, daily living skills,
and \"appreciation of sports\" that, when the syllabi were examined
online, could be offered to junior high school students. One has to
acknowledge the limitations of the data source, in addition to its
virtues. But the limitations, in these cases, were serendipitous because
the online search for concrete clues to the content of course work was
dispiriting.

Over the past two decades, states have paid increasing attention to
content standards for elementary and junior high school curricula, and
the *No Child Left Behind* legislation has stimulated a period of
intense review and refinement of these standards. But as *Achieve*
pointed out in its review of state high school graduation requirements
(2004), similar detailed sets of content standards at the secondary
school level are rare. We get generalized requirements that reference
course titles such as \"11th-grade English\" or \"Applied Biology,\" and
have no idea what precise learning objectives will be pursued. There
have been exceptions, of course, with mathematics being an often
revisited subject and in ways that demonstrated the difference between
what should be expected of all high school graduates and what should be
expected of entering postsecondary students (California Education
Roundtable 1997).

The past five years in particular have witnessed the birth and expansion
of a number of large-scale efforts to get beyond Carnegie unit credit
counting to comprehensive criterion-referenced statements of what
graduating high school students should know and be able to do in order
to

\"succeed\" in postsecondary environments. By \"succeed\" is meant
completing degrees (e.g. American Association of Universities 2003;
Achieve 2004). We have also witnessed the growth of high profile
alternative approaches to secondary-postsecondary transitions such as
\"early college high schools.\" These efforts have been aided and
abetted by comparative analyses of emerging state high school exit
examinations and the content and knowledge-objectives of lower division
college courses (Conley 2003; Venezia, Kirst, and Antonio 2003). The
American Diploma Project (Achieve 2004) pushes beyond general
knowledge-objectives to include samples of college assignments (e.g.,
profit-maximizing output analyses in microeconomics, pH calculations for
a complex solution in introductory chemistry, an essay assignment on
Plato's distinction between thinking and belief in introductory
philosophy) and workplace tasks (e.g., a bank loan officer's assessment
of an application from a corporation for \$1.7 million to purchase two
corporate aircraft, a report requiring measurements of DC supply voltage
for diffusion furnaces in semiconductor manufacturing and analysis of
furnace regulator modification costs, and the determination of dosages
in an insulin therapy regimen). These are superb examples of digging
below the credit count to the stuff of learning.

Granting that the academic quality and intensity of one's high school
curriculum is a key determinant of postsecondary success, there is no
assurance that either the standards of secondary school performance,
content coverage, or challenge of the material will come close to the
threshold demands of either four-year or community colleges. For the
vast majority of high school graduates, who will not attend selective
institutions, the \"disconnect\" is considerable. Indeed, Venezia, Kirst
and Antonio (2003) urge everyone to pay more attention than that to
which the media are accustomed to the \"broad access colleges,\"
including community colleges, because the service of these institutions
to the bulk of the nation's postsecondary learners has the greatest
potential to better \"the civic and economic well-being\" of every state
and region (p. 46).

It is with that in mind that the work of the American Diploma Project
(2004) is noteworthy because the sample assignments and examination
questions selected signal precisely the kind of learning expected of the
bulk of the nation's postsecondary learners. Such assignments and
questions provide clear expectations for students entering community
college occupational programs as well as those moving into the general
education portions of postsecondary education. The microeconomics
problems come from a community college, the chemistry from a research
university.

**Previews of the future and their risks**

In fact, it could be argued that these previews of lower-division
postsecondary learning object- tives and tasks should be part and parcel
of 11th- and 12th-grade curricula, equally accessible to students
intending traditional lines to a bachelor's degree and those following
career and tech- nical education paths that *may* include the
bachelor's, but certainly involve the occupationally oriented community
college associate degrees. We can get to these levels through a modest
amount of dual-enrollment for many students, but for those for whom dual
enrollment is inaccessible, special postsecondary preview modules could
be offered either by high school

faculty with the requisite knowledge or by visiting college and
community college faculty.[^51] Somehow, students should have a taste of
what will be expected, and whether their current knowledge and skills
puts them at least on the threshold of those expectations, if not
beyond. Some may argue that such previews will scare some students away
from continuing their education or that some secondary school teachers
will resist the intrusion. One has to be optimistic in both cases, and
come to the task with the conviction that it's worth the risk. The risk
to academic momentum of not providing these opportunities is greater.

While each state bears principal authority and responsibility for
linking the curricular pathways of secondary and postsecondary sectors
(Venezia et al. 2005), the examples set forth by the American Diploma
Project and the "previews of the future" strategies described above do
not treat state borders as Maginot lines. And for good reason: Roughly
one out of four undergraduates (and one out of three African-American
students) in *The* *Toolbox Revisited* universe started their
postsecondary careers in a state other than that in which they graduated
high school. The geographic mobility of our traditional-age
postsecondary populations suggests that, at the least, multistate
regions (e.g., South Atlantic) should be considered productive
information zones for providing those concrete signals of expectations
and specific examples of quality postsecondary student work.

**Moving the messages to students, families, and school teachers**

Let's take the best of what is offered by reports such as that of the
American Diploma Project and books such as Conley's recent (2005)
*College Knowledge*, and move it out to much larger audiences than
policymakers and others who habitually read such reports and books. It
might be more helpful for each college and community college to include
in its information packages for prospective students a sample of those
examination questions and assignments in courses typically taken by
lower-division students. One might go even further and provide examples
of exemplary student responses---even less-than-exemplary student
responses---to those examination questions and assignments.

A quarter century ago, the Educational Testing Service worked on
developing an experimental examination to assess lower college division
competencies across a matrix of cognitive operations (e.g., analysis,
synthesizing) and general curricular areas (e.g., science, humanities).
Called "Academic Competences in General Education," the questions were
open-ended (not multiple-choice) and required responses that could be
composed in roughly 10 minutes. For example, one question went something
like this:

Suppose a new method for producing energy had been developed that, when
brought

on-stream, would have the effect of slowing the rotation of the Earth
from 24 to 26

hours. Before we can flip the switch on this new form of energy, an
Environmental

Impact Statement (EIS) must be filed. What would be the chapter headings
and major

sub-headings of that EIS ? You need not fill in the details, but the
most important

questions about the potential effects of a 26-hour day ought to be
included.

In a trial of the examination, faculty sorted student responses to
questions such as "Earth's Rotation" into piles of descending quality.
They then described what the students whose responses were rated most
highly did to earn that rating, turned to the second most highly rated
collection of responses and arrived at a consensus of what these
students did *not* do that the first group did---and so on down the line
of the piles of student papers they had rated until a level
euphemistically described as "nonresponsive" was reached. The faculty
descriptions were subsequently aggregated and ironed out as performance
criteria. One could then turn to incoming freshmen with this question,
along with an example of a first-rate response and an example of a
fourth-rate response (out of seven levels), show them the performance
criteria and say, "This is what you can expect to be able to do by the
middle of next year; would you be better than the fourth level now?" A
light goes on somewhere---or should---when entering students see that
what it takes to respond effectively to the \"Earth's Rotation\"
question draws on a selection of knowledge from economics and business,
psychology, international relations, world history, cultural
anthropology, physical geography, technologies, visual arts---all in
addition to the core sciences. More important, the light goes on when
students see a good example of how to put all this together in an
outline of a document that is as much a product of daily work life as it
is a college exercise.

And a similar light can go on among high school seniors as well, nearly
all of whom think they are going on to something called "college," but
have little idea what that means beyond the fact that they will no
longer be bound by school rules. Prospective students are not the only
audience for this information: Their families and high school teachers
are equal players. Not all parents will understand the assignments,
laboratories, and examination questions, but certainly they will sense,
from the examples, that postsecondary education is serious business,
that their children will not get through with a carefree study schedule,
that colleges and community colleges have standards, and that such
examples are typical of what their children will learn. Inevitably
(being optimistic about this) they will be proud enough at the prospect
to ask their children to be prepared. High school teachers reading these
assessment \"prods\" will have to reflect on the

extent to which their graduating seniors possess the academic
foundations and momentum to respond successfully. To the extent to which
high school teachers have doubts, they may adjust the form and content
of their own assignments, laboratories, and examinations. Students are
bound to be the beneficiaries of the resulting \"postsecondary practice
runs.\"

**Postsecondary dimensions of content**

At the postsecondary level, the issue of content is somewhat easier to
address, but only in the context of a student's entire undergraduate
record. We know that students completing organic chemistry enrolled in
the course not only with general chemistry as a background, but also
mathematics at at least the precalculus level. We know that students
completing a course in American economic history would have a very
difficult time without prior learning in both U.S. history writ large
and the standard introductory micro/macroeconomics sequence. A course in
the psychological and cultural components of health care in a community
college allied health program will probably not be offered to anyone
without previous course work in general psychology. The chances that a
fine arts degree candidate's transcript shows an entry for a course in
color and color theory without prior foundations and studio courses are
remote. In higher education, we can use the second- and third-level
courses in a field as rough confirmations of learning at the
introductory level. There is a sufficient lattice-work within
disciplines to track traces of content from one point on the scaffolding
to another. No, the traces inherent in second- and third-level courses
in a field are not in themselves content standards, and nuance is
expected from school to school, but there is a generalizeable quality to
these content cues. In fact, the generalizeable portions of
upper-division curricula are what one is likely to see on the Graduate
Record Examination Board's subject matter examinations. This topic
witnessed a surge of interest in the 1980s (for a paradigmatic analysis,
see Oltman 1982), and is worth renewed exploration.

**THIS PAGE LEFT INTENTIONALLY BLANK**

**Part VII**

**Concluding Messages**

Compared to its predecessor, *Answers in the Tool Box*, the
preponderance of the *Toolbox Revisited* story has been on the
postsecondary side of the matriculation line. Implicitly, it calls on
colleges, universities, and community colleges to be a great deal more
interventionary in the precollegiate world, to be more self-reflective
about the paths they offer from high school through their own
territories. It also calls on them both to fortify their institutional
research capacities and integrate them more intimately with academic
advising and course scheduling. As noted above, we are witnessing
measurable ferment on the high school side of the passage, and as the
principles of the *No Child Left Behind* legislation move beyond grade
8, we will see more. The higher education sector cannot sleep through
these changes.

**To students as agents of their own futures**

Beyond that fundamental banner of institutional fortification, there are
three sets of messages impelled by both studies. The first set is for
entering high school students who, when asked, blithely shrug that \"of
course I'm going to finish college.\"

1.  Just because you say you will continue your education after high
    school and earn a college credential doesn't make it happen. Wishing
    doesn't do it; preparation does! So . . .

2.  Take the challenging course work in high school, and don't let
    anyone scare you away from it. Funny thing about it, but you learn
    what you study, so if you take up these challenges, your test scores
    will inevitably be better (if you are worried about that). If you
    cannot find the challenge in the school's offerings, point out where
    it is available on-line, and see if you can get it that way. There
    are very respectable Web sites offering full courses in precalculus,
    introductory physics, humanities, music theory, and computer
    programming, for example.

3.  Read like crazy! Expand your language space! Language is power! You
    will have a lot less trouble in understanding math problems, biology
    textbooks, or historical documents you locate on the Web. Chances
    are you won't be wasting precious credit hours on remedial courses
    in higher education.

4.  If you don't see it now, you will see it in higher education: The
    world has gone quantitative: business (obviously), geography,
    criminal justice, history, allied health fields---a full range of
    disciplines and job tasks tells you why math requirements are not
    just some abstract school exercise. So come out of high school with
    more than Algebra 2, making sure to include math in your senior year
    course work, and when you enter higher education, put at least one
    college-level math course under your belt in the first year---no
    matter what your eventual major.

5.  When you start to think seriously about postsecondary options, log
    on to college and community college Web sites and look not so much
    for what they tell you of how wonderful life is at Old Siwash, but
    what they *show* you of the kinds of assignments and examination
    questions given in major gateway courses you will probably take. If
    you do not see these indications of what to expect, push! Ask the
    schools for it! These assignments and questions are better than SAT
    or ACT preparation manuals in terms of what you need to complete
    degrees.

6.  See if your nearest community college has a dual-enrollment
    agreement with your school system, allowing you to take significant
    general education or introductory occupational courses for credit
    while you are still in high school. Use a summer term or part of
    your senior year to take advantage, and aim to enter higher
    education with at least six credits earned this way---preferably
    more.

7.  You are ultimately responsible for success in education. You are the
    principal actor. The power is yours. Seize the day---or lose it!

Given the story lines of *The Toolbox Revisited,* it is obvious that
students are partners in their own education fate, and shouldn't wait
around for someone else to do something to them or for them.

**Public discourse, part 1: Dissonant data and their discontents**

The second set of messages is for those who engage in public discourse
on education in general, secondary-to-postsecondary transitions, and
ultimately, degree completion rates (with all stops in-between). We have
some problems here.

Foremost among these problems is the sheer volume of dissonant
statistics that are thrown around about student progress, and all the
labels of "at risk," "minimal college-qualified," and \"failure\" that
get pasted to populations in the process. The "at risk" labeling default
has gone so far as to turn students into "patients," whose "illnesses"
must be diagnosed and followed up with early intervention, intensive
intervention, and continuous intervention (Seidman 2005, p. 298) that
may even continue after graduation---and for "a modest fee" (p. 299).
The data dissonance and deficit language cloud perceptions and preclude
constructive policy. We all have considerable cleaning up to do.

On any given day, the public will be offered a half-dozen different
statistics on high school graduation rates, college-enrollment rates,
college completion rates, grades, and time-to-degree. The data will
appear in respectable academic journals in articles that were reviewed
by peers who often are experts on statistical technique and (at best)
novices on the data sources. Or they will appear in publications and on
Web sites of respectable organizations, even though they were never
reviewed by anyone outside the organization. Anything that appears
between respectable

covers is taken as authoritative, and once it moves into the mainstream
press and onto the home pages, we read the headlines but not the
footnotes. Inference runs rampant.[^52]

For any of these statistics, we never ask who is in the denominator:
that is, who are we counting, and who are we not counting---and how? As
a consequence, what often pours out are scare stories that make for good
press and bad policy. The bad data-driven scare story, in fact, has
become the preferred narrative. We are scared by stagnant high school
graduation rates over a 30 year period during which the size of the
grade cohorts declined significantly then expanded dramatically with the
baby boom echo, and during which we witnessed increased immigration from
countries with mandatory school attendance ages much lower than ours. By
an alternative view, it's amazing we have maintained a stable high
school graduation rate (the quality of high school curriculum aside).
The same alternative view could be advanced with reference to rates of
postsecondary credentialing: It's remarkable we are maintaining the same
degree-granting rates in the face of significantly higher enrollments
(unless, of course, we are awarding an excess of cheap degrees).

**Dissonance by age and season: A plea for honest tracking**

The source of many unnerving postsecondary stories is one of the most
grievous errors in analyses of student progress: including in the
denominator students who started their postsecondary careers at age 29,
36, or 47 along with the mass of students who entered the postsecondary
universe at age 18 or 19. Common sense says that a 19-year-old and a
31-year-old are on completely different life trajectories, and the
national data from the Beginning Postsecondary Students longitudinal
studies back up the common sense. When the newspaper story uses the
term, \"college students,\" most adults think of their children, not
their brother-in-law or their coworker. Community and four-year college
administrators know the difference, and provide academic programs,
scheduling and services for those different populations.

But what are they to do when the press and the news Web sites complain
that nearly half of entering students do not return for their second
year or that the graduation rate is *only* 50 percent (thus assuming
everyone else is a dropout), and they are called before legislative
committees and boards of trustees to explain? There is an enormous
difference by age at entry to the postsecondary system in these
measures, and an even greater distortion when one restricts the

definitions of what it means to \"return to\" or \"graduate from\" to
those who started in the fall term, full-time, and who came back to or
earned a degree from the same school. That denominator knocks out half
of traditional-age students from the calculation, and denies the
realities of geographic mobility that the Bureau of the Census---let
alone NCES longitudinal studies---has documented for the 20-something
population (Schachter 2004; Adelman 2005b). Policies designed to
\"retain\" students who have already moved to another state or who are

*de facto* ghosts by not being included in the retention denominator in
the first place are, at best, wastes of energy.

What is *not* a waste of energy is the task of developing more universal
and efficient student tracking systems, and recapturing the headlines
from the mongers of scare. There are those who will not accept NCES
national longitudinal studies on the grounds that they are samples (no
matter how scientific the sampling design), that we can only afford to
start one every six or 10 years, and then have to wait for people to age
and accumulate academic history by which time, the grievance goes, \"the
data are old.\" Impatient to simulate instant longitudinal cohorts, they
impute sequences of data from different sources and with denominators
that include \"projections,\" and produce shock data that cannot be
validated by any sensible reference points, e.g., that only 18 percent
of ninth-graders will earn an associate or bachelor's degree within the
subsequent ten years (National Center for Public Policy and Higher
Education 2004).[^53]

But even the best of state tracking systems and the services of the
independent National Student Clearinghouse information system that
currently (2005) covers about 2900 institutions (and cites a burgeoning
interest in including high schools in the universe), will not produce
the wealth of information that a NELS:88/2000 or a Beginning
Postsecondary Students study yield. This essay cannot recommend policy
in these matters, but it can recommend creativity and cooperation,
serious reading of the papers and reports from Florida's tracking system
(e.g., Whitfield and Howat 1999; Goodman, Latham, Copa, and Wright 2001;
Goodman, Copa, and Wright 2004; Johnson, Coles, and Thomas 2004), and
reflection followed by activistic innovation, and will wager that the
long-term results look better than the scare stories assume.

**Public discourse, part 2: The language we use**

Language does more than reflect reality---it creates reality as well.
There are considerable problems with the language used in describing
what happens to students in our education system, and our choice of
terms sets boundaries and colors of reality. The boundaries and colors,
in turn, condition the terms of policy. Let us illustrate with a few
paired terms. These are contrary rhetorics, and this study frankly
admits to taking sides in their contention. But it does so in order to
urge a positive tone that, not so by-the-way, legislators,
superintendents of schools, college presidents and other leaders would
prefer to use. The language of leadership is a "can do" language, not a
punitive rhetoric.

**"Attrition" versus "Persistence."** When "attrition" is the governing
term, we worry about students who (it appears) leave school or college,
and seek explanations for departure that have included theories of
organizational turnover (Bean 1983) and failures of academic and social
integration (Tinto 1987). At the first sign of exit---even though the
student may return---we turn to negativity. There has to be something
wrong here, we say. The student was "at risk," the institution did not
respond---we witness a cycle of blame.

When "persistence" is the governing term, we take our directions from
students. What did they do that resulted in attainment? What structures
of opportunity do we need to offer so that future students can follow
the same paths? What do we think works? Can we test it out? This is a
far more positive approach. This essay endorses it: Drop \"attrition,\"
embrace \"persistence\"!

**"Retention" versus "Persistence."** Institutions "retain"; students
"persist." If our language is governed by "retention" all we see are
institutions determined to hold on to students, keeping them in places
that may be unproductive, at all costs, and for the sake of their public
ratings. If our language follows student "persistence," on the other
hand, we see those individuals making a series of rational choices that
take advantage of the opportunities offered by institutions so as both
to discover true interests and reach productive ends. Tinto would not
object if the rhetoric of leaving an institution was turned into a saga
of discovery. Students may go elsewhere; they may take extended time off
from higher education; but ultimately they may judge the change as
positive and not a result of failure (Tinto 1987, pp. 132--33). In the
rhetoric of "retention," students are passive: Something is done to
them, and that \"something\" assumes a deficit model. Under the rhetoric
of "persistence" they are actors shaping their fate, with a model of
success in mind. Wouldn't anyone rather have success?

**"Pipelines" versus "Paths."** As Bach et al. (2000) noted---and others
have followed---there is no linear path to a degree, particularly for
students who start out in community colleges. The default "pipeline"
metaphor, used to describe presumably linear learning experiences and
environmental sequences, is wholly inadequate to describe student
behavior. Pipelines are unidirectional closed spaces, and under the
"pipeline" metaphor students are passive creatures (as in "retention")
swept along or dropping out of the space completely through leaks at the
joints. But student behavior doesn't look like that at all: It moves in
starts and stops, sideways, down one path to another and perhaps
circling back. Liquids move in pipes; people don't.

At the high school level, for example, a student can acquire momentum in
science through a combination of statistics and biology, on the one
hand, or physics and calculus, on the other. These are different paths,
but who is to say that, once in a four-year or community college, these
students could not move in very different directions? The students
entering a community college with the statistics and biology background
thinking they were heading for further study in allied health fields
could easily discover business and computer programming, and transfer to
a four-year college to pursue an academic program in management
information systems with both quantitative background and empirical
habits of mind born of study in the life sciences. The paths to degrees
offer many such intersections.

Under the "pipeline" metaphor, we look for easy (sometimes glib)
causalities along a single line of explanation. "Paths," on the other
hand, allow for multiple analyses and discoveries of tools that suggest
(but do not predict) productive routes to education goals. This essay
obviously endorses \"paths.\"

## Reiterations

Virtually all reviewers of drafts of this study recommended a concluding
reiteration of its major

themes and conclusions. Three configurations of themes and conclusions
stand out in response:

**First**, there was a story about curriculum, the content of schooling,
that was compelling in its secondary school dimensions in the original
*Tool Box*, and is even more compelling now on both secondary and
postsecondary stages. What you study, how much of it, how deeply, and
how intensely has a great deal to do with degree completion. All of this
is common sense, but requires equitable execution with emphasis on
primary tools, which in this story means that:

-   Secondary schools must provide maximum opportunity-to-learn, by
    which we mean not merely course titles, but course substance. If we
    seek better preparation for any kind of postsecondary
    education---occupational, professional or traditional arts and
    sciences---we have to ratchet up the challenge of content.

-   Postsecondary institutions have got to be active players and
    reinforcers at the secondary school level---particularly in
    partnership with schools that are not providing or inspiring
    students---with opportunity to learn at those ratcheted-up levels of
    content. Pep talks, family visits, recruitment tours, and guidance
    in filling out application and financial aid forms are not enough.

-   Indeed, the first year of postsecondary education has to begin in
    high school, if not by AP then by the growing dual enrollment
    movement or other, more structured current efforts (for examples,
    see Hughes, Karp, Fermin and Bailey 2005). If all traditional-age
    students entered college or community college with a minimum of 6
    credits of \"real stuff,\" not fluff, their adaptation in the
    critical first year will not be short-circuited by either poor
    placement or credit overload.

**Second**, this curriculum story, joined by nuances of attendance
patterns that turn out to have significant leverage, continues into
higher education. These features of the saga of degree completion are
rarely attended to.

-   It's not merely getting beyond Algebra 2 in high school any more:
    The world demands advanced quantitative literacy, and no matter what
    a student's postsecondary field of study---from
    occupationally-oriented programs through traditional liberal arts---
    more than a ceremonial visit to college-level mathematics is called
    for.

-   Academic advisors and counselors have to target every first-time
    student for at least 20 additive credits by the end of the first
    calendar year of enrollment. We saw the same consequences in the
    original *Tool Box*, though now we understand better that the
    chances of making up for anything less than 20 credits diminish
    rapidly in the second year. Community colleges have some special
    challenges here, given increasing rates of transfer among
    traditional-age students. With 6 credits of dual-enrollment course
    work, even part-time students can reach 20 credits in the first
    calendar year, and community colleges enroll the bulk of
    traditional-age part-time students.

-   Excessive no-penalty withdrawals and no-credit repeats do
    irreparable damage to the chances of completing degrees. This
    phenomenon was also observed in the original *Tool Box*. Twice
    advised, institutions might think very seriously about tightening
    up, with bonuses of increased access and lower time-to-degree.

-   More than incidental use of summer terms has proven to be a
    degree-completion lever with convincing fulcrum. It's part of the
    calendar-year frame in which students are increasingly
    participating. Four-year and community colleges can entice students
    into fuller use of summer terms with creative scheduling.

**Third**, in contract to their treatment in the mass of literature on
academic progress, students are explicit, rather than implicit, in *The
Toolbox* Revisited. They are respected adults playing larger roles in
their own destinies in *The Toolbox Revisited*. What we call "variables"
are not bloodless abstractions: they are signs of what students do; and
our messages are about where and when the green lights and caution
lights will flash along the paths toward degrees. While we trust that
school and college actions will not leave them behind, they have equal
responsibilities.

**Legacy**

These are limited beginnings of change in the terms of the enterprise
with which any reader of this document is concerned. They are honest
terms and do not pretend to predict, rather help us draw a background
tapestry against which we can judge just how well we are doing for our
children as they cross the cusp of adulthood. The terms derive from the
story; the story derives from the wisdom of the U.S. Department of
Education in establishing and maintaining its longitudinal studies; and
our subsequent discussions and enlightenment derive from the leadership
of the National Center for Education Statistics in executing those
studies and providing us with archives of information that are the envy
of other nations. All of this constitutes an unmatchable legacy.

**THIS PAGE INTENTIONALLY LEFT BLANK**

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# APPENDIX A

**Changes in Demography, Geo-Demography, and Postsecondary**

**Entry From the High School & Beyond/Sophomores to the NELS:88/2000**

![](media/image37.wmf)

![](media/image38.wmf)

## APPENDIX B

# Principal Features of the NCES Grade-cohort Longitudinal Studies 

There are four grade-cohort longitudinal studies designed and conducted
by the National Center for Education Statistics. Three of these have
been completed:

-   National Longitudinal Study of the High School Class of 1972
    (NLS-72),

> started with a cohort of seniors in the spring of 1972, concluded in
> 1986;

-   High School and Beyond, with a cohort of seniors in 1980, concluded
    in 1986,

> and another cohort of sophomores in 1980 (HS&B), concluded in 1993;
>
> and

-   National Education Longitudinal Study of 1988, initiated with an
    eighth-grade class in 1988 (NELS:88), concluded in 2000.

The data from these studies are available in both public release and
restricted (license required) form on CD-ROM, with electronic code books
(ECBs) listing all variables, with descriptions and distributions.

The fourth, the Education Longitudinal Study of 2002 (ELS:2002),
starting with a sample of 20,000 10th-grade students in the spring of
2002, is in progress.

Curtin, Ingels, Wu, and Heuer (2002) offer a figure with a temporal
presentation of the four longitudinal studies,[^54] highlighting their
component and comparison points. Each of the studies begins with a
national probability sample involving a stratified sample of schools and
a random sample of students within the target grade in those schools.
Schools in minority communities are over-sampled. In some cases, the
samples are refreshed at later points in the longitudinal study (NELS:88
in 1990 and 1992)[^55] and, in some cases, augmented at a later point
(NLS-72 in 1973).

Each of these longitudinal studies includes a great deal more
information than what is used in *The Toolbox Revisited.* Not all of
them are comparable in terms of the depth with which various

topics are explored. The surveys of the NLS-72 were focused wholly on
students, whereas those of the subsequent longitudinal studies included
parents, teachers, and secondary school administrators. The cognitive
tests administered in the 12th grade to the NLS-72 cohort were
administered in the 10th and 12th grades to subsequent cohorts, thus
enabling measures of intellectual growth. High school course-taking for
the NLS-72 was summarized and reported by the school, whereas for the
HS&B/Sophomore cohort and NELS:88/2000 high school course-taking was
derived directly from transcripts. And the postsecondary transcripts for
the NELS:88/2000 were used to fill in missing information from the high
school transcripts in that cohort. Labor market histories were far more
detailed in the NLS-72 and HS&B/Sophomore cohort than they were for the
NELS:88/2000. Military records exist for the NLS-72 but not for any
subsequent study. Student financial aid information included an
unobtrusive Pell Grant file for the HS&B/Sophomore cohort, and that for
the NELS:88/2000 included data from the National Student Loan Data
System (though this file requires more cleaning and reconstruction in
order to be truly helpful).[^56]

Lastly, the shift from paper-and-pencil survey response forms to
computer-assisted telephone interviews (CATI) in the1990s constricted
the range of questions asked (e.g., there was no time to ask students
about reasons for changing majors, reasons for transferring from one
college to another, and degrees of satisfaction with different aspects
of postsecondary experience), whereas the NLS-72 paper survey forms
covered these topics in some depth.

Nonetheless, the archives of these data sets are the richest we have to
explore the nature of secondary and postsecondary education and its
consequences in the early adult life histories of

Americans over the past 30 years.

# APPENDIX C

**Differences Between the High School & Beyond/Sophomore Cohort and**

**NELS:88/2000 High School Record Variables, and Limited Imputation**

**Procedures for the NELS:88/2000**

The principal portions of the data sets in question are secondary school
transcripts and allied information derived from survey questionnaires
and computer assisted telephone interviews (CATI). The secondary school
transcripts were collected and coded by the same contractor for both
data sets, but the returns were very different. The High School &
Beyond/Sophomore cohort began with a stratified national sample of
secondary schools, all of which agreed to participate in the project and
provide transcripts, access to teachers and administrators. The
NELS:88/2000 began with a national stratified sample of schools with
eighth grades, all of which agreed to participate in the project and
provide appropriate information. As noted above in Appendix B, when
students moved into high schools, the NELS sample was refreshed in10th
and 12th grades to reflect the total enrolled population in those years
(Ingels et al. 1998), and, by necessity, the refreshing was based in the
high schools in which the vast majority of the existing NELS cohort
students were enrolled. The analysis file created for this study
includes the12th grade refreshed sample, but some of the high schools
that were not part of the original stratified sample did not provide
transcripts.

At the postsecondary level, on the other hand, the transcript return
rate increased from 89 percent for the HS&B/So to 93 percent for the
NELS:88/2000 (Curtin, Ingels, Wu, and Heuer 2002), and the proportion of
postsecondary participants with complete records increased from 88 to 97
percent.

**Editorial processes**

The postsecondary transcript-based versions of both data sets were
edited by the same person (the author of this study), and with the same
rules, a feature that increases reliability at the price of intra-coder
bias. If one thinks of two sets of archival documents: secondary and
postsecondary transcripts for two cohorts, i.e., four data files, in
only one did the editor actually see the paper documents submitted by
institutions, namely, the postsecondary transcript files of the NELS.
These artifacts contained information that allowed corrections and
fill-ins for missing information on the secondary school transcript
files, e.g., state location of high school, high school graduation date,
high school diploma type, Advanced Placement course credits (by
examination), and SAT and ACT test scores. Hence, the presentation of
secondary school transcripts on the restricted file with the
postsecondary transcript data (NCES CD#2003-402) is more accurate than
it is on earlier NELS restricted files. After a year of use, a
supplement to NCES 2003-402 was issued in June 2004, containing further
refinement of both high school and college transcript-derived variables,
in addition to new derived variables.

**Missing data and limited imputation**

The analysis files for both this study and *Answers in the Tool Box*
used high school transcripts with complete records for at least grades
10--12. But the NELS:88/2000 transcript data, as well as test score
data, fell short of the HS&Beyond/So coverage, even after preparation of
the 2004 Supplement to the original NELS Postsecondary Files that
included the second round of corrections and fill-ins of missing
information on the high school transcripts.

![](media/image39.wmf)

Class rank/GPA, the combined high school class rank/grade point average
quintile, is the major problem in the comparison displayed in table C1.
In both data sets this variable (called \"CLSSRNKQ\" for programming
purposes) was constructed in the same way, but the input data initially
yielded a far smaller universe for the NELS than was the case for the
HS&B/So.

The construction of this variable begins with class rank, expressed as a
percentile, for students whose high school graduating classes are
greater than 10. Class rank was chosen for the base reference because it
overrides variability in local grading practices. Not all high schools
compute class rank, so for a significant percentage of students, this
datum is missing. For these missing cases (as well as for the students
from very small high schools), the variable construction turns to high
school grade point average (where available, and only for students with
three years or more of course work in all high schools attended). In
both data sets, all known cases of high school GPA were weighted and set
out in quintiles. The missing cases of class rank, by quintile, were
then substituted by the GPA quintile (the correlation between the two
quintile scales was .84).

However, there are two significant differences in data input between the
HS&B/So and the NELS:88/2000. First, the HS&B/So grade point average was
for academic courses only, where- as in the NELS, the GPA applied to all
courses. Second, by the time of the NELS histories, some high schools
evidently were indicating neither class rank nor cumulative GPA of any
kind on transcripts (either that or the original data entry for the NELS
high school transcripts did not

compute GPA). While 13 percent of the HS&B/So students were missing the
combined CLSRANKQ variable, half again of that proportion (20 percent)
of the NELS students lacked a CLSSRNKQ value (see Glossary for further
details and citations).

This difference would have serious consequences in the replication of
the original *Tool Box* hypotheses. The universe of NELS students with
positive CLSSRNKQ values was initially smaller than those for the
curriculum variable (HSCURRQ) and senior year test score (SRTSQUIN).
Since the multivariate analyses of both *Tool Box* studies depend on
positive values for all three variables, the composite variable built
from a partition of the three would overestimate the value of CLSSRNKQ
at the expense of the other two components. In preparing the analysis
file for this study, plausible values for missing cases of CLSSRNKQ were
imputed when values for both curriculum quintile (HSCURRQ) and test
score quintile (SRTSQUIN) were positive and equal, e.g., both were in
the third quintile. In these cases, CLSSRNKQ was assigned the same value
as the other two variables. The impact of this imputation strategy
lowered the unweighted missing cases of CLSSRNKQ from 20 to 17 percent,
and the unweighted cases of NELS:88/2000 students missing one or more of
the high school performance variables from 24 to 21 percent (see table
C1).

**Bias and potential imputation**.

Even after this revision, a problem remained, and a multiple imputation
procedure was followed (Herzog and Rubin 1983). In the original edited
version of the NELS high school transcript data that appears on NCES
data CD 2003-402 (March 2003), and modified by its June 2004 supplement,
some 17.3 percent of the students were missing CLSSRNKQ, 13.8 percent
were missing HSCURRQ, and 13.5 percent were missing SRTSQUIN. Under NCES
statistical standards, CLSSRNKQ would have to be evaluated, since the
proportion of students with non-missing values was less than 85
percent.[^57]

The formula used to determine the nonresponse (i.e., missing) bias in
these three variables was:

A\*(b-c) where A is the percent of students missing data, b is the
percent of those

missing data who did NOT earn a bachelor's degree, and c is the percent
of those

not missing data who did not earn a bachelor's degree.

To obtain the relative bias with respect to the estimate, the result of
this formula is divided by b.

The initial nonresponse bias rates for the three variables were:

[Bias]{.underline} [Relative bias]{.underline}

HSCURRQ 0.015 0.021

CLSSRNKQ 0.034 0.049

###  SRTSQUIN 0.039 0.048

In other words, for example, if the estimate for the curriculum variable
was based only on those with positive values, it would overestimate the
percent who did not earn bachelor's degrees by 2 percent. These are all
small biases, and would not threaten tests of statistical significance.
But the missing cases were less than random. Students who never entered
postsecondary education by age 26 or 27 were overrepresented in the
missing cases of each variable. This is not surprising, since those who
never graduated from high school or who were still enrolled in high
school in the year of their scheduled graduation (1992) would not show
complete transcript records in1992.

In order to increase the number of students with positive and plausible
values for all three components of the Academic Resources variable,
another limited imputation was undertaken, focused on class rank/GPA.
The first question identified, of all students who were in the 12th
grade in 1992 and for whom the file showed positive values for both the
curriculum (HSCURRQ) and test score (SRTSQUIN) variables:

1\) those who also showed a positive quintile value for class rank/GPA

(CLSSRNKQ), and were in the *same quintile* on all three measures. 16.6%

2\) those who were in the same quintile on both curriculum and test
score

measures, also had a positive quintile value for class rank/GPA, but the
rank of this

quintile differed from the others by [+]{.underline} 1. 13.4

3\) those who were in the same quintile on both curriculum and test
score

measures, but were missing class rank/GPA. 2.7

4\) those who were missing class rank/GPA, and whose quintile positions

on curriculum and test score measures differed by 1. 2.5

5\) those who were in the same quintile on both curriculum and test
score

measures, also had a positive quintile value for class rank/GPA, but the
rank of this

quintile differed from the others by \> 1. 5.8

6\) those who were not in the same quintile on both curriculum and test
score

measures, whether or not class rank/GPA was missing. 59.0

The focus of imputation was on those members of groups 3 and 4 whose
high school transcripts showed 12 or more academic Carnegie units. This
small group was then examined for *prima* *facie* anomalies in variables
such as postsecondary attendance, selectivity of first institution of
attendance (if any), and postsecondary remedial work. There were none.
An algorithm was then developed that assigned a value to CLSSRNKQ, as
follows: (1) where HSCURREV = SRTSQUIN, the class rank/GPA quintile was
assigned the same value; (2) where

the difference between HSCURREV and SRTSQUIN was [+]{.underline}1,
CLSSRNKQ was assigned the lower value in half the cases, and the higher
value in the other half.

The result reduced the proportion of missing ("nonresponse") cases of
CLSSRNKQ from 17.3 to 15.8 percent. The nonresponse bias rates improved
as follows:

[Before imputation]{.underline} [After imputation]{.underline}

Bias rate 0.034 0.019

Relative bias 0.049 0.026

**The consequent reconstruction of Academic Resources**

The proportion of students with non-missing values for all three
components of the Academic Resources index rose from 70 to 72 percent as
a result of the imputation described in above. However small the
increase, it requires a recalculation of the comparative weights of the
three components of Academic Resources, in the following steps:

a\) A logistic regression is run with bachelor's degree attainment as
the dependent variable, the three components as independent variables,
and a universe limited to1992 12th-graders. The ratios of the
standardized beta coefficients for each of the independent variables
produce the weights for each variable in the composite. The changes
between the earlier version of these weightings and the post-imputation
version are small, but required, as table C2 shows.

![](media/image40.wmf)

b\) Each of the three components is then multiplied by its weight
brought forward from the logistic model. So, for example, a student in
the third quintile of HSCURRQ is credited with 1.272 points (3\*0.424).
The points are added, then weighted by the enhanced NELS high school
transcript weight for those in the 12th grade in 1992 (F4F2HWT), then
set out in quintiles of Academic Resources. The difference in
distributions of the values of Academic Resources, before and after
imputation, are indicated in table C3.

![](media/image41.wmf)

**THIS PAGE INTENTIONALLY LEFT BLANK**

# APPENDIX D

**Technical Issues**

**Accuracy of estimates and standard errors**

There are different kinds of statistics in *The Toolbox Revisited*, and
all of them are estimates derived from student samples. Two kinds of
error occur when samples are at issue: errors in sampling itself,
particularly when relatively small subpopulations (for example, American
Indians) are involved; and nonsampling errors. Even in surveys as large
as the three grade-cohort longitudinal studies used in this monograph,
sampling errors can affect estimates of statistical significance.

Non-sampling errors are more serious. A good example of a non-sampling
error would be the fact that transcripts are missing for some students
in all three grade-cohort studies. The transcripts are missing either
because the student did not tell the interviewer that he or she attended
the school (and there were no transfer credits on another transcript to
identify the school); the school refused to send the transcript; the
school could not find the transcript; the information sent by the school
was not really a transcript; or while the student may have enrolled at
the school he or she never registered for courses and did not generate a
record. In this case, we can mitigate the effect of missing transcripts
by differential weighting of the population, and, indeed, for both the
High School and Beyond/Sophomore and NELS:88/2000 files, the analyst is
given a choice of weights, one of which is confined to students with
complete records (see the discussion of weights and flags below).
Weighting, though, will not address the panoply of nonsampling errors.

The effects of sampling and non-sampling errors ripple through
databases. To judge the accuracy of any analysis, one needs to explicate
and judge these effects. When the unit of analysis is the student, this
is a straightforward issue because the original samples in the
longitudinal studies consisted of students. For example, when questions
are asked about the proportion of students who earned credits in an
aggregate category of courses (e.g., table 21), the questions are about
nonrepetitive behaviors of the students who were sampled. The
descriptive comparisons in *The Toolbox Revisited* dealing with
non-repetitive student behaviors require invocation of the Students'*t*
statistic to determine whether the difference between two independent
estimates is significant. The formula for computing Students' *t* values
is:

(P~1~ - P~2~)

*t* = (se~1~^2^ + se~2~^2^)

where P~1~ and P~2~ are the estimates to be compared and se~1~ and se~2~
are the corresponding standard errors. In this case, if *t*
[\>]{.underline}1.96, one has a statistically significant difference at
p \<.05, a standard marker. For the judgments of statistical
significance in all cross-tabulations in this document, an Excel
template developed by MPR Associates for the production of reports to
the National Center for Education Statistics, was used.

The formula becomes more complex, however, for multiple comparisons
among categories of an independent variable such as race/ethnicity. For
multiple comparisons, the critical value for *t* rises depending on the
number of comparisons that can be made in the family of the independent
variable. For race/ethnicity presented in five categories, there are10
possible comparisons, so the significance level of each test must be *p*
[\<]{.underline} .05/10 or *p* [\<]{.underline} .005. To determine the
significance level of *t* values in any comparison of means or
proportions, the result should be matched against standard published
tables of significance levels for two-tailed hypothesis testing.

When estimates are not independent, a covariance term must be added to
the Students' *t* formula

[(P~1~ - P~2~)]{.underline}\_\_\_\_\_\_\_

*t* = (se~1~^2^ + se~2~^2^) -2(r)se~1~se~2~

where *r* is the correlation between the two estimates. The
determination of correlations requires a statistical software package,
such as SAS or SPSS, and the invocation of proper weights for the
comparison.

Because none of the longitudinal studies invoked in *The Toolbox
Revisited* was based on a simple random sample of students, the
technique for estimating sampling error involves a more complex approach
known as the Taylor series method. To produce Taylor series standard
errors, the estimates presented used AM, a program developed by Jon
Cohen and associates at the American Institutes for Research under
contract to the National Center for Education Statistics.

#### Flags and weights

Each of the grade-cohort studies used in this monograph carries a
complex set of flags and weights to mark the populations for which
estimates are to be generated. The selection of these flags and weights
is very important for both the accuracy and meaningfulness of estimates.

For the postsecondary transcript sample of the High School and
Beyond/Sophomore cohort (HS&B/So), the process was somewhat complex.
Using the weights for the first follow-up survey (1982, the scheduled
12th-grade year for this cohort), three postsecondary transcript weights
were developed. The first was based on a ratio of the sum of weights for
all students in the 1982 panel who subsequently (in surveys of 1984,
1986 or 1992) claimed to have attended a postsecondary institution to
the sum of weights for those for whom a transcript validating the claim
was subsequently received. The ratio was then modified by factors
derived from the stratification cells in the 1982 survey design to
create multipliers that were applied to the raw weights for the students
for whom transcripts were received or for whom postsecondary attendance
was imputed from survey storylines. This is a generous formulation for
all likely postsecondary participants.

The second High School and Beyond/Sophomore weight involved the same
procedure as the first but a more restrictive ratio applied to those
students for whom a true postsecondary transcript was received. These
students are more than "likely" participants; they are "known
participants." The third weight followed the same procedure as the
second, but confined the population to only those students with complete
postsecondary records (i.e., no missing transcripts). This weight is
used in analyses of credit production and grades, since complete records
are necessary for the analysis of both these features of student
academic history. These weights are labeled PSEWT1, PSEWT2, and PSEWT3,
respectively.

To accompany these weights for the comparisons that hold the population
to students who were in the 12th grade in 1982, a special flag,
SENRFLAG, was constructed from variables in the HS&B/So that described
student status in 1982. Using the given flag for participation in the
1982 cohort sample would be insufficient and not wholly accurate because
not all students were in the 12th grade in 1982, e.g., students who
graduated early from high school in 1981. But there were also students
who were labeled "early graduates" on the data set (and thus candidates
for exclusion from a 12th-grade flag) whose high school graduation date
was listed as 1982. Early graduates were excluded, and erroneously
labeled "early graduates" were included in the population with SENRFLAG
= 1. If these students were not participants in the 1982 panel (even if
postsecondary transcripts were received) their weight = 0. Using the
1982 panel weight alone without this flag will not produce an accurate
universe of 1982 12th-graders.

For all calculations of HS&B/So data in this document, SENRFLAG = 1, and
the appropriate PSE weight invoked.

The weights and flags for the NELS:88/2000 are more complex, still,
because the cohort, established in the eighth grade, was "refreshed"
twice: first, to be representative of the census of 10th-graders in
1990, and second, to be representative of the census of 12th-graders in
1992. The weights deriving from the 1992 12th-grade refreshing are at
the core of weights subsequently developed for the postsecondary
transcript sample. The same three postsecondary weight types developed
for the High School and Beyond/Sophomores were employed here, but in
combination with the 12th-grade (second follow-up survey, or F2) weight
and the student's presence in the final (2000) survey panel, F4. In
addition, a set of weights based on the NELS high school transcripts in
combination with the three postsecondary weight types also was developed
when questions arise concerning the relationship between secondary
school variables derived from high school transcripts and postsecondary
variables derived from postsecondary transcripts.

The most frequently used NELS:88/2000 weights in *The Toolbox Revisited*
are:

F4F2P2WT For all known postsecondary participants who were 12th-graders
in 1992.

F4F2HP3W For all postsecondary participants with complete records who
were 12th-graders in 1992 and for whom high school transcripts are also
part of the file.

F4F2P3WT For all postsecondary participants with complete records who
were 12th-

graders in 1992.

As in the case of the High School and Beyond/Sophomore cohort, a special
flag was developed for 12th-graders in 1992. The existing flag on the
NELS:88/2000 files excluded over 250 students who, in fact, were awarded
high school diplomas in the spring of 1992 and who carry positive
weights for the panel (the descriptive windows of the Electronic Code
Book offer no reasons or clues for this anomaly). These students are
included in the flag, GRADE12A, used in this monograph.

The weighted Ns for samples used in a table are provided in the notes to
the tables. Even if the same weight and flag is used on two tables, the
weighted Ns may differ slightly because missing values in a particular
variable are excluded from the calculations.

**Multivariate analyses**

For all multivariate analyses in this monograph, special procedures were
employed in accordance with the complex sampling designs of NCES
longitudinal studies. These procedures are in the spirit, though not
exactly to the letter, of those discussed and recommended by Thomas and
Heck (2001). Thomas and Heck recommended alternative ways of producing
both regression models and their adjusted standard errors in a single
step, as opposed to the two-stage procedure used in this study. The
reader should be aware that the software employed in this study, AM,
correctly estimates standard errors associated with complex, cluster
samples.

For any model, an adjusted weight based on the population with
non-missing values on all variables in the model was calculated, in the
following steps:

1.  A weight appropriate to the question was selected. For example, for
    determinants of transfer from a community college to a four-year
    college, the weight for NELS students with received postsecondary
    transcripts, F4F2P2WT, was chosen.

2.  A simple tabulation of the dependent variable was then run for
    students who evidenced positive (non-missing) values for all
    variables in the model. Call this universe A. The selected weight
    was invoked.

3.  The log of the program for step 2 produces both unweighted and
    weighted Ns for universe A.

4.  The selected weight is then adjusted by what Thomas and Heck (2001)
    refer to as NORMWT, i.e., the weighted N / unweighted N of universe
    A.

5.  The selected weight is then multiplied by the NORMWT, thus adjusting
    the effective sample size.

6.  The example would look as follows:

F4F2P2WT / (f4f2p2wtA / unweighted N for A configuration of variables)

7\. The result becomes a variable in its own right, a weight with a
name, e.g., COREWT1.

A root design effect (DEFT) reflects the effect of departures from
simple random sampling, and in the methodology reports for the
NELS:88/2000, is calculated for sub-populations on each of a selection
of variables (Haggerty et al. 1996; Curtin, Ingels, Wu, and Heuer 2002).
For any logistic model in *The Toolbox Revisited*, a DEFT based on the
population with non-missing values on all variables in the model was
calculated in order to adjust the standard errors produced by
statistical packages such as SAS (used in the production of this study).
The DEFT is calculated in three steps:

1.  The requisite data for a simple standard error are produced by the
    same equation used for NORMWT, and set out as follows:

\_\_\_\_\_\_

[p(1-p)]{.underline} = s.e.

N

2\. A matching Taylor series standard error is produced by AM software
with the same dependent variable and equation, with the population
filtered by positive (non-missing) values for the same variables used in
the equation in step 1. The Taylor series s.e. takes into account both
stratum and primary sampling unit in combination with the weight
selected, hence accounting for the complex sampling design.

3\. The DEFT = Taylor Series s.e. / simple s.e.

Every discrete multivariate analysis has a unique DEFT. The DEFTs for
the NELS:88/2000 are rather substantial, e.g., 1.83, reflecting not only
the original sampling design in 1988 but also the successive
\"refreshings\" of the sample in 1990 and (for the analyses in this
monograph) in 1992.[^58] They are used to adjust the standard errors in
the multivariate analyses, and hence reduce the likelihood of
overestimating the effects of independent variables. The effect of the
DEFT also is reflected in the production of the *F* and *t* statistics,
for which the formulas used are:

\_\_\_\_\_\_ ^2^

s.e. x DEFT = F

and

\_\_\_\_\_\_\_\_\_

[F]{.underline}

DEFT^2^ = *t*

In the logistic models employed in *The Toolbox Revisited*, the level of
significance of the *t* statistic---*p*---for a two-tailed test is
determined by reference to a standard table of critical values of *t*
that can be found in any statistics textbook.

**Collinearity data**

This study includes Appendix J with tolerance statistics for
collinearity for all the logistic model tables in order to assure the
reader that the independent variables included in the models do not
exhibit a nearly perfect linear relationship, in other words, that they
do not overlap to such an extent that analysis of each variable, taken
singly, is impossible. There are sometimes situations in which one
variable is part of the definition of another, e.g., family income in
relationship to socioeconomic status or multi-institutional attendance
in relation to transfer. In cases such as these, collinearity statistics
are produced as by-products of Ordinary Least Squares regressions for
the variables in the logistic models.

Of these by-products, tolerance is the statistic of choice: It measures
how well one independent variable can be predicted by other independent
variables in the model, and is equal to 1-R^2^ for that variable.
Ideally one would want this predictive relationship to be close to 1.
The literature (e.g., Belsley, Kun, and Welsch 1980) suggests that there
are no hard and fast rules for determining collinearity using either
tolerance or its inverse, variance inflation, but that, in general, a
tolerance reading of .20 or less evidences collinearity problems. This
study adopted a tolerance threshold of 0.50, i.e., any reading above
that threshold indicates no serious collinearity problem. Any indication
below that point required further investigation of the independent
variable(s) in question through correlation matrices. If the variables
in question were part of the constructs of other variables, a choice was
made as to which variable would be dropped. Dropping independent
variables is one of the recommended options when potential
multicollinearity arises (Knight 2004).

**APPENDIX E**

**Populations Included and Excluded From the Study Universe**

The population subject to analysis in *The Toolbox Revisited* consisted
of 1992 12th-graders who subsequently attended a four-year college at
any time through December 2000, who earned their high school diploma by
December 1996, who presented complete high school transcript records and
a senior year test score, whose postsecondary records were complete, and
whose socioeconomic status was known. But there are other students who
participated in the 1992 NELS:88/2000 survey and who subsequently
attended a four-year college at some time who are not part of this
population principally because (a) one or more of these data elements
were missing or (b) because they were not in the 12th grade in 1992.

It is natural to ask about the demographic characteristics of the
students who are excluded from the analysis because they are missing
data or because they were not in the 12th grade in 1992, compared with
the demographic characteristics of the students who *are* included. In
order to compare distributions of this comparative demography, we
include all 1992 survey participants.

Considering those who attended a four-year college at some time but were
nonparticipants because one or more of the key data elements were
missing, key contrasts include:

1.  A higher proportion of minority students than white students;

2.  A higher proportion of students who were 20 years old or older in
    1992

than those who were less than 20 years old;

3.  A higher proportion of students from the lowest third of family
    income

distribution than those from higher income levels;

4.  A higher proportion of first-generation students than those whose
    parents

had either some college or who had earned at least a bachelor's degree;

5.  A higher proportion of nonnative speakers of English than those from

English monolingual backgrounds;

6.  A higher proportion of those with three or more siblings than those
    who

were either only children or had one or two siblings;

7.  A higher proportion of those who became parents by age 20 than those

who did not;

8.  A higher proportion of those who had been retained in grade at least
    once

than those who were never held back; and

9.  A higher proportion of those who came from high schools in urban
    areas

than those from suburban or rural areas.

Some 60 percent of this group was missing only one of the key data
elements, but it was a very important one: a high school transcript.

Of nonparticipants because they were not in the 12th grade in 1992, we
notice distinctively higher proportions by age (20 years or older),
origin in a second language household (though not among nonnative
speakers of English), and parental status, and among those who had been
retained in grade and those who earned General Education Diplomas.

![](media/image42.wmf)

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# APPENDIX F

# Gradations of Academic Intensity of High School Curriculum

The following figure sets forth the 31 gradations (in descending value)
of academic curriculum intensity and quality as used in the development
of the Academic Resources index and variable for the NELS:88/2000
cohort. The figures in the boxes represent the minimum rounded number of
Carnegie units required for the gradation on a given *row*. Where a cell
is empty, there are no minimum requirements. Where a cell indicates
\"none\" (for remedial math and remedial English), it means that no
remedial work is allowed for that gradation. Where the cell for AP
courses indicates zero, that means the student did not take any AP
courses, not a minimum. For the NELS:88/2000 cohort, computer science
was not nearly as widely offered as it is today. Therefore,
computer-related credits were brought into play only to disaggregate
lumps in the distribution. Total high school academic credits is an
empirically-derived factor that comes into play only in the very lowest
gradations.

The basic five-subject credit thresholds were constructed in the course
of examining the edited, coded transcript data for students who were
known high school graduates with graduation dates through Dec.31, 1996.
The editorial process paid particular attention to all cases that showed
less than 16 total high school credits. Where the evidence strongly
suggested dissonance with other variables in the student's record, all
transcript records from that student's *school* were examined. Where
nonstandard credit metrics were found, they were adjusted with reference
to state standards for high school graduation (Medrich, Brown, and Henke
1992), and major components (e.g., mathematics, English, etc.)
multiplied or divided by as much as (but no more than) two. For example,
when a group of students from the same high school showed 40--45
Carnegie units in a state that required 20 for an academic diploma, the
editorial process cut those 40--45 units in half---across all subjects
in which they were given. The editorial process also Windsorized cases
of total Carnegie unit counts above 32, adjusting the major components
down one-by-one, and dropped fragmentary transcripts with less than 6
Carnegie unit counts.

As noted in the parallel appendix in the original *Tool Box*:

These gradations of academic intensity and quality are based on the
history of

> one national high school class that was scheduled to graduate in 1982.
> The next graduating class for which we possess similar data is that of
> 1992. While the

specific number of Carnegie units, APs, and remedial indicators might
change,

the basic form and principles of the gradations will probably not
change. This

presentation of the possibilities of high school curricular attainment
is criterion-

referenced: theoretically, *everybody* can reach gradation level #1. (p.
114)

The account of curriculum for the class of 1982 had 40 gradations. This
account, for the class of 1992, has 31. One implication of the shrinking
number of gradations is that, in fact, more students were moving up the
academic intensity ladder, clustering at higher criterion-referenced

levels.

Table F1 presents the actual mean number of Carnegie units earned in
core academic fields, irrespective of the theoretical thresholds, for
students in each of the five quintiles of academic intensity derived
from the 31 more detailed gradations.

**Figure 3. Curriculum components of the 31 gradations of the high
school academic**

**intensity measure of the NELS:88/2000, by Carnegie unit minimums**

![](media/image44.wmf)

![](media/image45.wmf)

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# APPENDIX G

**Logistic Models for Two Alternative Presentations of**

**High School Academic Background**

![](media/image46.wmf)

![](media/image47.wmf)

# APPENDIX H

**The Timing of Departure**

When this narrative took up the topic of the second calendar year of
student histories and pointed out that roughly one out of five of our
subjects had become status dropouts by that point, the question
naturally arose: What happens to all those students who leave after the
first year---or even the first semester---when most attrition occurs?
How does one account for them? We need to provide some corrective data
in this excursion, since we considered status dropout status only in the
context of the paradoxes of first-to-second year persistence.

With rare exceptions (e.g., Tinto 1987), most attrition studies are (a)
short-term, as in first year to second year, without allowing for the
fact that students who skip the second year may return in the third or
fourth years, and (b) limited to attrition at the same institution,
without allowing that the student who can no longer be found at Old
Siwash may, in fact, be enrolled at Greentree Valley Community College.
Students who leave one school and attend another one are not
dropouts---they are most likely transfers. Tinto (1987) made that point
a long time ago, and it should be obvious. If they are not transfers,
they may be on temporary \"excursions\" or more sustained voyages that
end in either fragments or \"discovery\" (Adelman 2004b).

Given the systemwide perspective and the length of a longitudinal study
such as the NELS:88/2000, a more sophisticated question about withdrawal
can be asked, looking backwards from the last month of the longitudinal
study (December 2000):

What percentage of traditional-age students who entered postsecondary
education

during this period are no longer enrolled---anywhere---and never
completed a

credential of any kind, by timing of the gap between their first month
and last

month of enrollment?

This question follows the student---wherever the student goes. It tells
us who became a "status dropout" by age 26 or 27 (which does not
preclude even these students from returning at a later moment). And it
tells us *when* the student became a status dropout, setting up an
inquiry concerning the reasons for departure that follows Tinto's (1988)
common sense suggestion that these reasons change by point of departure.
Table H1 sets forth these data for *all* 1992 12th-graders who entered
postsecondary education, by type of institution first attended.

Yes, the highest attrition rate in postsecondary education occurs in the
first year (Schutz and Malo 2003), but table H1 shows that the
proportion of traditional-age students who leave in the first year and
never return is not radically higher than the proportion of those who
leave at later points in time, and differs by type of institution first
attended. Consider the face validity of these data: The mean number of
credits earned by students who ultimately became status dropouts, by
period of departure, matches roughly what one would expect---half or
less of the full-time norm for the period. Proportion, however, is not
the ideal way to assess the phenomenon.

Event-history accounts of attrition offer a more enlightening approach
(e.g., Ronco 1996; DesJardins, Ahlburg, and McCall, 1999). The driving
force of event history is risk or hazard, as befits a methodology
derived from medical history analyses (Singer and Willett 1991), as in:

given the patient's medical momentum and other configurations of the
patient's life-style, demography, and environment, when is the patient
at risk of dying (the ultimate censoring event) if the patient did not
die last year? The flip side of risk in event history is survival. While
the purpose of this study stops short of survival analysis, the first
step involved in setting up risk modeling involves determining hazard
probabilities, and these are instructive in light of the

![](media/image48.wmf)

first-year performance variables used in our analysis. That is, if we
start at the first month of the first term of attendance and, for each
calendar year following that point, asked what percentage of students
left the postsecondary system with no degree and had not returned to
school by December 2000, changing the denominator for each year to the
number of students who remained in the system, we have a \"declining
risk set\" (Ronco 1996) that serves as a rough guideline for the timing
of potential dropout. The annual metric is obviously more even than the
time brackets chosen for table H1.

The \"declining risk set\" for this study is presented in table H2. To
summarize: For all postsecondary students, the risks of becoming a
status dropout are highest in the first year, decline through the fourth
year, flatten out through the sixth year, and decline after that. For
students who attended a four-year college at any time, the risks of
becoming a status dropout are much lower across the temporal board, are
slightly higher in the first year, drop and then flatten from the second
year through the sixth, and drop again after that. This is only the
first step---and hardly the final analysis---of event history, but is
perhaps a more accurate way of describing the parameters for
understanding the phenomenon of when students leave postsecondary
education.

![](media/image49.wmf)

The reader of table H1 will note that community college beginners exit
sooner than do students who started at four-year colleges, and are more
likely to still be enrolled at the end of the longitudinal study period.
While there is comparatively little variance in the pace of permanent
dropout for students who started in community colleges when the periods
between the first and the fourth year are considered, there is no
question that beyond that point, attrition slows. The same cannot be
said for the pace of status dropout for students who started in
four-year colleges: The rate of permanent attrition appears to be stable
over time, a finding slightly different from that of the \"declining
risk set\" approach, and a product of the clumping of years in table H1.
As for sub-baccalaureate institutions other than community colleges,
which specialize in short-term certificate programs, the status dropout
rate drops dramatically from the first year to the second and subsequent
periods.

Advancing on Tinto's (1988) suggestion, Eaton and Bean (1995)
hypothesize that the factors affecting attrition are different for
first-year students who withdraw from higher education versus the
factors that come into play for students who leave at later points in
time.Unfortunately, Eaton and Bean could not investigate that hypothesis
because their study was confined to first- year and second-year students
at one institution (a public research university), and bracketed only
one year's account of retention/attrition (for a similar inquiry, see
Patrick 2001). The NELS: 88/2000 data, on the other hand, offer 8.5
years and a myriad of institutional types in which to explore and detail
the boundaries of the issue. As Ronco (1996) notes, the timing and
duration of \"enrollment events\" is a critical framework for
identifying factors associated with graduation, transfer, and
stop-out---the three modes of \"exit\" from an institution.

Table H3 provides a framework for future consideration of the
differential attrition hypothesis. The literature on the putatively
sophisticated economic decisionmaking of adolescents with respect to
entering higher education, even in the face of uncertainty of returns
(Altonji 1993), can be extended to reasons for leaving a path to
postsecondary credentials. As Beattie (2002) points out, human capital
theory is not rigid: it recognizes something called individual taste or
proclivity that may be only tangentially related to group membership
(e.g., ethnicity, gender, family income). At the least, students already
in the postsecondary system know that they will

eventually be better off for their education efforts (or they wouldn't
have been there in the first place). So, what did the students in our
universe who did not complete a bachelor's degree program (and who were
not still enrolled as degree candidates at the end of the 8.5 year
period) tell us of their reasons for leaving, by period during which
they became status dropouts?

![](media/image50.wmf)

When the NELS:88/2000 students were asked (in the spring of 2000) why
they left school, they were offered a list of reasons (though only 17
percent of students responding to the question indicated more than one
reason). As table H3 indicates, personal and family reasons for
departure dominate all other reasons for students who left postsecondary
education without a credential between the 12th and 47th month following
the first month of enrollment. The same factor ranks at the top versus
all other factors except mood/lifestyle for students who left in the
first year and students who left after the fourth year. Strictly
financial reasons are not as prominent in students' judgment as some
contend. \"Job/military considerations\" might be considered
\"financial,\" but there is too much ambiguity in that category of
response to leap to that conclusion. Some 6.6 percent (s.e. = 0.47) of
the1992 12th-graders subsequently served in the military, but 14.9
percent (s.e. = 4.95) of status dropouts who cited financial reasons for
leaving school had served in the military, and an identical 14.9 percent
(s.e. = 3.84) who cited \"job/military considerations\" for leaving had
served in the military. If the NELS files had offered a more complete
labor market history, we might be able to resolve the ambiguities.

As a partial confirmation of these observations, consider the work of Li
and Killian (1999), who surveyed 622 students of all ages and levels who
left a large state flagship university in 1997 (present in the winter
term but not the following fall) and elicited 45 discrete reasons for
departure. First, Li and Killian discovered that 20 percent of these
students were not really dropouts at all, rather either transfers to
other institutions (principally for reasons of academic program or
location) or stop-outs with intentions of returning. Of the remaining
students, 43 percent left for academic reasons (e.g., didn't like the
program, classes too large, poor performance), 34 percent left for
personal reasons (e.g., unstated personal problems, location issues
including homesickness, illness, "social" reasons), and 20 percent for
financial reasons. Of the financial reasons, Li and Killian advise us
that "individual patterns of money management, more than family income"
may be responsible for financially-driven attrition (p. 12), and that if
we are going to understand attrition at all so that student affairs
officers can establish realistic efforts to address what is within the
control of the institution to assist, we have to dig below the level of
large-scale concepts of academic and social integration. There is a
considerable range of reasons that students leave an institution, and,
as Li and Killian point out, students usually have more than one reason
for departure. We can't control homesickness; we can help students deal
with money management.

As for academic reasons for departure, table H4 reveals that compared to
those who earned bachelor's degrees, no one in the departure universe
was performing very well, no matter when they left, and even though a
tiny percentage (see table H3) cited academic reasons for walking away.
Braxton, Brier, and Hossler (1988) argue that when students are asked
about their reasons for withdrawal in post-hoc surveys, they offer
\"socially acceptable rationalizations.\" We should hence be
appropriately wary of the percentage distributions in table H3. Given
the low percentage of students who cited academic reasons, and GPAs and
cumulative credits for the same students that can be described as, at
best, marginal, there is some indirect support for this contention.

![](media/image51.wmf)

**APPENDIX I**

# Course Categories Included in Aggregates for Participation Rates

**In the First Two Calendar Academic Years of Attendance**

**[Aggregate]{.underline}** **[Course categories]{.underline}**

College-level writing English composition; technical writing; creative
writing; advanced essay

Oral communications Oral communications; public speaking/debate; voice

Computer-related Introduction to computer science; introduction to
computing; computer programming: general

Introductory biological General biology; human biology; cellular
biology; zoology:

sciences general; botany: general

Introductory physical General chemistry; general physics; general
geology

sciences

College-level mathematics College algebra, liberal arts mathematics,
finite mathematics,

statistics, precalculus, calculus

Core history Western civilization, world history, U.S. history surveys,
European history 1789--present, Asian history, African history, Latin-
American history

General psychology \[single course category\]

Micro/macroeconomics \[single course category\]

Humanities other than Humanities: general; introduction to philosophy;
ethics

literature and foreign (philosophy); religious studies surveys;
interdisciplinary

languages humanities; arts/humanities

Literature Literature: general; introductions to poetry, fiction, drama,
non-

fiction prose; English literature; American literature; Afro-American
literature

Core social sciences Anthropology: general; cultural anthropology;
geography: general;

introduction to political science; U.S. government; introduction to

sociology

Visual/graphic arts Visual communications; introduction to design; fine
arts: introduction; art history; drawing

Foundation business General business principles; business law/legal
environment;

introduction to accounting

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**APPENDIX J**

# Collinearity Statistic (Tolerance) for the Seven Steps of the Logistic Narrative

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### APPENDIX K

**So They Earned a Degree! Now, How Long Did It Take Them?**

The second most frequently asked question about U.S. higher education
concerns time to degree.

Despite accumulating evidence over the past quarter-century, the
normative benchmark for completing a bachelor's degree has remained at
four elapsed academic years. Our ideal seems not only to get it over
with, but to get it over with in normative time. An altruistic argument
in favor of the normative is that when students finish in a timely
manner, they make room for others, i.e., completion keeps the access
channels open. Yet recipients of bachelor's degrees are adults who have
made a variety of decisions concerning competing goals and obligations
that often do not include finishing a degree in four years. For example,
if one looks at all recipients of bachelor's degrees in 1999--2000, and
asks when they commenced their studies and how old they were when the
degree was awarded, one finds that 62.8 percent (s.e. = 1.5) of the 7.5
percent of bachelor's degree recipients who were over 40 in 2000 started
out in postsecondary education before 1980. At a minimum, the elapsed
time to degree for these people was 20 years (in fact, the average was
over 27 years). Of the 9.2 percent (s.e. = 0.4) of degree completers who
were between 30 and 39 in 2000, 73.3 percent (s.e. = 1.7) entered
postsecondary education prior to 1990, so, at a minimum, the elapsed
time to degree for these people was 10 years (in fact, the average was
nearly 15 years).[^59]

The key phrase for our purposes is \"elapsed time,\" as that is the
customary way of measuring time to degree. It is not surprising that the
older the baccalaureate recipient, then more likely that student had
taken at least two years off from higher education, and the more likely
that their principal reason for doing so was \"change in family
status,\" as in becoming a parent and raising children. The reader might
consider, in passing, when complaints are raised about excessive time to
degree, whether our system of higher education should be \"blamed\" for
providing the opportunity for adults with different life trajectories to
return to school and complete degrees, even if the time between initial
enrollment and degree award is 15 or more years. That is the practical
meaning of elapsed time.

There is an obvious difference between elapsed and enrolled time. When
DesJardins, Ahlburg, and McCall (2002) investigated factors leading to
\"timely graduation,\" they confined one of their universes to students
who had never stopped out---not even for the one term this study allows
stop-out without labeling the student a non-continuous enrollee.[^60] If
we followed this mode of analysis, we could focus in on student *uses*
of enrolled time to determine what contributed to and what detracted
from year-by-year progress. Knight (2002) includes types and timing of

remediation, majors and changes-of-major, course withdrawals and
repeats, course failures, credit hours earned and grades in general
education courses, hours per week working and studying, and first-year
grade point average among variables reflecting different aspects of the
uses of time.[^61] Volkwein and Lorang (1996) took up the phenomenon of
students with extended time-to-degree because they purposefully carried
lighter credit loads. Why did they carry less than the 15 credit per
semester norm for the institution that served as the site for this
study? To enhance GPA (an objective which precipitated dropping
difficult courses), and to generate more free time, some of which was
for work or family responsibilities, or both. Some respondents also
cited difficulty of enrolling in a course \"at the time I wanted,\" a
phenomenon familiar to anyone who has worked student registration lines.

We also know that many disciplines require credit hour production that,
when translated into standardized semester metrics, exceed the 120
credits that would be produced by students who attended only during the
regular academic year and carried a standardized full-time load of 15
credits per semester. In a survey of 91 public universities in all 50
states, Pitter, LeMon, and Lanham (1996) found combinations of
university and program requirements ranging from

122--124 credits in social sciences, foreign languages, psychology,
mathematics, and protective services, for example, to 130--142 credits
in such fields as engineering, architecture, and health professions
(e.g., nursing, physical therapy, etc.). They also confirm our
observation of five-year bachelor's degree programs in pharmacy, for a
noted case, with a median credit requirement of

161\. Any requirement above 120 credits will either add time to degree
or encourage students to

\(a\) earn credits by examination, including Advanced Placement, (b)
attend during summer terms, and/or (c) carry credit loads in excess of
15 per semester in order to graduate \"on time\".[^62]

As Garcia (1994) observed, whether the student is a community college
transfer or a native student in a four-year college, the "basic recipe\"
for completing a bachelor's degree within the standard \"templates for
time-to-degree is to maintain continuous enrollment and to earn more
than 30 semester units each academic year\" (p. 8). Sounds simple, but
the list of diverting phenomena is long, complex, and often best
assessed for *indirect* effects, as Garcia has done, using path
analysis.

What we learn from these studies of the uses of enrolled time in
relation to normative models of time to degree is what to include in
both descriptive and multivariate accounts of elapsed time---and elapsed
time is the measure used in both the original *Tool Box* and *The
Toolbox Revisited.* The descriptive statistics are offered to the reader
in Appendix L, table L13, but some basic observations are worth
repeating here. First, the mean elapsed time to degree for bachelor's
recipients in the NELS:88/2000 was 4.58 calendar years, and the median
time (which

is probably more meaningful) was 4.24 calendar years.[^63] Shorter time
to degree is observable among students from the highest quintile of high
school Academic Resources, students who first entered highly selective
institutions, among those who brought more than four acceleration
credits across the matriculation line, and among those who attended only
one school. Considerably longer time to degree is observable among those
who attended three or more schools, among both community college to
four-year college and four-year-to-four-year transfer students, among
those who took more than one remedial course, those who were not
continuously enrolled, and those who majored in the physical sciences.
Most of these relationships confirm common sense.

But it is the multivariate analysis that will tell us what counts, and
that is the purpose of table

K1. Table K1 presents a linear (Ordinary Least Squares) regression in
which the dependent variable, time to degree, is set on a scale with
four values: more than 6 calendar years, 5--6 years, 4--5 years, and
less than 4 calendar years (which encompasses the normative four-year
degree). With one exception, a dichotomous variable indicating whether
the student ever engaged in a cooperative education or internship
course, the independent variables selected were those previously
explored and (in most cases) used in the logistic narrative of Part IV
of this study. The statistically significant independent variables are
highlighted in bold. How do we read the table? What do we see?

On reading the table: First, the R^2^ indicates that this linear model
accounts for half the variance in timing of bachelor's degree completion
for the NELS:88/2000 cohort. That's a very convincing level. Second, the
positive parameter estimates mark variables that add time to degree,
while the negative parameter estimates indicate variables that shrink
it. Third, the following variables did not meet the significance
threshold for entering the model (set at *p* \< .05): race/ethnicity,
becoming a parent by age 20, multi-institutional attendance, and
freshman year remediation.

There is no question of the major contributors to extended time to
degree:

1.  Excessive no-penalty course withdrawals (W) and no-credit repeats
    (NCR)--- Damaging to degree completion, these are just as damaging
    to time to degree. Yes, we can keep students continuously enrolled,
    but if much of that enrollment is nullified by withdrawals and
    repeats, we have what Tinto calls retention without education. It's
    worse, though, because every seat at every available hour in every
    facility of an institution of higher education is at stake, and
    every seat marked with a W or NCR bars another student from sitting
    down. When the blocked seats reach a critical mass, general access
    is impeded as well. This observation is worth repeating.

2.  Transfer, both classic community college to four-year, and four-year
    to four-year---As previously noted, transfer often involves a hiatus
    in enrollment and extra effort to meet prerequisite requirements at
    the new institution.

3.  Change of major---Garcia (1994) observed that the more times the
    student changed major, the greater the elapsed time to degree.
    Knight (2002, 2004a, 2004b) also includes multiple changes of major
    among the set of variables with significant impact on both enrolled
    and elapsed time.

4.  Whether the student was ever part-time---Since our variable for
    part-time

> attendance was constructed partly with reference to course withdrawals
> that, in
>
> effect, produced lighter course loads, the result here backs up the
> conclusions of
>
> Volkwein and Lorang (1996).

![](media/image53.wmf)

And there is no question concerning which variables will contract time
to degree: continuous enrollment and no remediation (the highest value
of the \"total remediation\" variable). Socioeconomic status is a
marginally significant contributor to lower time to degree, while the
position of freshman year GPA quintile as a contributor to extended time
to degree is somewhat puzzling.

Of those variables that were admitted to the linear model but failed to
reach the threshold of statistical significance, enrollment in
cooperative education or internship courses deserves special attention
because it raises contrasting policy options with respect to influences
on time to degree. Knight (2004b) observes that:

Timely degree completion is not all that matters in terms of college
student outcomes.

> Both analytical and student self-report evidence supports the fact
> that enrollment in cooperative education classes, involvement in
> internships, etc., while extending time-to-degree, significantly
> improves student learning and skill development, affective outcomes,
> career prospects, and the like. Significantly reducing time-to-degree
> could perhaps demand a trade-off against other long-term (and maybe
> more important) outcomes. (p. 14).

It turns out that the NELS:88/2000 baccalaureate students who engaged in
cooperative education or internships or clinical externships did not
take longer than others to complete degrees. But Knight is really asking
readers to reflect on the principal objectives of conducting a
baccalaureate enterprise. The modes of instructional delivery in
professional and applied fields, in particular, often include carefully
designed, graded experience in occupational environments, involving
considerable time commitments that lie beyond the classroom. If we say
to a school of engineering, "You can't offer cooperative education any
more and cannot require more than 128 credits for a degree," what do we
accomplish in terms of the quality of student learning and the quality
of engineering graduates?

In contrasting spirit, if we observe institutions in which students can
withdraw from courses, without penalty, as much as 10 weeks into a
14-week semester, a volume of withdrawals equivalent to 15 percent of
all credits offered by the institution in a calendar year, and the
average time to degree for native students at that institution to be
well over five calendar years, we would accomplish a great deal by a
tightening of course withdrawal policy. Here is a prime candidate for
future research governed by quasi-experimental design: Find two
comparable institutions (mission, size, demography, distribution of
majors), one with lax withdrawal rules, the other with restrictive
rules. The hypothesis, from everything learned in this data essay: An
institution that restricts course withdrawal policy will witness higher
graduation rates and shorter average time to degree.

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![](media/image54.wmf)**APPENDIX L**

**Tables and Comments on Miscellaneous Topics Raised in the Text**

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![](media/image58.wmf)

As the reader will notice, about 48 percent of traditional-age students
in the BPS longitudinal study of 1995/96-2001 told us that they attended
part-time at some point in their undergraduate careers. In contrast,
only 38 percent of the NELS:88/2000 postsecondary cohort indicated in
their 2000 CATI interviews that they had attended part-time at any time.
Are the two cohorts, three years apart in their modal starting date,
that different? No.

NELS:88/2000:

Part-time by student report 37.7

Part-time by transcript evidence 9.7

Total part-time 47.4

BPS95/96--2001 students who started

before they were 21:

Always part-time 4.4

Mixed full-time and part-time 43.8

##  Total part-time 48.2

So a dichotomous variable indicating whether the student *ever* attended
part-time can be included in the logistic model in Step 5 (attendance
patterns).

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**GLOSSARY**

**VARIABLES AND THEIR CONSTRUCTION**

This glossary serves not only to expand the definition of the variables
considered for *The Tool- box Revisited*, but also to provide details on
their construction and allied guidance for interpretation that the
reader may find helpful. As in Part II of this study, the presentation
follows the order of the seven steps of the logistic narrative.

Where the initial definition of the variables in Part II was simple and
transparent, e.g., GENDER, no further elaboration is provided here.
Nearly all these variables were either taken directly or derived from
other variables on NCES 2003-402 and its June 2004 Supplement.

**Step 1a: Demographic Background**

**NNSE** **(Nonnative speaker of English)**---New in this analysis.

The most notable demographic change between postsecondary students from
the High School Class of 1982 and those from the High School Class of
1992 was a doubling of those who not only came from households where
English was a second language, but who themselves were users of the
heritage language. More than half of both Asian and Latino postsecondary
students were so classified (Adelman 2004a, table 1.3, p. 9).

**IMMIG** **(Family immigrant status)**---New in this analysis.

Allied to second language background is the immigrant status of
families. A dichotomous variable, IMMIG, was created to indicate whether
the student's parents were immigrants to the United States within the
previous 10 years. Among those who attended a four-year college at any
time, 27.5 percent (s.e. = 3.33) of Asian students and 8.8 percent (s.e.
= 1.61) of Latino students came from recent immigrant families. The
dichotomous variable did not meet the minimum *t* criterion for
retention in the demographic logistic model. Nonresponse bias undermines
this variable: Responses from nearly 15 percent of the NELS:88/2000
families are missing.

**BROSIS** **(Number of siblings)**---New in this analysis.

Some research has indicated that students from larger families have more
difficulty entering and successfully participating in higher education
(Stage and Hossler 1989; Leigh and Gil 2003; Perkhounkova, McLaughlin,
and Noble 2004). The dichotomous variable, BROSIS, marks students with
three or more siblings versus those with one, two, or none.

**FIRSTGEN (First generation postsecondary student)**---New in this
analysis.

A dichotomous variable under which the criterion for first-generation
status is that *neither* parent had attended a postsecondary
institution. Parents' education status was reported by parents
themselves, not by students. The discrepancy between students'
understandings of their parents' education status and parental accounts
was demonstrated in the original *Tool Box* (p. 36): For the High School
Class of 1982, only 50 percent of the students with at least one parent
who had earned a bachelor's degree (but not a graduate degree) could
correctly describe their parents' achievement. Parents' highest level of
education is a key component of socioeconomic status, and the original
*Tool Box* did not test it separately.

**FAMINC (Family income**)---New in this analysis.

Family income in 1991 (the year before NELS students were scheduled to
be in the 12th grade) was reported by parents, and set in six bands with
a fairly even distribution of all respondents across those bands. In
2005 dollars (adjusted for a Gross Domestic Product deflator[^64] of
1.288), as shown in figure 4, these bands were:

![](media/image68.wmf)

For purposes of our analysis, the bands were combined in pairs---highest
two, middle two, and lowest two---to produce a trichotomy. This version
is used in the Step1a logistic model (demographic characteristics only),
along with FIRSTGEN, as one of the proxies for socioeconomic status.

**NEWCHILD (Parenthood by age 20)**---Carried forward from *Answers in
the Tool Box.*

The variable, abbreviated as NEWCHILD, is a dichotomous marking of
students (of either sex) who became parents by age 20. It was a
powerful, negative, and consistently significant variable through all
stages of the logistic story of the HS&B/So. A decade later, the rate of
early parenthood had changed. For the entire cohort of the HS&B/So, 11.6
percent (s.e. = 0.43) became parents by age 20, a proportion that rose
to 16.4 percent (s.e. = 0.92) for the NELS:88/2000. For those who ever
entered a postsecondary institution, these percentages drop in half.
Georges (2000) would remind us of the common sense that students who
became parents by age 20 were not likely to enter college at all by that
time. Indeed, 59.4 percent (s.e. = 2.30) of

the NELS:88/2000 participants who had children by 1994 did not enter any
postsecondary

institution by 2000, compared with 20.9 percent (s.e. = 0.89) of those
who did not become parents by 1994.[^65]

**SESQUINT** (Socioeconomic status quintile)---Carried forward from the
original *Tool Box.*

In NCES longitudinal studies, socioeconomic status (abbreviated SES) is
a composite index of family income, parents' highest level of education,
prestige of parents' occupations, and the presence of items such as
books, regular newspapers, and a computer in the student's household.
Parents provide this information, and the 1992 parent interview was the
primary source. The NELS:88/2000 files presented this index in centiles,
as did the HS& Beyond/So file before it. To match quintile presentations
of high school curriculum intensity, high school class rank/Grade Point
Average, 12th-grade test score, and the composite variable, Academic
Resources (see below), the centile scale was collapsed to quintiles. SES
is an anchor of the education attainment literature, with recent studies
enlightening our understanding of the complex ways students of different
SES backgrounds experience higher education (e.g., Walpole 2003).

**Step 1b: High School Background**

**EDUANTIC (Education anticipations**)---Modified from *Answers in the
Tool Box.*

In both the original *Tool Box* and *The Toolbox Revisited*, this is a
composite variable describing the consistency and level of the student's
education expectations, hence, goal commitment (Allen and Nora 1995). It
departs considerably from measures of student education "aspirations"
that are based on the student's answer to a single question at one
moment in time. The variable was built from matched pairs of questions
asked in grades 10 and 12. The High School & Beyond/Sophomore cohort
surveys included six pairs of questions: highest level of education
expected, planned dominant activity in the year following high school
graduation, timing of college entry, choice of a two-year or four-year
college as entry point, lowest level of education with which the student
would be satisfied, and whether the student would be disappointed if he
or she did not graduate from college.

The NELS:88/2000 version does not have as strong a base. Only two pairs
of questions were asked in grades 10 and 12 that feed into the
construction: highest level of education expected and timing of college
entry.[^66] In grade12 only, the respondent was asked what was the most
likely type of postsecondary institution he or she would enter:
four-year, two-year, or trade school, and the answer to this question
also was used in building the variable. But the lack of parallelism

between the HS&B/So survey and the NELS:88/2000 lead to revisiting the
NELS categories and

applying stricter algorithmic standards to yield an education
anticipations variable closer to the structure of its predecessor, as
displayed in figure 5.

Even after this construction, the education anticipations variable
required an adjustment. Unlike the quintile variables for curriculum,
class rank/GPA, and senior year test score, in which meanings are
linear, the five-level anticipations variable is categorical. For
purposes of multivariate analysis, the five levels were reduced to three
as follows: (1) consistently expected to earn a bachelor's degree; (2)
raised expectations to the bachelor's degree between grades 10 and 12;
and (3) either lowered expectations from the bachelor's level between
grades 10 and 12 or never expected to earn a bachelor's degree. The
result is still a categorical variable, but the reference
point---expectations for earning a bachelor's degree---is now constant
in all three values.

**Figure 5. Comparison of the education anticipations composite variable
in the High School & Beyond/Sophomore cohort and the NELS:88/2000:
Changes in students' expectations between grade 10 and grade 12**

[HS& B/So]{.underline} [NELS:88/2000]{.underline}

Bachelor's consistent Bachelor's consistent

Raised to bachelor's Raised to bachelor's

Lowered from bachelor's to some college; Lowered from bachelor's to some

associate consistent college, inconsistent

Lowered to no degree; Raised to some college; consistent

associate inconsistent "some college"

No degree plans, don't know Sub-baccalaureate, including high

school diploma or less

**SOURCES:** National Center for Education Statistics: High School &
Beyond/Sophomore cohort, NCES 2000-194; NELS:88/2000 Postsecondary
Transcript Files, NCES 2003-402.

**CLSSRNKQ (Class rank/GPA quintile)**---Carried forward from the
original *Tool Box.*

This variable is a composite of high school class rank and GPA quintile.
In both the HS&B/So and NELS:88/2000 data sets the composite was
constructed in roughly the same way. The construction is described in
detail in Appendix C, but the key features are worth repeating here.

The construction of this variable began with class rank, expressed as a
percentile, for students whose high school graduating classes were
larger than 10. Class rank was chosen for the base

reference because it overrides variability in local grading
practices,[^67] and responds to the divergence between stable scores on
standardized tests such as the SAT or ACT and rising GPAs among the
college bound (College Board 1998). Not all high schools compute class
rank,[^68] so for a significant percentage of students, this datum is
missing. For these missing cases (as well as for the students from very
small high schools), the variable construction turns to high school GPA
(where available, and only for students with three or more years of
course work). Basing a percentage scale first on class rank, and filling
in the missing values with available GPAs from a matched scale using an
equipercentile concordance methodology (Houston and Sawyer 1991),
weighting the combined scale and cutting it by quintiles solves some of
the bias and validity problems that would result from relying on GPA
alone.

**SRTSQUIN (Senior year test score quintile)**---Carried forward from
the original *Tool Bo*x.

SRTSQUIN is the quintile version of a senior year test score. Comparing
the HS&B/So to the NELS:88/2000, this variable had the least variation
in construction among the precollegiate academic performance variables.
In both data sets, composite scores on an "enhanced mini-SAT" given to
survey participants in the 12th grade were set out in percentiles. For
missing cases, ACT scores were first converted to the SAT scale using
ACT's equipercentile concordance methodology (accounting for the 1989
revision of the ACT test battery), and a combined SAT/ACT variable
constructed. Scores on this variable were set out in percentiles, and
filled in for missing cases of the senior year test score percentile
using the equipercentile concordance method. SRTSQUIN reduces the noise
in the lumpy distribution with a quintile presentation. Despite these
efforts, 14 percent of the students in the NELS:88/2000 database are
missing a senior year test measure, compared to 9 percent in the HS&B/So
(see Appendix C). It must be acknowledged that the construction of
SRTSQUIN combines low-stakes test scores with high-stakes test scores,
though it is unclear how that ultimately affects a quintile
presentation.

**HIGHMATH** **(Highest level of mathematics reached in high
school)**---Carried forward from the original *Tool Box.*

In the original construction of this variable in both the HS&B/So and
NELS:88/2000 data sets, some editing of the original coding of high
school mathematics courses was required in light of postsecondary
transcript evidence. For example, if the original coding in 1992 judged
the student's highest level of high school mathematics to be
\"geometry,\" and the student's postsecondary transcript record of 2000
showed enrollment and completion of \"Calculus III\" in the first
semester of college, then it was obvious that the original coder did not
know the

difference between \"geometry\" and \"analytic geometry,\" and the
student's high school record had to be adjusted accordingly. HIGHMATH is
considered a categorical variable (as opposed to a continuous variable)
because the distance between its levels cannot be judged as ordinal.

**SCIMOM (High school momentum in science and mathematics**)---New in
this analysis.

This variable has three values: (1) A student who reached a level of
math beyond Algebra 2 and who earned three or more Carnegie units in
core laboratory science was labeled as having sufficient momentum in
STEM (Science, Technology, Engineering, and Mathematics)-oriented fields
to enhance that momentum even further in a postsecondary environment
(whether or not they chose to do so). (2) Students who reached Algebra 2
but no higher, and accumulated more than 1.5 units of core laboratory
science exhibited \"modest\" science momentum, and (3) those whose high
school records fell short of \"modest\" on either the mathematics or
science criteria were labeled \"weak-to-minimal\" in terms of science
momentum. SCIMOM is one of three variables tested together as proxies
for the combined measure of the academic intensity of a student's high
school curriculum, HSCURRQ.

**FLAN (Number of units of foreign language in high school)**---New in
this analysis.

This variable was developed as part of a configuration of proxies for
academic curriculum intensity so that we could test the proxies against
the consolidated academic curriculum index, HSCURRQ, described on pages
24--27 and in Appendix F. FLAN indicates the number of Carnegie units
earned in high school foreign language study, and has five values: more
than 3 units, from 2.01 to 3 units, from 1.01 to 2 units, from 0.1 to 1
unit, and 0 units. FLAN is one of three variables tested as proxies for
HSCURRQ.

**ADVANCE (Number of Advanced Placement courses)**---New in this
analysis.

This variable was constructed with three values based simply on the
number of AP courses recorded: three or more, one or two, and none. It
was tested, along with SCIMOM and FLAN, as a proxy for the consolidated
academic curriculum index, HSCURRQ.

The identification of Advanced Placement course work in the NELS:88/2000
was a complex task. The version of the NELS:88/2000 high school
transcripts to which researchers have referred in the past understates
participation in AP courses, though it was difficult to say precise-ly
by how much. Two proxy measures were employed to create the first
version of an AP varia- ble on the data file used in this study:[^69] AP
test scores recorded on the high school transcripts and AP entries on
the postsecondary transcripts (which do not include test scores). These
were com- bined to yield 7 percent of the NELS:88/2000 12th-graders,
compared with the College Board's

estimate of approximately 11 percent of 1992 12th-graders having taken
AP courses.[^70] Not everyone who takes AP courses takes AP
examinations, and while that might explain some of the gap in the
estimates, it still left an uncomfortable discrepancy between the NELS
and College Board accounts of Advanced Placement volume.

In light of this low yield and anomalies in the data, a new approach was
taken in the work that produced the 2004 Supplement to the original NCES
2003-402 files. Enough new cases of

AP course taking (*not* courses labeled \"honors\" or just \"advanced\")
were identified to raise the proportion of NELS 12th-graders with AP
courses to 9.4 percent.[^71]

# Step 2: Postsecondary Entry

**FIRST4 (First school attended was a four-year college)**---Carried
forward from *Answers in the Tool Box.*

The dichotomous variable indicating whether the first institution
attended by the student was a four-year school was active in the
original *Tool Box* account, but did not qualify for entry into the

model in this replication. It is not clear why this should be the case.
Some 81.9 percent

(s.e. = 0.82) of the class of 1982 who attended a four-year college at
any time started at a four-year college, versus 78.1 percent (s.e. =
1.04) of the class of 1992. There is no meaningful difference in those
numbers.

**DOCT (First school attended was a doctoral degree-granting
institution)**---Carried forward from the original *Tool Box.*

Another dichotomous variable indicating that the first institution
attended by the student was not only a four-year college, but a doctoral
degree-granting school. In the original *Tool Box*, this variable was
admitted to the steps of the logistic model but was never statistically
significant. In *The Toolbox Revisited* analysis, this variable did not
qualify for entrance in the model, even though roughly similar
percentages of students who attended a four-year college at any time
started in a doctoral degree-granting institution (33.8 percent; s.e. =
1.06 for the HS&B/So versus 34.1 percent; s.e. = 1.11 for the
NELS:88/2000).

The variable indicating the selectivity of the first institution of
attendance (SELECT) is, to a large extent, confounded with doctoral
degree-granting status (55 percent of the NELS:88/2000 students who
started at doctoral degree-granting institutions started at either
selective or highly selective schools).

**SELECT (Selectivity of first institution attended)---**Carried forward
from the original *Tool Box.*

A dichotomous variable indicating that the first institution attended by
the student was either highly selective or selective.[^72] Some 4.1
percent (s.e. 0.49) of the universe for this study started in highly
selective institutions (e.g., Princeton, the University of California at
Berkeley, and Harvey Mudd). Another 17.8 percent (s.e. = 0.98) began
their postsecondary careers in selective institutions (principally
flagship state universities such as Michigan-Ann Arbor, North
Carolina-Chapel Hill, Wisconsin-Madison, and Texas-Austin). More than
half of the universe of students in this study (56.3 percent; s.e. =
1.32) commenced study in nonselective four-year colleges, and 20.7
percent (s.e. = 1.19) in open-door institutions, a category that is just
about identical to community colleges. For the previous cohort of
students from the High School Class of 1982, selectivity of first
institution had a modestly positive and statistically significant
association with degree completion until the last step of that analysis,
extended postsecondary performance. Readers interested in the
distribution of first institutional selectivity by race/ethnicity,
gender, and socioeconomic status are referred to Appendix L, table L3.

**NODELAY (Direct entry to postsecondary education following high
school)**---Carried forward from the original *Tool Box.*

This dichotomous variable was built from a simple distinction: Among
students for whom we know both the month and year of high school
graduation and the month and year of a transcript-documented attendance
in a postsecondary institution following high school graduation, is the
difference (a) seven months or less, (b) 8--18 months, or (c) more than
18 months? The first of these options is regarded as \"direct entry.\"
Dual enrollment courses do not count in this determination. The student
who graduates from high school in June has until the following January
to enroll and be judged \"no delay.\" To those who might question the
seven month allowance and argue for four months, one would point to a
small percentage of graduates with April commencement dates who would be
judged late entrants in September under a four-month rule.

**ACCELCRD (Credits earned prior to high school graduation and by
examination)---**New in this analysis.

ACCELCRD sums all college credits earned by course work prior to high
school graduation, along with credits earned by examination---including
Advanced Placement, College Level Examination Program (CLEP), and
institutional challenge exams (the majority of these---in the records of
the NELS:88/2000---in foreign languages). Most of these credits were
earned either prior to matriculation or during the first term of
enrollment, though some were earned at later points in the student's
undergraduate career. The ACCELCRD values were set at three levels: more
than 4 credits, 1--4, and zero.

**Step 3: First-year Performance**

**LOWCRED (Less than 20 additive credits earned in the first calendar
year of**

**attendance)---** Carried forward from *Answers in the Tool Box.*

A dichotomous variable built on an analysis of the mean number of
additive credits (those that count toward degrees) earned by all
postsecondary students in the first calendar year following the date of
first enrollment. The threshold at which this broad population began to
earn any credentials (including certificates and associate degrees) was
20 credits (in the NELS:88/2000 population, 20.252 credits, to be
precise; s.e. = 1.016). LOWCRED is an early momentum indicator with
enduring consequences. As table L4 in Appendix L demonstrates, the more
additive credits earned in the first year, the more likely a degree will
be completed.

**FRSHGRAD (Grade point average in the first calendar year of
attendance)**---Carried

forward from the original *Tool Box.*

Grade point averages were determined for the first *full calendar year*
of postsecondary attendance, and were then set out in quintiles.
FRSHGRAD is a dichotomous variable that divides the highest two
quintiles from the other three. For the history of the HS&B/So used in
the original *Tool Box* study, the dividing line was 2.70. For that of
the NELS:88/2000 used in *The Tool- box Revisited*, the line is drawn at
2.88. The difference reflects the general trend in GPAs of the two
cohorts (see Adelman 2004a, table 6.1, p. 78).

**FREM (Any remedial course work in the first calendar year of
attendance)**---New in this

analysis.

FREM is a dichotomous variable marking students who took any remedial
courses during the first calendar year of attendance. Three variations
on first-year remediation were tried out in the process of arriving at
this formulation: one that focused only on remedial reading, another on
remedial math, and a third on all types of remediation. The dichotomous
version of the latter was the only form that could meet the minimal
statistical criteria for entrance into the stepwise logistic model and
allow us to track any association of early remediation with degree
completion.

**Step 4: Financial Aid**

In general, the NCES grade-cohort longitudinal studies have been weak on
financial aid information, where as the event-cohort Beginning
Postsecondary Students longitudinal studies have offered a panoply of
financing data. For example, if we were to ask about grants or
scholarships received in the first year of attendance (1995--96) for the
BPS:95/96--2001 by traditional-age students who attended a four-year
college at some time, we would find the information indicated in table
Glossary-1.

We would know, too, that for those who received grants/scholarships in
1995/96, the amount constituted an average of 69.3 percent (s.e. = 1.0)
of all aid received, and covered 33.4 percent (s.e. = 0.7) of the price
of attendance for the 1995--96 academic year. We could easily break
these averages out by type of institution first attended. And we would
know more, as the BPS:95/96--2001 covers PLUS (Parent Loan for
Undergraduate Students) loans, Perkins loans, Stafford loans (subsidized
and unsubsidized), need-based aid by source, merit-aid by source, Pell
grants, SEOG (Supplementary Educational Opportunity Grants) grants, and
other types of financial aid. If the grade-cohort longitudinal studies
such as the NELS:88/2000 had gathered even a third of this information,
a much richer analysis would be possible---though not necessarily an
analysis demonstrating a significant association of types, amounts, and
ratios of financial aid to degree completion.

![](media/image69.wmf)

**Step 5: Attendance Patterns**

**FOURTRAN (Transfer from one four-year college to another)**---New in
this analysis.

The algorithm for classic transfer from a community college to a
four-year college was fairly easy to construct. But to distinguish a
true four-year-to-four-year college transfer required an indirect route.
In the final survey of NELS longitudinal study (2000), respondents who
attended any postsecondary institution(s) were asked whether they ever
\"transferred credits.\" One cannot equate the yes/no answer to that
question with institutional transfer. One group of
four-year-to-four-year transfers was easy to identify: those who started
in a four-year college and earned a bachelor's degree from a different
four-year college. The second group was defined by the following
attendance characteristics: They started in a four-year college,
attended at least two four-year colleges, earned more than 30 credits
from four-year colleges, were *not* reverse transfers, and earned less
than 20 credits from community colleges and other sub-baccalaureate
institutions. For the most part, these students did not earn bachelor's
degrees, but they accumulated an average of 85.6 credits (s.e.=3.57)
from four-year colleges. Of those who did not earn a degree, 34.6
percent (s.e. = 4.17) were still enrolled and degree-candidates in 2000.

**MULTINS (Student attended more than one postsecondary institution as
an undergraduate)**---Carried forward from *Answers in the Tool Box.*

MULTINS is a dichotomous variable indicating that the student attended
more than one institution. This is a macro-vision of otherwise
multidirectional student behavior. One might suspect that when MULTINS,
TRANSFER, and FOURTRAN are in the same logistic model, at least one of
these variables will evidence an unacceptable degree of collinearity.
But within the context of the universe under study in *The Toolbox
Revisited*, the correlation between community college transfer
(TRANSFER) and MULTINS is 0.3363 and that between four-year-to-four-year
transfer (FOURTRAN) and MULTINS is 0.3246. These are modestly positive,
but not so high as to indicate collinearity problems. What that may mean
is that the three independent variables are making distinctly different
statements in the context of the logistic regressions in which they
appear.

**SUMMER (Number of credits earned during summer terms)---**New in this
analysis.

Attendance and credit generation during summer terms turned out to be a
strong proxy for high-octane persistence among community college
students (Adelman 2005a), and was, hence, brought into the model for the
population of those who attended a four-year college at any time. The
variable was set by three bands of the number of credits earned in this
manner: more than 4, 1--4, and 0. Some 54.8 percent (s.e. = 0.92) of all
1992 12th-graders who continued their education earned credits in at
least one summer term; 61.1 percent (s.e. = 0.96) of those who earned
more than 10 credits did so, as did 63.2 percent (s.e. = 1.10) of the
universe on which this essay focuses. Given the magnitude of those
percentages, it is not so much the fact of using summer terms, but the
volume of credit generation that should count.

**PARTTIME (Was the student's enrollment intensity *ever*
part-time?)**---New in this analysis.

The original *Tool Box* declined to confront part-time status and its
effects. If one is using transcripts as evidence, there are a number of
problems in determining which students are part-time and when. This
issue deserves extended attention, with support drawn from very
different data sources (see, e.g., O'Toole, Stratton, and Wetzel 2003).
Even if one standardizes credits on a semester metric across over 3000
institutions in the NELS:88/2000 postsecondary transcript files, it is
often difficult to know what is considered "part-time" in term X at
institution Y in program Z. With over 60 percent of students earning
credits in summer terms, we would be obligated to include such terms in
an account of enrollment intensity, and the question, "What is
'full-time' in a summer term?" would have to be answered in each
institution. In the last survey of the NELS:88/2000 cohort in 2000,
students were asked whether they had ever "attended less than full
time." Despite the ambiguity of the phrasing and students' understanding
of what \"less than full time means,\" student responses were accepted
as the first stage of creating a variable indicating part-time status at
some point in their careers. In their 1994 interviews, students were
also asked about their enrollment intensity status at the first
institution they attended. When they indicated part-time, that fact
overrode any denial of part-time status in their 2000 interview.
Proximate judgment supercedes retrospection.

The second stage in developing this rough proxy draws on the transcripts
and the notion of reducing credit load to part-time status. To identify
students who may start with a full-time schedule but reduce it to
part-time intensity by withdrawing from courses, we take the average
credit load per semester for bachelor's degree recipients---14.2
(average annual load of 30.8 minus the sum of summer-term credits,
credits by examination, and dual enrollment credits divided by
two)---and ask by what percentage that figure would have to fall to
bring the student's credit load below the threshold for full-time status
(12 credits). The answer is 16.2 percent. So for the sake of this crude
proxy measure, it is assumed that students who withdrew from attempted
credits at 16.2 percent rate or higher were---or became---part-time at
some time. With that group added to students who indicated part-time
status in the course of their 2000 interviews, the proportion of NELS
students who were part-time at some time in the undergraduate careers
was 47.4 percent---compared with 48.2 percent of traditional-age
students in the BPS longitudinal study of 1995/96--2001 (for an account
of enrollment intensity in both data sets, see Appendix L, table L5).

**Step 6: Extended Postsecondary Performance**

**REMPROB (Nature and intensity of remedial work)***---*Carried forward
from *Answers in the Tool Box.*

In both the original *Tool Box* and *The Toolbox Revisited*, REMPROB
describes the nature and extent of a student's remedial course work
without the boundary of the first calendar year of attendance. For that
reason, when REMPROB is tried out in the logistic narrative at the stage
of extended postsecondary performance, it replaces the freshman year
remediation variable (FREM).

REMPROB is created by an if-then-else logic that starts with remedial
reading as the most serious of remedial problems,[^73] and works its
logical steps as follows:

1.  Any remedial reading

2\. Two or more remedial courses (not reading, and, if math, more than
two)

3.  One or two courses of remedial mathematics only

4\. One remedial course (not reading, not math, thus leaving writing,

language arts, and general basic skills)

5\. No remedial course work

For the sake of presentation in the logistic sequence, REMPROB is a
dichotomous variable in which remedial reading plus more than one
remedial course falls on one side of the border, and

all other remediation (including no remediation) on the other side. In
the original *Tool Box*, REMPROB was admitted into the model, but did
not reach the threshold of statistical signifi- cance. In *The Toolbox
Revisited*, REMPROB did not meet the minimum statistical standard for
entry into the model when it replaced the freshman year remediation
variable in Step 6.

**TREND (Trend in student's grade point average)**---Modified from
previous presentation in

the original *Tool Box.*

This variable describes the trend in a student's postsecondary grade
point average (GPA), and applies only to those students with complete
undergraduate transcript records and computable GPAs. In its original
*Tool Box* version, two reference points were used: end of the first
calendar year GPA, and final undergraduate GPA. From these two markers,
one could observe whether GPA was rising, flat, or falling, using a
ratio of final GPA to first-year GPA. Ratios in the .95 to 1.05 range
were judged to indicate no change, with ratios above 1.05 indicating a
rising GPA, and ratios below 0.95 indicating a falling GPA. For a
slightly better set of markers, the NELS:88/2000 postsecondary
transcript files thus added a variable for GPA two years after entry,
thus providing three points of reference. With three points of
reference, ratios are not invoked, rather relationships (greater, less
than, or equal to)---and at three points in time. From the permutations
of these relationships one can determine whether the trend was rising,
flat/inconsistent, or falling.

**CUMMATH (Number of credits earned in college-level
mathematics)**---New in this analysis.

This variable, setting out cumulative credits earned in college-level
mathematics in three bands (more than four, 1--4, and 0) replaces the
parallel variable for first-year college-level mathematics credits in
the context of an extended postsecondary history account. The motivation
for including this curriculum marker is the same: Even if postsecondary
students do not concentrate their studies in science, technology,
engineering, or mathematics/computer science (STEM), their quantitative
background will be called upon (in business and the social sciences, in
particular). Student academic momentum, it is hypothesized, will be as
much enhanced by quantitative study on the post-matriculation side of
education history as it was in secondary school.

**CHANMAJ (Change of major)**---New in this analysis.

If transcripts are our principal source of evidence, the only moment at
which we are sure of a student's major is the moment of degree award.
Sometimes, the NELS:88/2000 transcripts with no degree indicated a
major, which was verified by hand-and-eye reading by two judges only
when the transcript carried a minimum of 15 credits and the major field
indicated carried a minimum of 12. But that still leaves a large swath
of missing accounts of students' major. It is wholly possible, for
example, that a student earning a B.S. in computer science changed
majors twice along the way, and in two different institutions. It is
also possible that a nondegree transcript had no disciplinary character
to it at all while the student indicated he or she was majoring in X. In
the matter of major---and change-of-major---the transcript is not as
credible as the student. So the last NELS survey in 2000 asked students
whether they had changed majors at any time, but unfortunately did not
ask "from what to what."

A dichotomous change-of-major variable was developed and tried out for
this study. Basically, it took the universe of students who said they
changed majors, and added to that universe community college transfer
students who moved from general studies to a discrete major, and cases
where the student presented two transcripts with no degrees but
different majors. It also took student responses in 1994 to questions
about their major at the first institution attended and that at the most
recent institution attended. Where the student reported two different
disciplinary majors, e.g. electrical engineering at the first
institution and biology at the most recent institution, that, too, was
marked as a change of major no matter what the student told interviewers
in 2000. Unfortunately, all these steps created a collinearity problem
with the TRANSFER variable, and CHANMAJ did not qualify for entrance
into the logistic narrative. On the other hand, it was admitted and
played a notable role in the linear account of time to degree (see
Appendix J).

**Step 7: Final Model**

**NOSTOP** **(Continuous enrollment)**---Carried forward from *Answers
in the Tool Box.*

Given the extended potential undergraduate periods of 12 years (National
Longitudinal Study of the High School Class of 1972), 11 years (High
School and Beyond/Sophomores), or 8.5 years (NELS:88/2000), it makes no
sense to describe stop-out behavior as one semester or its equivalent.
In all three NCES postsecondary transcript-based grade-cohort studies,
non-continuous enrollment was defined as *more than* a one semester (or
its equivalent, e.g., two quarters) stop-out period. In the dichotomous
variable, NOSTOP, the student is considered continuously enrolled even
with one semester (or two quarters) off. From the moment of its
introduction, NOSTOP was the strongest independent variable in the
logistic narrative of the original *Tool Box*.

**WRPT Ratio (Ratio of non-penalty withdrawal and no-credit repeat
grades to all grades**

**received)---**Carried forward from the original *Tool Box.*

In the original *Tool Box*, this variable was called the DWI (drops,
withdrawals, and incompletes) index. DWI is not a wholly accurate
acronym. What is really described is a ratio in which the number of
courses from which the student withdrew without penalty *plus* those the
student repeated is the numerator, and the total number of courses in
which the student enrolled is the denominator. The ratio counts course
attempts, not credits. Withdrawals without penalty are not the same as
courses "dropped" within set periods that most colleges and community
colleges mark for "drop-and-add." Courses "dropped" are not included in
the ratio. Nothing here involves penalty grades. All cases at issue are
noncredit grades. The variable WRPT ratio is dichotomous: On one side of
the dividing line are students who withdrew from or repeated 20 percent
or more of all courses in which they enrolled.

[^1]: Out of print but available at
    http://www.ed.gov/students/prep/college/thinkcollege/early/aboutus/edlite-resources.html.

[^2]: The first was the National Longitudinal Study of the High School
    Class of 1972 (1972--86).

[^3]: For a description of the grade-cohort studies, see Appendix B.

[^4]: A fourth-grade-cohort longitudinal study is currently in progress.
    Called the ELS2002, it began with a national sample of 10th-graders
    in 2002 and is expected to run at least through 2012. We obviously
    will have to wait some years before we see its full results.

[^5]: For an account of changes in high school graduation requirements
    in the years immediately following issuance of *A Nation at Risk*,
    see Stedman and Jordan (1986).

[^6]: For African-American students in the HS&B/So who reached the 12th
    grade and entered postsecondary education, 52.3 percent started in
    four-year colleges, a percentage that rose to 54.2 in the
    NELS:88/2000. The comparable percentages for Latino students, who
    are more likely to start in community colleges, were 38.9 percent
    for the HS&B/So and 38.6 percent for the NELS:88/2000. For white
    students, the proportions starting in four-year colleges were 54.3
    percent for the HS&B/So and 57.4 percent in the NELS:88/2000.

[^7]: Odds ratios, as Peng, So, Stage, and St. John (2002) remind us,
    are not odds. Their interpretation is not as transparent as the
    original *Tool Box* assumed them to be. And while an R^2^ statistic
    is presented in the logistic tables of this study, it cannot be read
    the way one would interpret an R^2^ in a linear regression, i.e., it
    does not indicate the percent of variance in the dependent variable
    that is explained by the independent variables (Long, 1997). For
    that reason, it is called a \"pseudo R^2^\" (Cabrera 1994) and is
    one of a number of measures of goodness-of-fit. As blocks of
    variables are added to the model in the stepwise manner followed
    here, the pseudo R^2^ should increase.

[^8]: For the computation of Delta-p, I am using a shortcut recommended
    by Paul Allison of the University of Pennsylvania: *b*p(1-p), where
    *b* is the logistic coefficient and p is the probability for the
    dependent variable in the model. This heuristic produces slightly
    higher values than the formula advanced by Petersen (1985).

[^9]: For all technical issues, please see Appendix D.

[^10]: For details on the high school graduation status of those who
    were eighth-graders in 1988, see Appendix L, table L1.

[^11]: For details on those in the NELS:88/2000 cohort who, though in
    the 12th grade in 1992 along with others, had previously been held
    back at least one year in the course of their schooling, see
    Appendix L, table L2.

[^12]: Only 21.3 percent (s.e. = 1.17) of the NELS:88/2000 who were in
    the 12th grade in 1992 were missing high school transcripts,
    compared with 73.7 percent (s.e. = 2.58) of those who had either
    dropped out of high school or were not in-grade. Nearly 100 percent
    of the former group graduated from high school with a standard
    diploma.

[^13]: The reader should note that, unlike the High School &
    Beyond/Sophomore cohort study, the NELS:88/2000 sample was
    \"refreshed\" in 1992 to be representative of 12th-graders in that
    year. The \"refreshed\" students are included in our analyses.

[^14]: The difference in the African-American proportion of the two
    universes is not statistically significant.

[^15]: Nonnative speakers were defined as those who said their first
    language was not English and, in grade 10 and/or 12 (the 1992
    survey) indicated that they spoke to their mothers most or all of
    the time in their first language.

[^16]: Though to the extent to which the group includes students who
    commenced their postsecondary studies in community colleges---and it
    does---that majority will be a little less.

[^17]: Institutional selectivity in the postsecondary files of all three
    grade-cohort longitudinal studies conducted by the National Center
    for Education Statistics has five values: highly selective,
    selective, nonselective, open-door, and not ratable. The first three
    of these values were based on the selectivity cells developed by the
    Cooperative Institutional Research Project (CIRP) at UCLA for its
    annual survey (since 1966) or entering freshmen. For the
    distribution of NELS:88/2000 postsecondary students by selectivity
    of first institution attended, see Appendix L, table L3.

[^18]: The category of \"calculus\" includes not only the standard
    sequence but also special \"short calculus\" or \"brief calculus\"
    courses, and specialized introductions to calculus for business,
    economics, and life science majors.

[^19]: Even there, the variable floated in and out of significance over
    the steps of the logistic model (see Adelman 1999, pp. 80--81).

[^20]: A Carnegie unit is the basic credit system for U.S. secondary
    schools. It is generally recognized as representing a full year
    (36--40 weeks) in a specific class meeting four or five times per
    week for 40--50 minutes per class session (Martinez and Bray 2002).

[^21]: It is important to note that the Carnegie unit thresholds
    indicated, e.g., 3.75 units of English, are not determined *a
    priori*, but rather from the empirical distribution of Carnegie
    units standardized across the NELS high school transcripts in their
    edited version. See the descriptive windows for all the high school
    curriculum variables on the NCES data sets in CD \# 2003-402 and its
    June 2004 Supplement.

[^22]: For mean numbers of Carnegie units earned in major curriculum
    areas, see Appendix L, table L6.

[^23]: The National Longitudinal Study of the High School Class of 1972,
    the first, most elaborate, and longest (1972--86) of the NCES
    grade-cohort longitudinal studies

[^24]: The High School Class of 1982 data in table 7 are slightly
    different from those in the previous presentation in *Answers in the
    Tool Box* (table 6, page 17) because a more accurate 12th-grade flag
    for that data set has been developed to match the NELS:88/2000.

[^25]: Among all NELS:88/2000 students who participated in the 1992
    survey and subsequently attended *only* community colleges, 64.5
    percent (s.e. = 1.88) took at least one remedial course and 43.7
    percent (s.e. = 1.98) took more than one. Among those who attended
    only sub-baccalaureate trade schools, which often do not require
    remediation, 32.4 percent (s.e. = 5.89) took at least one remedial
    course and 21.9 percent (s.e. = 6.07) took more than one. There is a
    considerable difference between the norms and requirements of
    community colleges versus those of other sub-baccalaureate
    institutions in the matter of remediation, and we should not mix the
    two in analyses of remediation.

[^26]: Financial aid comes *after* first-year performance because the
    story line is more interested in the potential relationship of aid
    to completion among those who are *already enrolled*. If the topic
    was initial access, then the financial aid package for the first
    year would be part of the postsecondary entry configuration of
    variables. The NELS:88/2000 unfortunately does not allow us to
    distinguish modes of financing postsecondary education in the first
    year from those of the second year.

[^27]: Those who earned a high school diploma of any kind *after*
    December 1996 constituted 2.7 percent of all 1992 12th-graders (s.e.
    = 0.16) and 0.7 percent of all 1992 12th-graders who subsequently
    attended a four-year college (s.e.= 0.16).

[^28]: The "true" first institution of attendance excludes (1) colleges
    and community colleges in which the student was enrolled prior to
    high school graduation; (2) institutions in which the student was
    enrolled during the summer immediately following high school
    graduation and prior to fall term postsecondary entry (unless the
    institution was the same in both periods); and (3) "false starts,"
    that is, cases in which the student enrolled, but then withdrew
    during the first term of attendance, only to enroll and complete
    course work in a different institution at a later point in time (in
    these cases, the second institution is the "true first
    institution"). The true first *date* of attendance is the first
    month of enrollment at the true first institution.

[^29]: Hanson's (1998) list from the University of Texas at Austin
    ranges from Ecology, Evolution, and Society, to Introduction to U.S.
    and Texas Government, to General Psychology, to Calculus I and II
    for Science and Engineering Students.

[^30]: For more discrete details on credits earned in college-level
    mathematics, the reader is directed to table

    L9, Appendix L.

[^31]: National Center for Education Statistics, BPS95/96--2001 Data
    Analysis System; NCES 2003-173.

[^32]: Nora, Barlow, and Crisp (2005) offer a potentially promising
    analysis of a cohort at one nonselective four-year institution that
    is undercut somewhat by lack of data on age distribution and the
    fact that retention and six-year graduation rates are confined to
    that institution. But the authors include cumulative GPA to the
    second year, enrollment intensity, remediation, three core courses
    (what this study calls \"gateways\"), and a rough course withdrawal
    factor---all of which speak in favor of their approach.

[^33]: As Tinto (1987) noted, "The point of retention efforts is not
    merely that individuals be kept in college, but that they be
    retained so as to be further educated." (p. 136) Poor retention
    quality significantly lowers the odds of further education.

[^34]: The persistence rates for all 1992 12th-graders noted in this
    paragraph are slightly different from those previously reported
    (Adelman 2004a, table 3.4, p. 42), where the weight for known
    postsecondary participants (not the weight for students with
    complete records) was used.

[^35]: Compressed signals are used to mark extremes of academic
    performance. The American Association of Collegiate Registrars and
    Admissions Officers has reported that 90 percent of its member
    institutions enter graduation with honors on transcripts (AACRAO
    2002), and, in a 2005 survey of transcript practices , found that 70
    percent enter academic probation or dismissal
    (www.aacrao.org/pro_development/surveys/transcript05.htm).

[^36]: The most recent version, *Taxonomy of Postsecondary Courses Based
    on the National Transcript Samples, 2003*, is available at
    www.ed.gov/rschstat/research/pubs/empircurr/index.html.

[^37]: Though their enrollments were substantial, physical education
    activities, health information, physical conditioning, orientation,
    and personal development courses were excluded.

[^38]: The variable for cumulative credits to the end of the second
    calendar academic year was constructed in a manner different from
    the dichotomous presentation of first calendar academic year
    credits. Cumulative credits is a categorical variable with four
    levels based on empirical mean credits earned and standard deviation
    (49 and 19 respectively): 0--29, 30--49, 50--69, and 70 or more.

[^39]: \"Non-incidental\" means students who earned more than 10 credits
    in their undergraduate careers. Those who earned 10 or fewer credits
    do not accumulate enough history for analysis of attendance
    patterns.

[^40]: Kuh et al. (2001) found that 53.2 percent of the 32 thousand
    seniors who participated in the 2000 National Survey of Student
    Engagement had attended more than one institution.

[^41]: Up to 12 years for the High School Class of 1972 (NLS-72), 11
    years for the High School Class of 1982 (HS&B/So), and 8.5 years for
    the High School Class of 1992 (NELS:88/2000).

[^42]: Only 5.4 percent (s.e. = 1.54) of NELS students who started in
    highly selective four-year colleges transferred to another four-year
    college, versus 15.7 percent (s.e. = 1.71) for those who began in
    selective institutions and 20.0 percent (s.e. = 0.99) for those who
    started in nonselective four-year schools.

[^43]: Adelman (1999), table 39, pp. 80-81.

[^44]: In a case of a continuous dependent variable for student
    engagement, and sets of independent variables describing both
    student and institutional characteristics (half of them continuous),
    Porter (2005) demonstrates the statistical superiority of multilevel
    analysis versus Ordinary Least Squares analysis. There are three
    significant differences between Porter's illustration and the story
    line of *The* *Toolbox Revisited* : (1) the dependent variable
    (bachelor's degree attainment) and most of the independent variables
    in this data essay are dichotomous, hence, our method is logistic,
    not linear, (2) Porter's model assumes that students attend only one
    institution, whereas more than half the students in this analysis
    attended two or more, and (3) while multilevel analyses can create
    models for institutions \"even for schools with few student
    observations\" (Porter 2005, p. 110), of the 3,258 institutions in
    the NELS:88/2000 postsecondary transcript files, 1,003 had only one
    student in the sample. An institution-level model with a population
    of one is out-of-scope.

[^45]: Kuh et al. (2001) reported that less than 20 percent of seniors
    in 2000 indicated experiencing these modes of nonstandard faculty
    contact. By 2004, that proportion had not changed, while 58 percent
    of seniors indicated they had talked often or very often with
    faculty outside of class about their grades (a ritualistic
    interaction). See www.nsse.iub.edu/\~nsse/2004_annual\_
    report/html/responses \_senior sfi.html. (Accessed 7/31/05).

[^46]: There are other large longitudinal studies of degree completion,
    but their samples of institutions and students are not
    representative. For example, Saupe, Smith and Xin (1999) used the
    Consortium for Student Retention Data Exchange information from 174
    public four-year colleges to track six-year (1989--96) institutional
    graduation rates. While these 174 institutions enrolled nearly half
    of entering four-year college students in 1989, they represent a
    class, not a universe. For another, but more dated example,
    Stoecker, Pascarella, and Wolfle (1988) used a 1980 CIRP follow-up
    to an initial 1971 sample of roughly 10,000 students who had
    attended only one four-year college in the interim. Some 487 college
    and universities were represented. Stocker, Pascarella, and Wolfle
    were interested in institutional effects, so their restriction of
    the universe to students who had attended only one school is
    justified, and their findings revealing. But that doesn't justify
    using the conclusions as a generalized model of degree
    completion---certainly not under contemporary conditions of student
    mobility. For state-level postsecondary longitudinal studies, only
    Florida has produced data sets comparable to the national accounts.

[^47]: Some 7.4 percent (s.e. = 0.56) of white students earned between
    15 and 19 credits in their first calendar year of attendance,
    compared with 11.1 (s.e.=1.86) of African-Americans and 18.5 percent
    (s.e. = 3.30) of Latinos.

[^48]: The Pacific census division includes California, Oregon,
    Washington, Alaska, and Hawaii; the Southwest Central encompasses
    Texas, Oklahoma, Arkansas, and Louisiana.

[^49]: Some 8.3 percent (s.e.= 0.68) of white students were in the high
    ratio category, versus 12.2 percent

    (s.e. = 3.04) of Asian students, 12.3 percent (s.e. = 1.96) of
    African-American students, and 19.6 percent

[^50]: There were too few American Indians in the base group to follow
    through a narrowing population as conditions for academic momentum
    were added.

[^51]: Dual enrollment has made huge strides since the NELS:88/2000
    cohort went to high school. Some 38 states now have formal policies
    (Karp, Bailey, Hughes, and Fermin 2004), though these vary widely in
    terms of what is offered and by whom, who pays tuition, who gets
    credit toward what, academic eligibility, grade levels, course
    enrollment limits, and whether credits earned are placed in escrow
    (though that varies more by institution than state). The 2002--03
    NCES survey of dual enrollment practices at postsecondary
    institutions distinguished between high school students who took
    courses within formal agreements and those who took courses outside
    of those agreements. Our NELS:88/2000 transcript data cannot make
    that distinction, so they lump together all postsecondary credits
    earned at colleges or community colleges prior to the date of high
    school graduation.

    Kleiner and Lewis (2005) estimate that 813,000 high school students
    took courses at postsecondary institutions, either within and/or
    outside of dual enrollment programs and agreements, in 2002--03,
    compared with the weighted 213,000 NELS:88/2000 students who earned
    any postsecondary credits through dual enrollment during their high
    school years (1989--92). While not exactly comparable populations,
    those figures are testimony to the growth of student participation
    in these arrangements.

[^52]: For example, consider the following statement in a respectable
    publication: \"One of the key reasons that low income students have
    such low completion rates in postsecondary education is that many
    work long hours in order to be able to afford college. They struggle
    to balance work with part-time enrollment in college . . .\" (Allen,
    Goldberger, and Steinberg 2004, p. 222). The data source for this
    assertion is the National Postsecondary Student Aid Study of 2000, a
    one-year snapshot that includes no \"completion rate\" data.
    Analyses of the NPSAS 2000 data files show that the statement does
    not reach the threshold of justification unless one divides the
    population by age bracket. At that point, one finds that, and among
    traditional-age students (presumably the group referenced by the
    scare), poor kids are no more likely to be working longer hours at
    their jobs than anyone else, though they are more likely to use
    their wages for education expenses. That, at least, is an honest
    statement---for a snapshot population. And it is not what we really
    would want to know.

[^53]: There has never been a national longitudinal study of
    ninth-graders. But we do have a national longitudinal study of
    eighth-graders---the NELS:88/2000---with transcripts, not
    imputations, projections, and dubious math. If we follow these
    eighth-graders, including high school dropouts, all the way through
    to age 26, ultimately 34 percent earned either an associate or
    bachelor's degree (see the full account offered in Appendix L, table
    L12). That percentage at least puts us in range of doing better. If
    we accept the putative (and utterly false) 18 percent, we risk
    abandoning all hope and effort.

[^54]: Curtin, T.R., Ingels, S.J., Wu, S., and Heuer, R (2002).
    *National Education Longitudinal Study of 1988: Base-Year to Fourth
    Follow-up Data File User's Manual* (NCES 2003-323). Washington, DC:
    U.S. Department of Education, National Center for Education
    Statistics (http://nces.ed.gov/pubs2002/2002323.pdf, p.3).

[^55]: As Lucas and Berends (2002) remind us, the high schools attended
    by students in the NELS study are not a true representative sample.
    The reason stems from the decision to begin the longitudinal study
    in the eighth grade. When students move into high schools from the
    eighth grade (or, in some districts, from the ninth grade), it is
    impossible for the sampling framework to be based on high schools.
    Roughly 1,000 middle schools and junior high schools became 4,000
    high schools by grade 10, and there was no way to follow the
    students into all 4,000 of those schools. So the NELS sample was
    refreshed in 10th and 12th grades to reflect the total enrolled
    population in those years (Ingels et al. 1994), and , by necessity,
    the refreshing was based in the high schools in which the vast
    majority of the existing NELS cohort students were enrolled.

[^56]: See the brief discussion of financial aid data in the
    NELS:88/2000 in Adelman, C. *Principal Indicators of Student
    Academic Histories in Postsecondary Education, 1972-2000*.
    Washington, DC: U.S. Department of Education, 2004, p. 98.

[^57]: See NCES 2002b.

[^58]: Curtin, Ingels, Wu, and Heuer (2002) report the mean DEFT for all
    students in the fourth follow-up (2000) survey of the NELS as 1.954
    (p. 209). The range of DEFTs in *The Toolbox Revisited* is 1.76 to
    2.19.

[^59]: All data in this paragraph were generated from the National
    Center for Education Statistics: Baccalaureate and Beyond
    Longitudinal Study, 2000: Data Analysis System.

[^60]: The research here involved a \"competing risks\" model in which
    the histories of students who had never stopped out were compared to
    the histories of those who had stopped out, hence, embraced both
    elapsed and enrolled time.

[^61]: Knight's list for a "hypothesized model of effects upon total
    semesters elapsed" (Knight 2002, p. 6) also includes provisions for
    variables derived from student surveys that are parallel to those
    used in the National Survey of Student Engagement, e.g., in Kuh et
    al. 2001.

[^62]: The small number of NELS:88/2000 bachelor's recipients who
    completed the degree in three elapsed calendar years or less entered
    with a mean of 10.6 acceleration credits (s.e. = 2.81) and
    subsequently accumulated a mean of 12.2 credits during summer terms
    (s.e. = 1.94).

[^63]: Broh (1991) presented an intriguing argument for an alternative
    time to degree calculation that began with the *median*, not the
    mean, and included students who had not finished the degree but who
    were still enrolled as degree candidates. In *The Toolbox
    Revisited*, the median for students who had completed degrees is
    4.24 calendar years. Including students who had not earned degrees
    by December 2000 but who were still enrolled as bachelor's
    candidates, the median time to degree would be 4.49---very close to
    the mean of 4.58.

[^64]: For the GDP deflator calculator, go to
    http://www1.jsc.nasa.gov/bu2/inflateGDP.html

[^65]: These percentages are based on the entire panel of participants
    in 1992 who also participated in the 1994 and 2000 follow-up
    surveys.

[^66]: Georges (2000) used a similar level-of-expectations by
    consistency-of-expectations construct for parental visions of their
    children's future education in the NELS:88/2000 cohort. Parents were
    interviewed on this issue when students were in the eighth grade and
    again when students were scheduled to be in the 12th grade.

[^67]: Among the divergent policies found by the College Board (1998):
    (a) 9 percent of high schools do not use A-F or numeric grading
    systems; (b) 8 percent of high schools do not give credit for grades
    lower than C-; (c) 19 percent of high schools are in districts where
    grading systems vary; and (d) 43 percent of high schools exclude
    some courses when calculating GPA.

[^68]: In its survey of high school grading practices, the College Board
    (1998) found that 19 percent of high schools did not calculate class
    rank.

[^69]: NCES CD 2003-402.

[^70]: See indicator #14 in *The Condition of Education, 1999*.
    Washington, D.C.: National Center for Education Statistics, 1999, p.
    56.

[^71]: This approach began by isolating students who were consistent in
    their claims to have taken an \"advanced placement course,\" planned
    to take an AP test, and reported taking at least one AP test between
    1990 and 1993. From this group, those for whom AP course work had
    already been recorded were dropped. The balance were first matched
    against the HIGHMATH variable. For students who reached calculus or
    precalculus, responses to another question as to whether they took
    the course to earn college credit were invoked. If the student
    responded positively, the record was credited with an AP course.
    College transcripts were also examined for foreign language study at
    advanced levels in the first year of attendance (along with more
    than 2 years of foreign language study in high school), etc. Where
    matches were found, the student record was credited with an AP
    course.

[^72]: Institutional selectivity in the postsecondary files of all three
    grade-cohort longitudinal studies conducted by the National Center
    for Education Statistics has five values: highly selective,
    selective, nonselective, open-door, and not ratable. The first three
    of these values were based on the selectivity cells developed by the
    Cooperative Institutional Research Project (CIRP) at UCLA for its
    annual survey (since 1966) of entering freshmen. Community colleges
    and area vocational-technical institutes (AVTIs) were assigned the
    value of "open-door." Theological seminaries, music conservatories,
    and sub-baccalaureate vocational schools were considered "not
    ratable."

[^73]: For an elaboration of REMPROB in relation to student demographic
    backgrounds, high school performance, and degree attainment, see
    Adelman 2004a, pp. 87--94, and Wirt, et al. (2000), indicator 14, p.
    52 and supplemental tables (p. 152).