Retaking the SAT
Jacob L. Vigdor Charles T. Clotfelter
a b s t r a c t
Using data on applicants to three selective universities, we analyze a col- lege applicant’s decision to retake the SAT. We model this decision as an
optimal search problem, and use the model to assess the impact of col- lege admissions policies on retaking behavior. The most common test
score ranking policy, which utilizes only the highest of all submitted scores, provides large incentives to retake the test. This places certain
applicants at a disadvantage: those with high test-taking costs, those attaching low values to college admission, and those with ‘‘pessimistic’’
prior beliefs regarding their own ability.
I. Introduction
As the nation’s premier college entrance exam, the SAT holds an undeniably important role in who gets into college, particularly into the most selec-
tive colleges. Yet it has been the subject of intense scrutiny in recent years,
1
with a growing list of colleges and the University of California system having made or
proposed to make the test an optional admissions requirement.
2
Critics of the test
Jacob L. Vigdor is an assistant professor of public policy studies and economics at Duke University, Box 90245, Durham NC 27708, e-mail: jvigdorpps.duke.edu. Charles T. Clotfelter is Z. Smith Reyn-
olds Professor of public policy studies, economics, and law at Duke University and National Bureau of Economic Research, Box 90245, Durham, NC 27708, email: cltfltrpps.duke.edu. The authors are
grateful to Christopher Avery, Charles Brown, Philip Cook, Helen Ladd, three anonymous referees, and seminar participants at Duke, Vanderbilt, the APPAM 2001 fall conference, the 2002 AEA meet-
ings, Chicago GSB, and the NBER higher education working group for helpful comments, to Gary Barnes for assistance in obtaining the data, and to Robert Malme and Margaret Lieberman for re-
search assistance. [Submitted March 2002; accepted May 2002]
ISSN 022-166X
2003 by the Board of Regents of the University of Wisconsin System 1. The test is officially referred to as the SAT I. Formerly known as the Scholastic Aptitude Test, the
exam is now named for its former acronym. We will refer to the exam as the SAT in this paper. 2. See Lemann 1999 and Schemo 2001.
T H E J O U R N A L O F H U M A N R E S O U R C E S • X X X V I I I • 1
2 The Journal of Human Resources
Table 1 Frequency of Retaking the SAT, All U.S. Test Takers and Applicants to Three
Universities
U.S., 1997 Applicants to Three
Graduating Class
a
Universities for Fall 1998
b
Number of students 1,119,984
22,678 Percentage who took SAT I
Once 50.7
17.8 Twice
38.1 48.7
Three times 9.6
27.0 Four times
1.4 Four or more times
6.5 Five times
0.2 Total
100.0 100.0
a. Based on students who took SAT I one to five times in their junior or senior years. Source: College Board, Handbook for the SAT Program 1999–2000 1999, Table 6b.
b. Source: College Board and unpublished admissions data on 1998 applicants to three universities, au- thors’ calculations.
cite various kinds of bias and decry the test as an inappropriate apparatus for selecting a ruling class. ‘‘The Big Test,’’ as Lemann 1999 terms it, has drawn a significant
amount of attention from academic researchers. Several studies have attempted to explain variation in SAT scores across states Graham and Husted 1993 or individ-
ual test takers Dynarski 1985. SAT scores have frequently been used as an outcome measure in evaluating characteristics of school systems Dynarski and Gleason 1993;
Southwick and Gill 1997; Card and Payne 1998; see Hanushek and Taylor 1990, for a critique of this strategy or a measure of ability Ballou and Podgursky 1995.
Additional research has investigated the predictive relationship between SAT scores and college outcomes Boldt, Centra, and Courtney 1986; Bowen and Bok 1998;
Rothstein 2002.
Despite this considerable controversy and analysis, very little attention has been paid to test-taking behavior itself. One important component of this behavior is the
tendency for many college applicants to take the test multiple times. Nationwide roughly half of these who take the SAT do so more than once, and the rate of retaking
appears to be even higher for students applying to selective institutions, as indicated by the calculated rates of retaking among applicants to three selective universities,
presented in Table 1. If these students are retaking the SAT in hopes of improving their standing with college admissions offices, these hopes are often fulfilled, owing
to two factors. The first is the widespread policy stated by college admissions offices to use only the highest score actually, the sum of the highest verbal and the highest
math score, even if these scores were obtained on different dates for purposes of ranking applicants, ignoring the scores from all other attempts. Although this policy
Vigdor and Clotfelter 3
is not used universally, it is by far the most common among institutions that publicly reveal them.
3
The second reason why retaking the SAT often pays off is the actual tendency for test takers to score higher when they retake the test. This tendency, revealed
both in our data on applicants to three colleges and in nationwide College Board data, could theoretically be attributable to selection into the pool of retakers. We
present evidence below to suggest that the gains associated with retaking the test are too large to be attributed to selection alone, and thus reflect benefits associated
with familiarity or increases in knowledge between administrations.
From the standpoint of public policy, the subject of retaking is worth exploring for both equity and efficiency reasons. First, retaking is important to the extent that,
in combination with the highest-score policy noted above, it affects admissions out- comes. It seems intuitive that the current highest-score policy provides an advantage
to applicants with low costs of taking the test. Our results confirm this intuition. In light of the growing scrutiny of race-conscious college admissions criteria within
the larger national debate over affirmative action, it is important to ask whether the ‘‘high-cost’’ applicants now disadvantaged by current policy are drawn selectively
from certain groups—including racial minorities and the poor. If so, then the current policy almost surely warrants scrutiny.
Another reason to study retaking is allocative efficiency: such activity employs resources that have valuable alternative uses, and our results suggest that the current
highest-score policy strongly encourages retaking.
4
If colleges could obtain much the same information by following other policies that result in less test-taking, the
current highest-score policy could justifiably be faulted as inefficient. It might be
3. We examined the admissions websites of the 50 top-ranked universities and the 50 top-ranked liberal arts colleges, according to U.S. News and World Report. Of fourteen that made a statement about how
multiple SAT scores are treated in admissions decisions, ten explicitly stated the highest-score policy as described in the text, three specified the highest combined score at one sitting, and one said ‘‘primary
consideration’’ would be given to the highest individual scores. Eight of the sampled colleges do not require the SAT, and the remainder stated no explicit policy on multiple scores.
The possibility exists, of course, that admissions committees, contrary to their stated policies, in practice make some adjustment in the case of applicants who have taken the test many times. Christopher Avery
has shown us unpublished evidence that applicants who take more than one SAT are less likely to be admitted to selective colleges, controlling for their highest math and verbal scores and certain other
characteristics. This evidence might indicate that multiple takers are penalized, or that multiple test tak- ing is correlated with negative factors observable to admissions officers but not econometricians. In
any event, the magnitude of the penalty Avery observes is not sufficient to offset the benefits of retak- ing revealed below. The informal conversations we have had with admissions officers lead us to believe
that most selective colleges do indeed follow the stated policy of using the highest math and verbal scores.
4. Consider the following rough estimate of the costs associated with retaking. The College Board reports that 1.3 million applicants seeking college admission in 2001 took the SAT, and the average applicant
took the test 1.7 times. These figures imply that about one million unnecessary tests were administered to the high school class of 2001. Costs associated with each of these include the basic fee of 25, the
value of time spent taking the test, and the disutility associated with the act of test-taking. Valuing the four hours of test-taking time at the Federal minimum wage, and setting the psychic costs equal to direct
and opportunity costs, we arrive at an estimate of 90 million per year. A similar calculation can be performed for applicants taking the ACT rather than the SAT.
4 The Journal of Human Resources
more efficient, for example, if colleges were to use the average of an applicant’s SAT scores instead of the highest, if such a policy reduced the amount of retaking
without significant loss of information.
5
This paper examines retaking and its consequences using data on the undergradu- ate applicants to three selective research universities. Section II describes the data
and Section III examines the characteristics of those applicants who retake the SAT. We are especially interested in finding out whether the tendency to retake the SAT
differs by gender, race, or socioeconomic status. The fourth section of the paper discusses the reasons why test scores tend to increase upon retaking. Section V dis-
cusses a model of retaking. The applicant’s problem is analogous to one of optimal search: additional draws from a distribution of possible test scores can be had for
a certain cost, and the applicant must decide whether the expected benefits of retaking exceed this cost. The sixth section reports the results of simulations that investigate
the impact of college test score ranking policies on the frequency of retaking. The simulations are calibrated to match observed behavior under current policy. Alterna-
tive test score ranking policies are compared along four criteria: accuracy does rank- ing reflect true ability?, precision are the ranking errors small?, bias does the
policy disproportionately favor certain groups?, and resource cost how costly is the policy in terms of time and money spent taking the test?. Of nine policies com-
pared, the current highest-score policy turns out to be the costliest, least accurate, and most biased. It may serve other interests of colleges, however, as we note in
the paper’s final section. Following the simulations, we use our data to determine the impact that one particular policy change, limiting consideration to a student’s
first SAT only, might have on applicant rankings. Section VII concludes the analysis.
Although the data that we use are very instructive, two of their limitations should be noted at the outset. First, the institutions to which these data apply are not repre-
sentative of all colleges and universities in the country. Thus, the results should be thought of as applying most to institutions with selective admissions. Second, no
information is available in this data set on the potentially important activity of coach- ing and test preparation courses. If equity concerns are raised by differences between
groups in the frequency of retaking, then differences in the access to test preparation courses should also be of concern.
6
Given the nature of our data, we are simply unable to address this issue. Moreover, we would emphasize that our analysis is
incomplete to the extent that it focuses on one aspect of behavior—retaking—but not on other aspects that might be involved as individuals respond to incentives
created by colleges’ admissions policies. Two such aspects are decisions about when to take the test and what kinds of preparation to make before taking the test. We
return to this issue in Section VII.
5. As discussed in the concluding section, efficiency gains from changing the test score ranking policy may be reduced or reversed if applicants respond to the policy change by substituting into costlier forms
of securing advantages in college admissions. Moreover, we may overstate the efficiency losses associated with retaking if applicants actually increase their human capital by learning something in the process.
6. Powers and Rock 1999 examine coaching and the claims made by some companies providing such services. Although coaching increases scores less than what is suggested in some of the claims, it does
appear to lead to some improvement in scores. In addition, those receiving coaching tended to have higher incomes than those that did not.
Vigdor and Clotfelter 5
II. Data
