Vigdor and Clotfelter 5
II. Data
The data used in the present analysis are based on first-year under- graduate applicants to three research universities in the South, two public and one
private. All three are selective institutions. For the class enrolling in the fall of 1998, the three institutions accepted an average of 42 percent of their applicants, and their
average yield rate was 50 percent.
7
All three require the SAT I as part of the complete application. For each applicant, information was obtained from the Educational Test-
ing Service ETS from its Student Descriptive Questionnaire SDQ, which is filled out by students taking the SAT. This questionnaire provides the applicant’s race,
gender, residence, high school academic performance, and self-assessed ability as well as information on the income and education of the applicant’s parents. The ETS
also provided a complete history of SAT scores, regardless of whether the student reported all those scores to the institution. These data were matched with information
from the college applications.
The resulting sample included 22,678 students who applied to at least one of the three institutions for the fall of 1998 and who also took the SAT at least once.
8
Of these, more than 82 percent took the SAT at least twice, compared to the 49 percent
who were multiple test-takers nationwide, as shown in Table 1. This large difference most likely reflects the comparatively selective character of the institutions in the
current sample and therefore the possibly more competitive nature of the applicants to those institutions. The differences may be further influenced by the fact that rela-
tively few applicants in the South take the ACT, as compared to the Midwest and West, where many applicants might conceivably be taking the SAT only once. What-
ever the cause, this difference should be noted.
III. Who Retakes the SAT?
Table 2 presents distributions showing what kinds of students in our sample most often took the SAT multiple times. Retaking was significantly more
common among students who receive lower scores on the first test administration. By gender, women were more likely to take the test more than once; whereas 20
percent of men took the test only once, only 16 percent of women did. Most of this difference is reflected in the percentages who took the test three times. By race,
blacks were somewhat more likely to take the test multiple times 83.5 versus 82.2 percent. Hispanic applicants were about as likely as blacks to take the test more
than once but less likely than blacks or whites to take it more than twice. The most distinctive racial group was Asian Americans, who exceeded all other groups in their
rate of retaking. Whereas 32.5 percent of whites took the SAT three or more times, 42.6 percent of Asian Americans did. With respect to parents’ income, no very clear
7. Data from Peterson’s Guide to 4 Year Colleges, 30th Edition 2000. 8. Excluded from the sample are 1,664 applicants we could not match to neighborhood demographic data
on the basis of their reported zip code. Inclusion of these applicants, where feasible, does not substantially affect any of the results presented here.
6 The Journal of Human Resources
Table 2 Number of Times Taking SAT, by Selected Characteristics
Percentage, by number of times taking SAT
Number of Applicants
1 2
3 4 or more
All test takers 22,678
17.8 48.7
27.0 6.5
Combined score on initial test 1500 and above
661 83.1
15.0 2.0
0.0 1300–1490
5,870 29.0
54.2 15.4
1.5 1100–1290
9,084 12.2
51.8 30.2
5.8 1090 or below
7,063 9.7
43.1 34.8
12.4 Gender
Male 10,286
20.0 48.7
25.0 6.3
Female 12,392
16.0 48.6
28.6 6.8
Race White
16,935 18.2
49.3 26.4
6.1 Black
2,358 16.5
49.0 27.0
7.5 Native American
147 17.7
47.6 27.2
7.5 Asian American
2,096 15.1
42.4 32.9
9.7 Hispanic
642 16.4
53.3 25.4
5.0 Other
500 24.4
47.0 22.4
6.2 Approximate parents’ income
Less than 40,000 3,561
17.9 49.0
26.5 6.7
40–60,000 3,404
15.9 48.9
27.9 7.3
60–80,000 3,396
15.6 48.9
27.9 7.5
80–100,000 2,530
17.2 48.8
28.3 5.7
More than 100,000 5,675
19.4 48.2
26.4 6.0
Unknown, not reported 4,112
19.5 48.5
25.8 6.2
Self-reported class rank Top 10
9,967 19.6
47.3 26.6
6.5 11 to 40
8,084 15.8
50.1 27.4
6.7 Bottom 60
1,229 16.2
49.3 28.5
6.0 Unknown, not reported
3,398 18.1
48.9 26.6
6.4 Self-reported math ability
Highest 10 9,168
21.4 47.4
25.3 5.9
Above average, not top 10 8,801
14.9 50.4
28.1 6.6
Average or below average 2,776
14.3 49.3
29.0 7.3
Unknown, not reported 1,933
18.9 45.7
27.0 8.4
Self-reported writing ability Highest 10
7,148 22.2
48.6 23.6
5.6 Above average, not top 10
9,567 15.8
49.0 28.7
6.5 Average or below average
4,000 14.3
48.5 28.9
7.4 Unknown, not reported
1,963 18.9
45.8 26.9
8.4 Average income of home ZIP code
Less than 20 50,000 or more 9,601
15.2 46.5
29.4 8.8
20–100 50,000 or more 13,077
19.7 50.2
25.2 4.9
Vigdor and Clotfelter 7
Table 2
continued
Percentage, by number of times taking SAT
Number of Applicants
1 2
3 4 or more
Urbanization of home ZIP code Less than 80 urban
7,812 15.3
47.6 28.8
8.3 80–100 urban
14,866 19.2
49.2 26.0
5.6 Percentage black of home ZIP code
Less than 20 black 17,860
18.6 49.6
26.0 5.7
20–100 black 4,818
14.9 45.1
30.5 9.6
Note: Based on those who took the SAT at least once and graduated from high school in 1998. Row percentages may not add up to 100.0 due to rounding. Source: College Board and unpublished data on
1998 applicants to three universities, authors’ calculations.
patterns emerge.
9
Retaking was slightly more prevalent among applicants from fami- lies in the middle income categories, but the differences were not large. By contrast,
the patterns of retaking differed markedly according to the student’s reported class rank. Those ranked in the top 10 percent of their high school class were least likely
to take the test more than once. Applicants who ranked themselves among the highest 10 percent of students in either math or writing ability were significantly less likely
to retake the test than those applicants with lower self-rankings.
The last three sets of categories shown in Table 2 apply to characteristics of the ZIP code where the student resided. Perhaps surprisingly, those in more affluent
areas and in highly urbanized areas were less likely than others to take the test multiple times. With respect to the racial composition of ZIP codes, those living in
areas with higher percentages of blacks were more likely to retake the SAT.
To summarize, Table 2 identifies several groups that were more likely than others to take the SAT multiple times: those with low initial scores, women, Asian Ameri-
cans, those who rate themselves as average or below in ability, and those who live in less affluent, rural, or predominantly black neighborhoods. On their face, these
simple correlations seem to dispel any notion that retaking is the exclusive or even preponderant domain of the affluent or urbanized.
For a fuller answer to the question of who retakes the test, it is necessary to examine the partial effects of various characteristics, holding other things constant.
Our model, described in Section V below, suggests that there are three basic reasons why two individuals with the same initial test scores might be differentially likely
to retake the test. First, individuals might have different expectations regarding the scores they would receive on the next test. Second, they may face different direct
and indirect costs of retaking the test. Finally, they may attach different values to
9. In contrast, Boldt, Centra, and Courtney 1986, p. 4, using data for 87 colleges, found the highest rates of retaking among whites and upper-income applicants. This difference in findings may be attributable to
the differences in selectivity in the institutions studied.
8 The Journal of Human Resources
Table 3 Probit Equations Explaining Taking SAT at Least Two, Three or Four Times
Dependent variable: Indicator for whether applicant takes n
th test conditional on having taken n ⫺ 1 Variables
n ⫽ 2 n ⫽ 3
n ⫽ 4 Previous SAT math score
⫺0.005 0.0002 ⫺0.004 0.0002
⫺0.003 0.0003 Previous SAT verbal score
⫺0.004 0.0002 ⫺0.002 0.0002
⫺0.002 0.0003 Female
0.038 0.023 0.058 0.021
⫺0.051 0.036 Family income
Less than 40,000 excluded
excluded excluded
40,000–60,000 0.035 0.043
0.060 0.037 0.060 0.062
60,000–80,000 0.077 0.044
0.085 0.038 0.083 0.064
80,000–100,000 0.083 0.048
0.112 0.042 ⫺0.042 0.072
More than 100,000 0.078 0.043
0.181 0.037 0.093 0.064
Unknown, not reported 0.082 0.049
0.103 0.044 0.044 0.079
Father’s education Up to high school graduate
excluded excluded
excluded Some college
0.045 0.048 0.110 0.041
0.082 0.073 College graduate
0.142 0.047 0.150 0.041
0.216 0.071 Professional degree
0.139 0.049 0.156 0.043
0.305 0.076 Unknown, not reported
0.129 0.100 0.051 0.086
0.018 0.157 Mother’s education
Up to high school graduate excluded
excluded excluded
Some college 0.001 0.043
0.065 0.037 0.026 0.065
College graduate 0.110 0.044
0.126 0.038 0.015 0.065
Professional degree 0.111 0.047
0.071 0.041 0.055 0.072
Unknown, not reported ⫺0.057 0.112
0.175 0.099 0.171 0.169
Class rank Top 10
excluded excluded
excluded 11 to 40
⫺0.187 0.029 ⫺0.168 0.026
⫺0.148 0.044 Bottom 60
⫺0.371 0.060 ⫺0.245 0.051
⫺0.280 0.090 Unknown, not reported
⫺0.103 0.043 ⫺0.114 0.040
⫺0.117 0.072 Self-reported math ability
Among highest 10 excluded
excluded excluded
Above average, not in top ⫺0.032 0.029
⫺0.065 0.026 ⫺0.063 0.046
10 Average or below average
⫺0.274 0.049 ⫺0.162 0.041
⫺0.103 0.070 Unknown, not reported
0.075 0.183 0.028 0.152
0.075 0.215 Self-reported writing ability
Among highest 10 excluded
excluded excluded
Above average, not in top 0.017 0.028
⫺0.015 0.026 ⫺0.116 0.045
10 Average or below average
⫺0.126 0.040 ⫺0.154 0.035
⫺0.209 0.060 Unknown, not reported
0.055 0.174 0.064 0.146
0.110 0.206 Race
White excluded
excluded excluded
Black ⫺0.213 0.043
⫺0.156 0.037 ⫺0.040 0.063
Vigdor and Clotfelter 9
Table 3
continued
Dependent variable: Indicator for whether applicant takes n
th test conditional on having taken n ⫺ 1 Variables
n ⫽ 2 n ⫽ 3
n ⫽ 4 Native American
⫺0.093 0.147 ⫺0.163 0.127
⫺0.150 0.212 Asian American
0.334 0.042 0.402 0.035
0.358 0.056 Hispanic
0.071 0.069 ⫺0.045 0.063
0.184 0.115 Other
0.011 0.070 0.141 0.072
0.283 0.125 Percent black in home ZIP
0.002 0.001 0.001 0.001
0.001 0.001 code
Percent Hispanic in home 0.002 0.002
0.003 0.001 ⫺0.002 0.002
ZIP code Percent urban in home ZIP
0.002 0.0004 0.002 0.0004
0.002 0.001 code
Percent of households with 0.003 0.001
⫺0.0001 0.0008 ⫺0.004 0.002
income more than 75,000 in home ZIP code
First SAT in Fall 1995 4.107 0.259
1.611 0.418 0.303 0.652
First SAT in Spring 1996 4.319 0.230
1.418 0.414 0.209 0.650
First SAT in Fall 1996 3.652 0.213
0.858 0.412 ⫺0.375 0.650
First SAT in Spring 1997 3.103 0.209
0.057 0.412 ⫺0.857 0.649
First SAT in Fall 1997 1.446 0.210
⫺0.935 0.417 ⫺0.745 0.672
First in Spring 1998 excluded
excluded excluded
Sample size 22,678
18,638 7,631
Log likelihood ⫺8006.6
⫺10,548.6 ⫺3418.0
Pseudo R
2
0.2465 0.1636
0.1368
Notes: Table entries are probit coefficients. Standard errors are in parentheses. denotes coefficients significant at the 1 percent level.
being admitted to a selective college. To examine the basic relationships between observed applicant characteristics and these underlying traits, Table 3 presents a
series of probit equations explaining the decision to take the test twice, the decision to take the test a third time conditional on two administrations, and the decision to
take it a fourth time conditional on three administrations. Included as explanatory variables are scores from the preceding test administration, gender, family income,
father and mother’s education, self-reported class rank, self-reported math and writ- ing ability, race, and characteristics of the student’s ZIP code area. Finally, the equa-
tions include dummy variables for the date of initial test administration.
In sharp contrast to the impression given by the simple distributions shown above, the effect of holding constant previous scores and other variables is to reveal that
retaking is indeed associated with greater affluence and parental education, among other things. The equations make clear, first of all, that retaking is strongly associated
with scores on the previous SAT, those scoring high being less likely to retake the test. For example, an increase of 50 points on both the math and verbal scores on
10 The Journal of Human Resources
the initial SAT test is associated with a decrease of 8 percentage points in the proba- bility of taking it a second time.
10
Holding constant previous scores, family income now has a much clearer associa- tion than it appears to have in Table 2. Those whose parents made more than 60,000
had a 1.5 percentage point higher probability of retaking the test than those whose family incomes were below 40,000. Conditional on taking twice, applicants from
these higher-income families were between 3.3 and 7 percentage points more likely to take the test a third time. Income does not significantly influence whether a three-
time taker returns for a fourth test administration. Similarly, both mother’s and fa- ther’s education have a statistically significant effect, with those whose parents were
college graduates more likely to retake the test, other things equal. As with income, the strongest effects of parental education appear in the decision to take the test a
third time. Two-time takers whose fathers obtained a college degree were 6 percent- age points more likely to retake the test than otherwise identical applicants with a
high-school-educated father. The marginal effect of mother’s education is of some- what smaller, though still significant, magnitude.
High school rank also has a significant association, with those in the top 10 percent being most likely to retake the test a second, third, or fourth time, with all other
characteristics including prior test scores held constant. Similarly, those who as- signed relatively low ratings to their own math and writing ability were less likely
to retake the test than those putting themselves in the top 10 percent. As with family income and parental education, the impact of class rank and self-assessment appears
strongest in the decision to take the test a third time. In that case, either a class rank outside the top 10 percent, a low math self-assessment, or a low verbal self-assess-
ment predicts a 6 to 9 percentage point decrease in the probability of retaking.
By race, blacks were less likely than whites to take the test two or three times. Other things equal, the probability of a black student taking the test at least twice
was 4.5 percentage points less than that of an otherwise identical white student; conditional on taking the test twice, the black-white differential in the probability
of taking the test a third time was 5.9 percentage points.
11
Asian Americans, on the other hand, were consistently more likely to retake the test: they were 5.5 percentage
points more likely than an otherwise identical white student to take the test a second time. Conditional on taking twice, Asian applicants were 15.9 percentage points
more likely to take the test a third time relative to otherwise identical white appli- cants. The test taking behavior of other racial or ethnic groups is not distinguishable
from that of whites.
Applicants living in urban areas were more likely to retake the test a second, third or fourth time. As with many indicators, the strongest effect of urbanicity on retaking
10. Table 3 reports the actual probit coefficients, which have no natural interpretation. Our interpretation of the estimated effects in the test considers the impact of a unit change in one variable when all other
variables are set equal to their means. In general, the effect of a variable on the probability of retaking will depend on the values of all variables in a probit equation.
11. This finding relates to Bowen and Bok’s 1998 result that controlling for other factors, SAT scores are less predictive of college class rank for blacks than for whites. Controlling for other factors, blacks
retake the test less frequently than whites, implying that their reported SAT scores will be noisier point estimates of their true ability. Greater measurement error should lead, in turn, to poorer predictive power
when SAT scores are used as an explanatory variable.
Vigdor and Clotfelter 11
occurs in the decision to take the test a third time, where an applicant from a com- pletely urban ZIP code was 8 percentage points more likely to retake the test than
an applicant from a completely rural ZIP code. Other ZIP code characteristics, such as racial composition and income, do not display a consistent relationship with re-
taking.
Finally, those who took their first SAT early were generally more likely than others to retake the test. This result is not surprising, since those applicants who
initially took the SAT on a late date would simply not have had many chances to retake the exam.
In conclusion, the empirical analysis of who retakes the SAT indicates significant differences by race, income, parental education, self-reported class rank and ability,
and type of community. Most of these relationships are obscured in the raw data, presumably by the extremely strong tendency for students who score well on the
test to refrain from taking it again. These explanatory variables might measure differ- ential expectations regarding future test scores, variation in test-taking costs, or varia-
tion in the benefits associated with admission. Many of the applicant characteristics associated with a lower propensity to retake are also correlated with lower overall
SAT scores, suggesting that applicants may form expectations in a manner that re- sembles statistical discrimination.
12
The greatest amount of selection into the pool of retakers appears to occur in the decision to take the test a third time.
IV. Explaining the Increase in Scores
Kategori