This paper examines the effects of cancelling a 4th grade instrumental music program in the Saint Paul Public School District. The author uses a difference-in-difference analysis comparing test scores between schools that cut the program and schools that kept it. The results show that economically disadvantaged students who had the music program showed statistically significant improvements in math scores but no difference in reading scores. The author notes limitations including selection bias and a short time period but suggests music education may benefit academic performance, especially for low-income students.

1. Paul Larson
Economics 101, Policy Analysis, Spring 2012
Professor Camille Landais
Final Paper
Music education improves academic skills for financially disadvantaged
public elementary schools students
Introduction:
A particularly formidable and long-standing challenge to researchers is to quantify the
value of an education in music and the arts. For several decades, researchers have been trying
to find a provable theory that links education in music with overall academic achievement.
Using the results of modern brain imaging technology and statewide standardized testing, this
goal is becoming more achievable. Since the 1960s, experimental research has sought to
investigate the effects of music education in particular. The main idea has been that interaction
with music, either through targeted listening (e.g. the “Mozart effect”), or through formal music
lessons, can improve certain cognitive and psychosocial skills in children and adults. In this
paper, I will first review the relevant academic literature. Then, using a data set of statewide
standardized test results from the Minnesota Public Schools from 2008 to 2010, I will examine
the short-run effects of cancelling in 2009 of the mandatory 4th grade instrumental music
program in the Saint Paul Public School District, using a difference-in-difference analysis. My
results show that economically disadvantaged students (those who are eligible for subsidized
meals), gain the largest relative improvements in math and reading test scores when provided
with 4th grade instrumental music instruction. Students who had the music program on average
show statistically significant improvements on standardized math test scores, but show no
significant difference in reading test score improvements.

2. Lastly, I will discuss the limitations of my empirical approach, including details about the
quasi-experimental setting, the non-random assignment of schools to the treatment group, and
the short, three year sample period. By addressing these shortcomings I will make suggestions
for future research.
Background Information:
If elementary school music education is positively correlated with overall academic
achievement, and overall academic achievement is positively correlated with worker productivity
and lifetime earnings, then a policy requiring this type of music education could lead to long-
term economic improvements.
Since 2001, all American public schools that receive federal funding are subject to the
No Child Left Behind Act. This act requires that each state teach and assess the learning of a
basic skill set, which is focused on reading, writing, and mathematics. Student learning is
measured by performance on statewide standardized tests, and this directly affects the school’s
level of federal funding. When schools fail to achieve Adequate Yearly Progress, as designated
by the Act, the school or district may have its federal funding reduced or cut, potentially making
it more difficult for these troubled schools to improve. It is therefore very important to
understand the effects of different educational policies regarding curriculum, and in particular
how these policies affect the economically disadvantaged, in order to maximize the overall
return on investment for public education.
The recent economic recession has increased pressure on public schools to cut costs by
cutting programs, and since 2007 nearly 71% of schools have reduced instruction time in
history, arts, language, and/or music. The quasi-natural experiment setting for this study was
created by such a cut. Prior to the fall of 2009, all 46 schools in the Saint Paul Public School
District required instrumental music instruction as part of their 4th grade core curriculum. The

3. program was cut throughout the district, in all but eight schools, due to budgetary constraints. I
will use a difference-in-difference analysis to compare the test performance of students between
these two groups of schools.
Literature Review:
In recent decades many researchers have searched for a causational effect between
music education and academic performance. The beneficial effects have been thought of in two
general categories: passive enhancement (through targeted listening) and active transfer (from
formal music lessons). To briefly describe passive enhancement, two well-known studies
(Rauscher et al., 1993, 1995) document improvement in college student performance on spatial-
temporal tasks when listening to 10 minutes of music composed by Mozart. However,
subsequent research has not supported the idea that brief exposures to music can have a
significant positive effect on overall cognition (Stough, Kerkin, Bates, & Mangan, 1994;
Carstens, Huskins, & Hounshell, 1995; Rideout & Taylor, 1997; Nantais & Schellenberg, 1999;
Crncec, Wilson, & Prior, 2006).
Studies on the active transfer effects of formal music education, however, have had
more consistent findings. The idea behind active transfer effects is that training in one domain
(here, music), transfers over to a certain skill set found in other domains (here, math and
reading). One of the earliest and most-cited experimental studies of the effects of childhood
music education uses the Kodaly music training method as a treatment. Hurwitz, et al (1975)
find that this intensive music instruction (40 minute classes, five days a week, for seven months)
significantly improves reading ability in first graders. The study continued for a second year, in
which the students in the Kodaly-trained group again outperformed the control group on reading
tests. Although their sample size was small (10 boys and 10 girls in both the treated and
untreated groups, 40 students total), their experimental method was rigorous. The subjects

4. were matched by age, IQ, social class, and birth order, the experimental testing done was
extensive. They controlled for many difficult things, such as teaching style, by comparing
students of the same teacher, both with and without the Kodaly program. This study
demonstrated successful methods to control for many important unobserved variables when
trying to measure the effects of musical training.
In more recent years, advancements in medical imaging technology have allowed
neuroscientists to investigate the effects of music education on brain development and activity.
Overall, these studies find that learning to play a musical instrument at an early age causes
physical differences in brain development (Schlaug, et al., 1995). However, this difference only
becomes measurable if the musicians start music lessons before age 7, suggesting that in order
to obtain the physical advantages in brain structure, musical instruction must begin during a
period of intense brain plasticity. If elementary school children obtain relatively greater returns
on the investment of musical education than their older counterparts, educational policy should
allocate a greater share of the resources for musical instruction to the elementary school
curriculum. Other neurological studies have shown that musical training affects the growth of
neural architecture in both children and adolescents, in the regions used in processing
mathematics (Bahr & Christensen, 2000; Shaw, 2000; Schmithorst and Holland, 2004;
Helmrich, 2010). Using neuroimaging, Pascual-Leone (2005) finds that plasticity changes occur
in the human brain when learning to play piano, and Giedd, et al. (1999) find that during early
adolescence the brain experiences a synaptogenesis (a surge in the formation of new
synapses), which peaks between the ages of 10 and 12. These findings suggest that, because
of the brain’s neural plasticity, early adolescence is a critical phase for physical brain
development in one’s educational career.
Piro and Ortiz (2009) study the effects of piano lessons on 2nd grade students, and find
a surprising result. Although the students already had received 2 years of private piano
instruction at the beginning of the study, their initial literacy test scores were not statistically

5. different from those of students with no prior instruction. However, by the end of the study the
following year (also the end of the students’ third year of private piano instruction), students with
piano instruction significantly outscored their counterparts. This further suggests that rapid
neural development occurs between the ages of 8 and 10, which is also the age group of the
students in my data set.
Using a sample of over 6,000 adolescents from Maryland, Helmrich (2010) finds a
significant improvement in high school algebra achievement on standardized tests for students
who had enrolled in formal instrumental or choral instruction during middle school. The positive
correlation with higher algebra scores was strongest among students who had studied formal
instrumental instruction, and weaker (but still significant) for students who had choral instruction.
The achievement gap was largest among African American students, where the average scores
were failing the state’s standardized test in 5th grade, but, among the African American students
who had received choral or instrumental instruction in middle school, the means became
passing by 9th grade. Among the African American students who did not receive musical
instruction, the means were still failing in 9th grade.
When studying ability levels in very young subjects, it is difficult to separate correlation
from causation. Anvari et al. (2002) examine musical skills, phonological processing, and early
reading ability in preschool children, and find that musical skills are significantly correlated with
both phonological ability and reading development. However, because it is extremely rare that
preschool students have already received formal music instruction, I interpret this correlation to
mean that musical ability in preschool-age children is more likely an early indicator of natural
intellectual ability, rather than a result of formal music education or training. Unfortunately,
without more information about these children’s home environments regarding music, or the
musical background of the parents, there is strong potential for omitted variables biasing these
results.

6. Despite the problems with identification, evaluation, and estimation, music education has
become increasingly justified on the basis that it may enhance ability in areas like math and
language. Ho, et al. (2003) and Rickard, et al. (2010) both report that it enhances verbal
memory. Schellenberg (2001, 2004) finds that it enhances general intelligence. Wilson, et al.
(2006), Orsmond & Miller (1999), and Rauscher & Zupan (2000), all report that it improves
spatial learning. O’Connell (2005) finds it improves schools attendance and motivation. In
preschool and primary school students, regular music classes and instrumental training have
been associated with improved pre-reading and writing skills, higher mathematics scores, and
improved memory and differential brain development (Cheek & Smith, 1999, Fujioka et al.,
2006). And many other researchers have found that music education improves overall
academic achievement (Anvari et al., 2002, Hodges & O’Connell, 2005, Southgate & Roscigno,
2009; and others; see Schellenberg, 2001; Bolduc, 2008; and Hallam, 2010 for extensive
reviews). The College Board reported in 2004 that students who have had coursework or
experience in music performance outscored their peers on the SAT by 43 points on the math
section, and by 57 points on the verbal section (out of a possible 800 points each). A common
shortcoming among these studies, however, is being able to convincingly control for the omitted
and unobservable variables.
Other researchers have found some conflicting evidence for the above findings,
suggesting that the positive effects of a music education are quite variable, difficult to measure,
and not yet fully understood. Johnson and Memmott (2007) compare low- and high-quality
music education programs, and find, unsurprisingly, that students in schools with the highest
quality music programs perform better on language and math tests. However, students in
schools with “deficient” music programs still outperform those in schools with no music program
at all. Upitis et al. (2001) find that only elementary students with private music instruction
outside of school show improvements in language and mathematical abilities, suggesting that
the group class format for musical instruction is not as beneficial to brain development in

7. children. Rickard et al. (2010) find that the improvements in math and language abilities are
only associated with programs in economically-disadvantaged schools, and not in schools which
are “arts-poor” in the same neighborhood.
Empirical Strategy:
For my analysis, I use statewide standardized math and reading test data collected from
the Saint Paul Public School District over the years 2008 to 2010. This large data set includes
51 variables with 1,052 observations at the classroom level, 918 for the untreated group and
136 for the treated group. Prior to the 2009-2010 academic year, all 4th grade students in the
46 elementary schools of the Saint Paul Public School District received instrumental music
instruction. Of these schools, 38 cut this program due to budgetary constraints, but 8 of the
schools chose to continue requiring the program in the curriculum (Lorenzen, personal
communication). The treatment group, therefore, will be the students in the 8 schools that
chose not to cancel this program during the 2009-2010 academic year. I will examine student
performance on the Minnesota statewide standardized math and reading tests by comparing
test scores of students who lost instrumental music as part of their core curriculum (the
“untreated” group) with the scores of students in the 8 schools that kept the program (the
“treated” group).
My regression equation format is:
averagescore (reading or math) = (fixed effects parameters) + B(post_treatment) + error
This is a simple, fixed effects, difference-in-difference regression, where “B” is the
coefficient of interest, measuring the effect on “average test score” of being in the treatment
group after the treatment has occurred.

8. I focus my statistical analysis on the performance of students who were in 3rd grade in
2008. As 4th graders in 2009, they become separated into treated and untreated groups, and
are then tested at the end of the 2009, and again at the end of 2010.
In order to verify the findings of previous studies, I examine the treatment effect on some
of the subgroups within my data, such as students who are eligible for subsidized meals,
students receiving special education services, students eligible for Limited English Proficiency
(LEP) services, as well students of African American heritage.
There are several factors that complicate my analysis. First, the 4th grade instrumental
music program was only cancelled as a part of the uniform required curriculum during the
school day. Most schools in the Saint Paul Public School District continued offering similar,
optional classes twice a week after school, but data was not available for this program.
As with most studies into the effects of music education, unobserved variables may bias
my results. The data set does not include information on extracurricular music instruction,
parental musical experience, or the amount of musical exposure children have in their homes,
which could create one or more omitted variable biases. In addition to the selection bias among
which schools chose to keep the program, there is potentially another selection bias, as parents
may have non-randomly transferred children into schools that did not cut the 4th grade
instrumental music education program.
Lastly, I am examining a short time period with panel data, and it may be that the most
important treatment effects on academic performance only become statistically significant
further in the future. Researchers have shown that physical differences occur in brain
development among this age group when they are given instrumental music instruction.
Hopefully by observing longer-term correlations with these physical differences, we may be able
to gain a better understanding of how the brain’s physiology affects academic achievement.

9. Results
My most interesting result came by including only students who are eligible for free or
reduced-price meals in my data set. This group shows a 4.75 point improvement in math test
scores, and this result is significant at the 95% level. Among this “low economic status” group,
there is also a 2.93 point increase in relative reading test scores associated with the financially-
disadvantaged students in the treatment group. This correlation is significant at the 90% level.
When the students eligible for free or reduced price meals are removed from the data set, there
is no statistically significant association between the treatment group and average math or
reading scores (See Appendix B: Economic Status).
My general analysis shows that continuing the 4th grade instrumental music education
program is associated with an overall 3.58-point improvement in math scores, which is
significant at the 90% level. However, I find no significant correlation between continuing the
music program and reading scores (See Appendix A: General Findings).
My other subgroup analyses were inconclusive. Among the students receiving special
education services, and when these students are removed from the sample, there is no
significant correlation between treatment group and test scores. The students eligible for
Limited English Proficiency (LEP) services the results are similarly inconclusive, with low
coefficients and high standard errors on the “post_treatment” variable. However, when the
students eligible for LEP services were removed from the sample, the coefficient on the
post_treatment variable returns to nearly the exact same level as when the regression was run
on all students (3.56, also significant at the 90% level). For the African American student
subgroup, the findings were inconclusive (See Appendix C: Special Education, LEP, and African
American).

10. Discussion
Schools which kept the program also have higher average test scores, both before and
after treatment, and this shows that the selection of schools into the treatment group was non-
random. The schools in the treatment group have significantly higher average student test
scores, both before and after treatment. However, by using difference-in-difference analysis I
find that the schools which kept the program, on average, also show a relative improvement in
students’ average math scores. Students eligible for subsidized meals show the most robust
results among the treatment group, which is consistent with the findings from Rickard et al.
(2010). This finding supports the idea that economically disadvantaged students will enjoy the
largest relative gains from an early music education. If these same economically disadvantaged
students are also, as a group, less likely to graduate high school, attend college, or become
skilled productive workers, then the long-term effects of early music education on this group
should be carefully considered when designing policy.
Music education in public elementary schools, especially among the poor, is fertile
ground for economic policy research at this time. In the aftermath of the financial meltdown and
amidst a slow-to-recover recession, the federal budget continues to face many program cuts.
Public education will continue to take its share of these, so more opportunities for quasi-natural
experiments like this are likely to appear. My hope is that future researchers will continue to
search for a provable theory linking education in music and the arts with overall academic
achievement and other measures of success. In particular, there is a dearth of academic
literature examining the long-term effects of having a music education during childhood, and I
believe that variables such as high school dropout rates, college graduation rates, average
yearly income, divorce and even incarceration rates, may show interesting correlations with
being musically-trained and educated during childhood.

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14. APPENDIX A: General Findings
All St. Paul School District Math Scores
(1)
VARIABLES averagescore
post_treat 3.58*
[1.807]
yd1 0.33
[0.712]
yd3 0.64
[0.670]
Constant 546.64***
[0.600]
Observations 154
R-squared 0.08
Number of schoolnumber 55
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1
Summary Statistics - All Saint Paul School District Math Scores
-> treat = 0, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 263 449.2373 80.36244 316.2 567
-> treat = 0, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 520 450.2027 80.62629 318.1 567.3
-> treat = 1, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 48 457.2021 80.68595 343.5 566.9
-> treat = 1, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 88 456.0966 80.16654 340 567.9

15. APPENDIX A: General Findings (continued)
All Saint Paul School District Reading Scores
(1)
VARIABLES averagescore
post_treat 0.76
[1.271]
Constant 550.05***
[0.434]
Observations 153
R-squared 0.19
Number of schoolnumber 55
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1

16. APPENDIX A: General Findings (continued)
All Saint Paul School District Reading Scores Summary Statistics
-> treat = 0, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 263 449.2373 80.36244 316.2 567
-> treat = 0, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 520 450.2027 80.62629 318.1 567.3
-> treat = 1, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 48 457.2021 80.68595 343.5 566.9
-> treat = 1, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 88 456.0966 80.16654 340 567.9

17. Appendix B: Economic Status
Saint Paul School District Math Scores
Economic Status "Low" (eligible for free/reduced price
meals)
(2)
VARIABLES averagescore
post_treat 4.75**
[1.997]
Constant 544.60***
[0.663]
Observations 151
R-squared 0.08
Number of schoolnumber 55
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1
St Paul School District Math Scores Summary Statistics
Economic Status "Low" (eligible for free/reduced price meals)
-> treat = 0, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 256 446.9746 80.85825 313.1 557.6
-> treat = 0, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 514 447.7031 80.38121 318.7 559.5
-> treat = 1, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 48 451.6083 80.46089 342.7 556.6
-> treat = 1, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 84 447.3631 81.0165 340 559.8

18. Appendix B: Economic Status (continued)
Saint Paul School District Reading Scores
Economic Status "Low" (eligible for free/reduced price
meals)
(2)
VARIABLES averagescore
post_treat 2.93*
[1.502]
Constant 547.30***
[0.498]
Observations 151
R-squared 0.22
Number of schoolnumber 55
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1

19. Appendix B: Economic Status (continued)
All Saint Paul School District Reading Scores Summary Statistics
Economic Status "Low" (eligible for free/reduced price meals)
-> treat = 0, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 256 446.9746 80.85825 313.1 557.6
-> treat = 0, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 514 447.7031 80.38121 318.7 559.5
-> treat = 1, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 48 451.6083 80.46089 342.7 556.6
-> treat = 1, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 84 447.3631 81.0165 340 559.8

20. Appendix B: Economic Status (continued)
(Additional summary statistics are located in APPENDIX Z: Additional Summary Statistics)
Saint Paul School District Math Scores
Economic Status "Regular" (not eligible for reduced price
meals)
(2)
VARIABLES averagescore
post_treat 1.11
[2.180]
Constant 555.49***
[1.665]
Observations 67
R-squared 0.28
Number of schoolnumber 28
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1

21. Appendix B: Economic Status (continued)
Saint Paul School District Reading Scores
Economic Status "Regular" (not eligible for reduced price
meals)
(2)
VARIABLES averagescore
post_treat -2.21
[1.811]
Constant 560.16***
[1.449]
Observations 68
R-squared 0.32
Number of schoolnumber 28
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1

22. Appendix C: Special Education, Limited English Proficiency (LEP) and African American
Saint Paul School District Math Scores
Special Education Students
(2)
VARIABLES averagescore
post_treat 6.96
[5.827]
Constant 536.12***
[1.393]
Observations 53
R-squared 0.10
Number of schoolnumber 29
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1
Saint Paul School District Reading Scores
Special Education Students
(2)
VARIABLES averagescore
post_treat -3.29
[4.398]
Constant 540.58***
[1.296]
Observations 58
R-squared 0.17
Number of schoolnumber 31
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1

23. Appendix C:
Special Education, Limited English Proficiency (LEP) and African American (continued)
Saint Paul School District Math Scores
Not Including Special Education Students
(2)
VARIABLES averagescore
post_treat 2.21
[1.721]
Constant 549.48***
[0.591]
Observations 149
R-squared 0.08
Number of schoolnumber 52
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1
Saint Paul School District Reading Scores
Not Including Special EducationStudents
(2)
VARIABLES averagescore
post_treat 0.27
[1.217]
Constant 552.46***
[0.418]
Observations 149
R-squared 0.23
Number of schoolnumber 52
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1

24. Appendix C:
Special Education, Limited English
Proficiency (LEP) and African American
(continued)
Saint Paul School District Math Scores
Limited English Proficiency (LEP) Students
(2)
VARIABLES averagescore
post_treat 3.47
[4.599]
Constant 543.99***
[1.044]
Observations 91
R-squared 0.20
Number of schoolnumber 38
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1
Saint Paul School District Reading Scores
Limited English Proficiency (LEP) Students
(2)
VARIABLES averagescore
post_treat 2.31
[2.120]
Constant 545.66***
[0.608]
Observations 100
R-squared 0.39
Number of schoolnumber 41
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1

25. Appendix C: Special Education, Limited English Proficiency (LEP) and African American
(continued)
Saint Paul School District Reading Scores
Non Limited English Proficiency (LEP)
Students
(2)
VARIABLES averagescore
post_treat -0.43
[1.616]
Constant 552.54***
[0.557]
Observations 150
R-squared 0.08
Number of schoolnumber 54
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1
Saint Paul School District Math Scores
Without Limited English Proficiency (LEP)
Students
(2)
VARIABLES averagescore
post_treat 3.56*
[1.846]
Constant 548.27***
[0.621]
Observations 150
R-squared 0.07
Number of schoolnumber 54
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1

26. Appendix C: Special Education, Limited English Proficiency (LEP) and African American
(continued)
Saint Paul School District Math Scores
African American Students
(2)
VARIABLES averagescore
post_treat 3.09
[3.891]
Constant 542.90***
[0.814]
Observations 104
R-squared 0.06
Number of schoolnumber 45
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1
Saint Paul School District Reading Scores
African American Students
(2)
VARIABLES averagescore
post_treat -3.80
[3.452]
Constant 547.06***
[0.728]
Observations 103
R-squared 0.16
Number of schoolnumber 44
Standard errors in brackets
*** p<0.01, ** p<0.05, * p<0.1

27. APPENDIX Z: Additional Summary Statistics
Saint Paul School District Math Scores Summary
Statistics
Economic Status "Regular" (not eligible for reduced price
meals)
-> treat = 0, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 106 461.3858 78.29727 354.9 570.2
-> treat = 0, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 195 457.3805 81.26991 345.8 570.5
-> treat = 1, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 42 463.6405 80.61837 357.8 570.7
-> treat = 1, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 77 462.4234 80.63973 355.5 571.2
Saint Paul School District Reading Scores Summary
Statistics
Economic Status "Regular" (not eligible for reduced price
meals)
-> treat = 0, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 106 461.3858 78.29727 354.9 570.2
-> treat = 0, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 195 457.3805 81.26991 345.8 570.5
-> treat = 1, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 42 463.6405 80.61837 357.8 570.7
-> treat = 1, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 77 462.4234 80.63973 355.5 571.2

28. APPENDIX Z: Additional Summary Statistics
All Saint Paul School District Math Scores Summary
Statistics
Limited English Proficiency (LEP)
Students
-> treat = 0, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 193 440.6943 79.06928 332.6 557
-> treat = 0, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 359 441.7808 80.81343 316.2 563.2
-> treat = 1, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 33 437.5818 76.62015 340.2 552.8
-> treat = 1, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 60 436.06 77.40521 341.9 554.3
Saint Paul School District Math Scores Summary
Statistics
Non Limited English Proficiency (LEP)
Students
-> treat = 0, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 255 450.3706 80.76034 315.5 567.5
-> treat = 0, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 510 452.0112 80.19104 318.7 568.7
-> treat = 1, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 46 464.3239 79.56314 353.5 567.7
-> treat = 1, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 88 458.2284 80.34004 335.6 568.9

29. Saint Paul School District Reading Scores Summary
Statistics
African American
Students
-> treat = 0, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 204 442.8809 79.89926 332.2 560.6
-> treat = 0, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 396 442.5184 79.30829 318.7 559.5
-> treat = 1, post = 0
Variable Obs Mean Std. Dev. Min Max
averagescore 19 448.5526 84.67098 345.8 559.2
-> treat = 1, post = 1
Variable Obs Mean Std. Dev. Min Max
averagescore 52 440.2135 79.94242 332.8 563.3