Running Head: COACHES AREN’T BAD TEACHERS
1
Coaches Aren’t Bad Teachers: Evidence from New York City Middle Schools
Albert Cheng, Jay P. Greene, and Collin Hitt
University of Arkansas
EDRE Working Paper No. 2014-02
Last Updated May 2014
Please do not cite without author permission
Abstract
There is a popular stereotype that teachers who also coach sports are less effective than teachers
who do not coach. We use publicly available data from New York City middle schools that
include value-added ratings of teachers in math and English to test this stereotype. Specifically,
we use ordinary least squares regression analysis to detect whether there is a negative
relationship between coaching and teacher effectiveness. We find the opposite. Coaches who
teach math have higher value added scores than math teachers who do not coach, a result that
appears to be driven by female coaches. Among English teachers, male coaches produce
significantly positive value-added scores, while the results for the overall sample are positive but
insignificant. Thus, our results provide no support for the claim that coaches are bad classroom
teachers and may even provide evidence suggesting that they tend to be more effective teachers
than their non-coaching peers.
COACHES AREN’T BAD TEACHERS
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Coaches Aren’t Bad Teachers: Evidence from New York City Middle Schools
Middle schools often have sports teams, and teachers often serve as coaches. There are
various concerns about the appropriate role and stature of athletics in public schools. Whether it
is prudent for teachers to take on a second occupational role is not clear. This study, in particular,
focuses on the following research question: Are coaches of sports teams who also teach English
or math more or less effective than their non-coaching peers? In other words, how much do these
coaches contribute to the academic progress of their students relative to other teachers?
Coaching and Teacher Effectiveness: A Review of Literature
There are two conflicting views to this question. On the one hand, a prevailing
stereotype, which we refer to as the “jock coach,” is that coaches are ineffective classroom
teachers. Some teachers attest to the jock coach stereotype, reporting that administrators simply
use a coach to fill a teaching vacancy regardless of his qualifications to be a classroom teacher.
While hiring a teacher, administrators seeking to fill a coaching vacancy may select someone
who is able to coach rather than other, more-qualified teaching candidates who are unwilling or
unable to coach sports (Dickerson, 2012).
Regardless of a teacher’s qualifications, it’s possible that coaching itself could have a
negative impact on classroom results. Coaching could distract from teaching. Teachers who also
coach may invest more of their limited time and effort towards improving their teams instead of
ensuring that their students learn the required curriculum (Templin, Anthrop, & Franklin, 1980).
Better performance by a sports team may consequently come at the expense of better classroom
performance (Conn, 2012; Fouts, 1989).
In contrast, some argue that good coaches are likely to be good teachers. An
administrator from a Texas school once opined that the organizational and motivational skills
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that are necessary to be an effective coach are also necessary to be an effective teacher. Skills
that coaches or teachers develop while performing one role might enhance performance in the
other (Pybus, 2012). Moreover, a teacher who is also a coach has additional opportunities to
build healthy relationships with students participating in a sport, which translates into greater
rapport in the classroom and student outcomes (Fouts, 1989). Finally, teachers who chose to
coach might do so simply because it allows them to spend additional time with their students. If
this heightened interest in students leads to both classroom success and a desire to coach, it
would be unsurprising to find that coaches are also effective teachers.
These conflicting views have rarely been subjected to empirical tests. Although some
studies have measured teacher characteristics, such as innovation or organizational skills, and
have compared coaches to non-coaches based upon those characteristics, those studies use small
samples and have been conducted many years ago (Fouts, 1990; Van Deraa & Schug, 1993).
More importantly, these studies have measured teacher characteristics, which are not equivalent
to student outcomes. Insofar as teacher characteristics do not predict student progress, those
studies cannot directly reveal whether teachers who are also coaches are more or less effective
than non-coaches. That is, one cannot be certain that higher ratings on particular characteristics
always lead to improved student outcomes. For example, a teacher by virtue of being more or
less innovative may not necessarily bring about greater student progress. Research is currently
mixed, regarding which teaching behaviors most often lead to academic success (MET Project,
2013; Rothstein & Mathis, 2013).
While the classroom effectiveness of coaches has not been studied, several researchers
have attempted to determine whether student participation in sports is beneficial for those
students. For example, Pederson and Seidman (2004) found that urban adolescent girls had
COACHES AREN’T BAD TEACHERS
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higher self-esteem if, as early adolescents, they had participated in team sports and experienced
some degree of self-reported success. Findings such as these suggest that athletics — and thereby
coaches — improve students' chances of academic success, irrespective of coaches’ roles in the
classroom. This thesis is consistent with Bowen and Greene (2012) who find that Ohio schools
with larger athletics programs have significantly higher graduation rates for all students. They
also find that a school’s win-loss record in high profile sports was correlated with higher
academic performance, at the high school level.
Recently-released public datasets from New York City middle schools includes teacher
value-added scores. This data allow us to empirically explore the effectiveness of coaches who
also teach relative to other teachers who do not coach, not only with a larger sample size but also
with an outcome that is a direct measure of student academic progress. The data provide the
opportunity to bring more cogent evidence to bear upon the unexplored question of how
coaching status is related to teacher effectiveness. This present study is exploratory in nature. It
is an initial attempt to fill the existing gap in this area of research and to provide some
preliminary results to better inform ongoing discussions about teacher quality as well as the
proper scope of athletics in schools.
Methods
Data Sets
NYDOE Value-Added Scores. From 2005 to 2010, the New York City Department of
Education (NYDOE) began assigning value-added scores for its fourth- through eighth-grade
math and English teachers. These were designed “to identify the extent to which teachers
contribute to the improvement of student achievement outcomes in their classrooms” (Value
Added Research Center, 2010, p. 1). NYDOE contracted with the Value-Added Research Center
COACHES AREN’T BAD TEACHERS
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at the University of Wisconsin to develop and calculate the ratings. These ratings are based upon
the standardized tests that the state of New York regularly administers to its students. For each
teacher in a given year, NYCDOE first forecasts the average standardized test score that a
teacher’s students are expected to receive. This estimate is based upon the students’ prior test
scores and demographic background characteristics as well as the characteristics of the students’
schools and classrooms. A teacher’s value-added score is determined by taking the difference
between the forecasted average score and the actual average score of each teacher’s students at
year-end. Value-added results are then separated into groups of teachers who have similar
amounts of experience and who teach the same subject area and grade level. Specifically,
NYCDOE grouped teachers into four different experience categories: (a) first-year teachers, (b)
second-year teachers, (c) third-year teachers, and (d) teachers who have taught for more than
three years. Teacher scores are then rank-ordered and converted to percentile scores within their
respective groups (Value-Added Research Center, 2010). This process is done on a yearly basis,
producing single-year results. It is also done over a multi-year basis, producing a “career” score
for each teacher.
In 2012, NYCDOE released for public viewing its teachers’ names, their 2010 singleyear percentile rankings and their overall career rankings from 2007 to 2010 along with the
subject, grade-level, and school at which they taught. We use the data that provide value-added
scores for teachers over the course of their career.1
This dataset, however, did not contain any identifiers of the teachers’ genders. To obtain
this information which would be useful for our analysis, we reviewed the first names of every
teacher and independently coded each name as male or female. Tests for inter-coder reliability
showed that the results were consistent. Some first names were ambiguous in their gender; we
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identified such entries, and found no significant difference in our results if those names were
excluded from the sample.
The CHAMPS Initiative. NYCDOE also maintains an organization for various sports
leagues and clubs for its middle-school students. This organization, called CHAMPS, is aimed at
promoting fitness and well-being among middle-school students. Each year, about 400 teachers
work as coaches for about 1000 sports clubs throughout 200 of the 515 middle schools in New
York City (New York City Department of Education, 2013a, 2013c). Currently, almost 24,000
students out of the approximately 193,000 middle-school students in New York City participate
in CHAMPS (New York Department of Education, 2013b, 2013d).
On its website, NYCDOE publishes a list of sports offered through CHAMPS and lists
the coaches and schools where students may participate in these sports. We matched this list to
the value-added data detailed earlier. In addition to knowing which sport a teacher coaches, we
were able to determine whether the sport has coed, male or female sport participation from the
websites of individual schools and CHAMPS. We are interested in these different sports
classifications because factors that lead a teacher to select into coaching a particular type of sport
may also affect her teaching effectiveness. Table 1 lists each sport that is coached by a teacher in
our sample; whether the sport has boy, girl, or coed participation; and the number of male and
female teachers who coach each sport.
Study Sample. We restrict our study sample to middle schools where at least one of the
teachers is a CHAMPS coach so that schools without athletic programs are excluded from the
analysis. We impose this restriction because we are comparing teachers who coach with those
who do not coach and work at the same schools. After matching the CHAMPS database to the
NYCDOE value-added database, our study sample included 142 out of the approximately 200
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schools that participate in CHAMPS. The schools in our sample serve middle-school students
(i.e. sixth-, seventh-, or eighth-graders), though some schools with different grade
configurations, such as K-8 schools, may serve additional grade levels.
All teachers in our study sample teach courses such that they were assigned a valueadded score in math or English by NYCDOE. Altogether our data include 1,530 teachers with
value-added scores in math and 1,275 teachers with value-added scores in English. This
represents 16.4 percent and 15.0 percent of math and English teachers, respectively, in the
NYCDOE database. Of the 2,805 teachers in our sample, 259 are also coaches of a sports club.
≪INSERT TABLE 1 APPROXIMATELY HERE≫
Analysis Procedures. For our initial regression analysis, we conduct a regression
analysis using ordinary least squares where the dependent variable is the career percentile
rankings of each teacher based on his performance from 2007 through 2010. The independent
variable of interest is a dummy variable indicating whether the teacher is a coach or not. In our
model, we also statistically control for the school at which the teacher works, since factors
specific to a school may affect teachers’ value-added scores or their decision to accept a
coaching position for CHAMPS. For instance, principals have influence over school discipline
and the assignment of students to each classroom, which can affect teachers’ value-added scores.
Principals may also approach particular types of teachers, say, those that are more effective, and
ask them to be a coach. Without controlling for such observable and unobservable school-level
characteristics, our results will be biased.
In a second, more-detailed model, we control for the grade-level that each teacher taught
as well as the teacher’s gender and add a coaching-gender interaction. This second model is our
preferred specification.
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We include a third model where the dependent variable is the teacher’s value-added score
but the independent variables that indicate the genders of students who are participating in the
sport (i.e., the variables indicate whether the sport is a boys, girls, or co-ed sport). The aim of this
analysis is to explore whether coaches who select into a certain type of sport have substantively
different outcomes in teacher effectiveness. Results of all three regression analyses are discussed
in the next section.
Results
Preliminary Results from Visual Plots
Even before conducting a regression analysis, a plot of value-added scores for coaches
and non-coaches helps to anticipate the results. Figure 1 shows value-added scores on the
horizontal axis and the percentage of coaches and non-coaches who received that value-added
score on the vertical axis. The top panel displays results for math teachers and the bottom panel
displays results for English teachers.
≪INSERT FIGURE 1 APPROXIMATELY HERE≫
A brief glance at the plot of value-added scores for math teachers shows that coaches are
far less frequently found at in the bottom quintile of the value-added-score distribution than noncoaching teachers. Instead, coaches are more likely found in the top quintile of the value-addedscore distribution for math.
On the other hand, the plot of English value-added scores and the percentage of teachers
who received those scores is not as revealing. More English teachers who do not coach seem to
score between the 40th and 70th percentiles. And although more coaches than non-coaches
appear at the higher end of the value-added-score distribution, there are also more coaches than
non-coaches appearing in the lower end of the distribution — between the 15th and 30th
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percentiles. It is difficult to adjudicate what type of relationship there is between coaching and
English value-added scores based on this plot.
Results from Initial Regression Analysis: Preliminary Findings
Turning to our primary regression analysis, the positive, significant relationship between
coaching and teaching effectiveness for math is confirmed. Coaches earn value-added scores in
math that are 5 percentile points higher than the scores of their non-coaching peers. This result is
significant at the 0.05 level. However, the regression analysis English teachers reveals no
significant relationship between coaching status and value-added scores in English. Table 2
displays these overall regression results.
≪INSERT TABLE 2 APPROXIMATELY HERE≫
Results from Second Regression Analysis: Effects by Gender
Yet as shown in Table 1, females are less likely than males to be a coach, which suggests
that gender may impact our results. To control for gender, we add variable indicating whether the
teacher is female. We also include another variable in which we interact gender with coaching
status to better understand how coaching and gender are synchronously linked to teacher
effectiveness.”
Including these additional variables prove to be important to answering our research
question. Table 3 shows that females have significantly higher value added scores in English and
math, by about 6 and 10 percentile points, respectively. This result warrants further investigation
and discussion, which we undertake in a separate analysis that finds a positive gender effect for
female teachers citywide (Anonymous, 2013).
≪INSERT TABLE 3 APPROXIMATELY HERE≫
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Using our interaction term, we are able to analyze the relationship between coaching
status and teacher effectiveness in each subject while holding teacher gender constant. The
results are displayed in Table 4. The table simply shows the sums of relevant coefficients from
Table 3, as well as the results of an F-test for significance. We found that male coaches had
significantly higher English scores than their non-coaching peers (by almost 11 percentile
points), while there was no significant difference in math. In English, female coaches and noncoaches had similar value-added scores, but in math, female coaches outperformed other female
teachers (by about 15 percentile points), suggesting that the overall positive effect on math
scores was principally being driven by female coaches.
≪INSERT TABLE 4 APPROXIMATELY HERE≫
Results from Third Regression Analysis: Effects by Type of Sport
In a separate sub-analysis, we separate coaching status by the gender of the participating
students: coed, male or female. Per Table 1, female coaches are much more likely to coach girls
and coed sports, while male teachers are more likely to coach boys’ sports. Given the results
above, which find that female coaches post strong scores in math and male coaches post strong
scores in English, one would expect to see positive results in math for coaches of girl’s sports
and in English for coaches of boy sports. That is largely what Table 5 shows.
≪INSERT TABLE 5 APPROXIMATELY HERE≫
Coaches of girl’s sports posted value-added scores in math that were, on average, 14
percentile points higher than other teachers who do not coach. Coaches of coed sports also
possessed math scores that were higher than non-coaches, but the 4 percentile-point difference
was statistically insignificant. Math results were uncorrelated with coaching status for coaches of
boy’s sports. On the other hand, there were no significant findings by gender of participating
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student in English, mirroring the overall result. These finding are unsurprising, given that our
earlier analyses restricted by gender found that females largely drive the overall positive results
for coaches who teach math; most coaches of girl’s and coed sports are women.
Discussion and Conclusions
We find no empirical evidence to support the belief that coaches are ineffective
classroom teachers, at least in middle school level. In fact, math teachers who are also coaches
receive higher value-added scores than math teachers who are not coaches. When examining
results by gender, it is apparent that female coaches are driving the positive math results. In
English, male coaches received higher value added scores than other male non-coaches, though
this result is derived from a fairly small sample.
At best, our models demonstrate that coaching status is descriptively related to positive
classroom results in English and math, not that teachers who coach a sport become more
effective. That is, we cannot claim that there is a causal relationship between coaching status and
teaching effectiveness because, given the limitations of our data, there are possibilities of
selection bias that we are unable to account for in this analysis. For example, teachers who are
more interested in effectively serving their students may not only have higher value-added scores
but may also be more likely to take on an additional coaching position. Just as principals may
plausibly base hiring decisions upon an individual’s ability to coach, principals may also select
coaches based in part on their classroom performance. They may refuse to open coaching
positions to ineffective math and English teachers, rewarding effective teachers with the
additional pay and responsibility of coaching while preventing less effective teachers from
spreading themselves too thin. An interpretation of our results is certainly consistent with such
an explanation.
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Furthermore, many coaches teach untested subjects, such as physical education, social
studies, science, and health classes. Our analysis does not suggest anything about whether these
coaches would be effective at teaching tested subjects, in this case math and English. Our data is
limited only to teachers who, for numerous unobserved reasons, were offered and accepted the
opportunity to teach math or English and to be coaches.
Future research may be able to make stronger causal claims about coaching and teacher
effectiveness by exploring how teachers are offered the opportunity to coach and how they are
assigned to tested subjects such as math or English. But given the dearth of any systematic
information on the effectiveness of coaches versus non-coach teachers, even the descriptive
information contained in this analysis is a significant contribution to the field.
There are other limitations to the analysis we present here. For example, the years of the
teacher value-added calculation (2007-2010) do not overlap with our identification of whether
teachers are coaches (2011-2012). Our results should be viewed as the relationship between
longer-term teaching effectiveness and ever being a coach, not the effect of coaching in a given
year on value-added scores in that same year. Our analysis is reasonable if we assume that valueadded scores and coaching status are relatively stable over a span of a few years.
Of course, there is considerable controversy in the literature about the stability and
reliability of value-added calculations as a measure of teacher effectiveness. We are taking no
position on those debates in this paper. We are simply assuming that NYCDOE’s teacher valueadded scores contain at least some information about teacher effectiveness. We have no opinion
on whether those scores are as good as they could be, are incomplete, or are stable enough on
which to make personnel decisions. They just have to shed some light on whether coaches appear
to be any more or less effective in the classroom than their non-coaching peers.
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In general, we must be careful to not overgeneralize these findings. Data are only
available for middle math and English teachers. We cannot conclude anything about the
classroom effectiveness of high school coaches. Nor can we conclude anything about teachers in
other, non-tested content areas. Notably, the belief that coaches are bad teachers may have been
derived from people’s experiences with social studies teacher who are also coaches (Conn, 2012;
Dickerson, 2012; Fouts, 1989). It is also possible that our results are unique to New York City.
The CHAMPS program in New York City appears to emphasize wellness over competition,
which may make the role of coaches in New York different from other school systems. New
York City also has a teacher labor market and other characteristics that limit the ability to
generalize to other locations.
With these limitations in mind, we find no evidence to support the jock coach stereotype
that coaches are usually less effective as teachers. The evidence we have been able to gather
suggests, on the contrary, that coaches may even be more effective in the classroom than their
non-coaching peers. Additional research is required to determine if there is a causal relationship
between coaching and effective teaching and if the positive results we find from New York City
middle school math and English value-added scores are consistent with those in other school
districts, other grade levels, and other class subjects.
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References
Anonymous. (2013). Gender and value-added scores among New York City teachers. University
of Arkansas, Working Paper.
Bowen, D., & Greene, J.P. (2012). Does athletic success come at the expense of academic
Success?. Journal of Research in Education, 22(2), 2-23.
Conn, S. (2012, April 15). In college classrooms, the problem is high school athletics. The
Chronicle of Higher Education. Retrieved from http://chronicle.com/article/In-CollegeClassrooms-the/131550/
Dickerson, B. (2012, May 26). Too many coaches in classrooms. Amarillo Globe-News.
Retrieved from http://amarillo.com/opinion/opinion-columnist/guest-columnist/2012-0526/too-many-coaches-classrooms
Fouts, J.T. (1989). Coaching athletics and the social studies curriculum. Social Education, 53(2),
117-119.
MET Project. (2013). Ensuring fair and reliable measures of effective teaching: Culminating
findings from the MET Project’s three-year study. Retrieved from the MET Project
website: http://metproject.org/downloads/MET_Ensuring_Fair_and_Reliable_Measures
_Practitioner_Brief.pdf
New York City Department of Education. (2013a). About CHAMPS. Retrieved from
http://schools.nyc.gov/Academics/FitnessandHealth/Champs/About/default.htm
New York City Department of Education. (2013b). Activities. Retrieved from
http://schools.nyc.gov/Academics/FitnessandHealth/Champs/Activities/default.htm
COACHES AREN’T BAD TEACHERS
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New York City Department of Education. (2013c). School demographic snapshot [data file].
Retrieved from http://schools.nyc.gov/NR/rdonlyres/F318E6F9-5787-403E-8ABD139656D7A06E/0/DemographicSnapshot2012Public.xlsx
New York City Department of Education (2013d). 2012-2013 Updated Class Size Report [data
file]. Retrieved from http://schools.nyc.gov/NR/rdonlyres/17D748A9-71E5-41B0-8F91CC8227238C59/0/20122013UpdatedCityLevelDistributionFinal.xlsx
Pedersen, S., & Seidman, E. (2004). Team sports achievement and self‐esteem development
among urban adolescent girls. Psychology of Women Quarterly, 28(4), 412-422.
Pybus, J.W. (2012, June 7). Coaches care too. Amarillo Globe-News. Retrieved from
http://www.amarillo.com/opinion/letters-editor/2012-06-07/coaches-care-too
Rothstein, J., & Mathis, W.J. (2013). Review of two culminating reports from the MET Project.
Retrieved from the National Education Policy Center website: http://nepc.colorado
.edu/thinktank/review-MET-final-2013
Templin, T.J., Anthrop, J.L., & Franklin, L.H. (1980). Teacher/coach role conflict: An analysis
of occupational role dysfunction. (ERIC Document Reproduction Service No. 204334).
Value-Added Research Center. (2010). NYC teacher data initiative: Technical report on the
NYC value-added model. Retrieved from the New York City Department of Education
website: http://schools.nyc.gov/NR/rdonlyres/A62750A4-B5F5-43C7-B9A3F2B55CDF8949/87046/TDINYCTechnicalReportFinal072010.pdf
Van Deraa, A., & Schug, M.C. (1993). Coaching athletics and the social studies classroom: A
replication study. Social education, 57(3), 116-119.
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Table 1. Sports Coached by Teachers
Type of Sport
(boy’s, girl’s, or co-ed)
Number of
Female Coaches
Number of
Male Coaches
Total number
of coaches
Baseball
Boy’s
3
4
7
Boys
Basketball
Boy’s
3
12
15
Cheerleading
Girl’s
13
0
13
Crew
Coed
2
0
2
Cross Country
Coed
6
2
8
Dance
Coed
21
1
22
Developmental
Basketball
Coed
3
3
6
Double Dutch
Girl’s
15
0
15
European
Team
Handball
Coed
1
0
1
Fitness Club
Coed
19
6
25
Coed
11
23
34
Flag Rugby
Coed
4
2
6
Floor Hockey
Coed
0
6
6
Girls
Basketball
League
Girl’s
4
2
6
Golf
Coed
0
1
1
Gymnastics
Coed
1
0
1
Lacrosse
Coed
0
1
1
One-Wall
Handball
Coed
1
0
1
Soccer
Coed
8
13
21
Flag Football
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Softball
Coed
4
1
5
Step
Girl’s
1
0
1
Swimming
Coed
3
1
4
Table Tennis
Coed
4
4
8
Tennis
Coed
1
1
2
Track and
Field
Coed
20
8
28
Volleyball
Coed
9
3
12
Yoga
Coed
8
0
8
Note: Data adopted from http://schools.nyc.gov/Academics/FitnessandHealth/Champs/Activities
/default.htm
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Table 2: The Relationship between Coaching Status and Teacher Effectiveness
Percentile Ranking
English
Math
Coach
-0.343
(3.026)
5.325**
(2.388)
Constant
47.812
(3.449)
41.963
(3.451)
N
1,264
1,497
R2
0.211
0.235
Note: Standard errors in parentheses; *** p<0.01, ** p<0.05.
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Table 3: The Relationship between Coaching Status by Gender and Teacher Effectiveness:
Model Specification and OLS Estimates
Percentile Rankings
English
Math
Coach
14.966**
(5.943)
2.642
(3.084)
Female
5.886**
(2.392)
10.243***
(1.856)
Female-Coach Interaction
-20.220***
(6.984)
7.906
(4.942)
Constant
42.185
(2.437)
32.070
(3.808)
N
1,264
1,497
R-squared
0.219
0.259
Note: Standard errors in parentheses. ***p<0.01, **p<0.05. We also control for grade-level and
school-level fixed effects but do not report them.
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Table 4: The Relationship between Coaching Status by Gender and Teacher Effectiveness:
Summary
Percentile Rankings
English
Math
Male Coaches
14.879**
(3.804)
2.642
(5.942)
Female Coaches
-5.253
(3.564)
10.548***
(1.856)
Note: Standard errors in parentheses. ***p<0.01, **p<0.05.
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Table 5: Teacher Effectiveness by Type of Sport Coached
Percentile Ranking
English
10.898
(11.863)
-6.878
(7.840)
-0.505
(3.393)
48.036
(3.455)
Math
3.996
(7.288)
14.303**
(5.938)
3.767
(2.721)
41.855
(3.452)
N
1,264
1,497
R-squared
0.212
0.236
Coached Boy’s Sport
Coached Girl’s Sport
Coached Coed Sport
Constant
Note: Standard errors in parentheses. ***p<0.01, **p<0.05.
COACHES AREN’T BAD TEACHERS
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Math Value-Added Scores: Coaches and Non-Coaches
0
.005
Density
.01
.015
Figure 1: Value-Added Scores of Coaches and Non-Coaches
0
20
40
60
80
Math Value-Added Percentile Score
Non-Coaches
English Value-Added Scores: Coaches and Non-Coaches
.008
.006
.004
.002
Density
.01
.012
Coaches
100
0
20
40
60
80
English Value-Added Percentile Score
Coaches
Non-Coaches
100
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1
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We also conducted the same analysis using single-year value-added scores. The results from using single-year and
career value-added scores are not substantively different, so we only report the career value-added scores in this
study.