F. Chris Curran - Am MIT spezialisierte KI-Forschung

F. Chris Curran

School of Public Policy

University of Maryland,

Baltimore County

Baltimore, MD 21225

curranfc@umbc.edu

ESTIMATING THE RELATIONSHIP BETWEEN

PRESCHOOL ATTENDANCE AND

KINDERGARTEN SCIENCE ACHIEVEMENT:

IMPLICATIONS FOR EARLY SCIENCE

ACHIEVEMENT GAPS

Abstrakt
Recent evidence demonstrates that disparities by race/ethnicity
and socioeconomic status in science achievement are present in
the earliest grades of school. Preschool represents one potential
policy solution; Jedoch, little research has explored the relation-
ship between preschool attendance and science outcomes. Das
study examines whether preschool participation may improve sci-
ence outcomes overall and reduce science achievement gaps by
race/ethnicity, Geschlecht, and socioeconomic status. Using data from
the Early Childhood Longitudinal Study of 2011, this study uses
school and classroom ﬁxed eﬀects models with a robust set of
controls to estimate the relationship between preschool atten-
dance and early science outcomes. Results suggest that attend-
ing preschool is predictive of higher teacher-rated science ability
in the fall of kindergarten but that preschool is not predictive of
higher science achievement in the spring of kindergarten. Der
relationship is not found to consistently diﬀer by student race,
socioeconomic status, or gender,
though descriptive results
demonstrate that subgroups have diﬀerent patterns of preschool
attendance. Implications for policy and practice are discussed.

https://doi.org/10.1162/edfp_a_00247

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F. Chris Curran

I N T RO D U C T I O N

1 .
Advancing science achievement among American youth is a pressing policy goal for
educational stakeholders. Bedauerlicherweise, results from international assessments show
the United States lags other countries in a number of indicators of science achieve-
ment (Lee and Buxton 2010; OECD 2018). Außerdem, within the United States, dis-
parities exist across groups in science performance. It is well documented that women
and racial minorities are underrepresented in the science workforce, a gap that is link-
able to disparities in science participation in higher education and K–12 schooling
(Chen and Weko 2009; Riegle-Crumb and King 2010; Beede et al. 2011; Neuhauser
2015).

Although science achievement in the postsecondary and secondary sectors has been
well studied (z.B., Maltese and Tai 2011; Wang 2015; Gottfried and Bozick 2016), weniger
attention has been given to science in the earliest grades of school. Emerging evi-
dence, Jedoch, suggests that trajectories of science achievement and disparities be-
tween groups are present in the early years of school (Kohlhaas, Lin, and Chu 2010;
Maerten-Rivera et al. 2010; Quinn and Cooc 2015; Curran and Kellogg 2016; Morgan
et al. 2016; Curran 2017). Zum Beispiel, Curran and Kellogg (2016) document substan-
tial race/ethnicity gaps in science achievement as early as kindergarten, and other work
demonstrates that general knowledge achievement, including science, is one of the
strongest predictors of science achievement through the end of eighth grade (Morgan
et al. 2016). Such work suggests the need for an increased focus on early intervention as
a mechanism for improving overall levels of science achievement while also improving
equity in science achievement between subgroups.

Preschool is one of the most promising interventions for improving early academic
Leistung. Although a large body of literature has demonstrated the positive eﬀects
of high-quality preschool on early elementary achievement (z.B., Magnuson, Ruhm, Und
Waldfogel 2007a; Gormley, Phillips, and Gayer 2008), most of this work has focused
on the impacts of preschool on reading and mathematics outcomes. Comparatively,
few studies have explored the relationship between participation in preschool and early
elementary science outcomes, and those that do tend to focus on limited geographic re-
gions or speciﬁc preschool programs (Henry, Gordon, and Rickman 2006; Greenﬁeld
et al. 2009). Infolge, we have little evidence on the average relationship between
preschool participation and science outcomes and the degree to which preschool par-
ticipation might serve to mitigate early science achievement gaps.

The purpose of this paper is to provide evidence on the relationship between
preschool participation and science outcomes in the kindergarten year. Außerdem,
the study seeks to assess the degree to which preschool participation may mitigate early
science achievement gaps as well as the ways in which structural, policy-amenable
characteristics of preschools may contribute to diﬀerential science outcomes. To this
end, this study uses the newly released Early Childhood Longitudinal Study of 2011
(ECLS-K:2011) to address the following research questions:

(1) What is the relationship between participation in preschool and science achieve-

ment during the spring of kindergarten?

(2) What is the relationship between participation in preschool and teacher-rated sci-

ence ability during the fall of kindergarten?

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211

Preschool Attendance and Science Achievement

(3) Do these relationships vary by student characteristics such as race/ethnicity, gen-

der, or socioeconomic status?

(4) Does the relationship between participation in preschool and teacher-rated sci-
ence ability or science achievement vary by the location of the preschool (in a K–12
school or not) or by full-time or part-time attendance?

This study has the potential to provide important information to policy makers and
educational practitioners seeking to improve overall levels of and equity in science
achievement. In the following sections, I provide an overview of the extant research
on preschool and science achievement. I then present the data and methodology, Und
conclude with the ﬁndings and implications for policy and practice.

2 . P R I O R L I T E R AT U R E
Early Science Achievement
Student achievement in science has been an active area of research for quite some time,
reﬂecting policy priorities around developing a workforce capable of engaging in sci-
entiﬁc ﬁelds (National Science Technology Council 2013). This research, Jedoch, hat
tended to focus on science achievement in the collegiate, secondary, or upper elemen-
tary levels of schooling, with far less work examining science achievement during the
ﬁrst years of formal schooling (z.B., Maltese and Tai 2011; Wang 2015; Gottfried and
Bozick 2016).

Emerging evidence, Jedoch, suggests that early elementary science achievement
is important for future science achievement, and that such achievement is not equal
across subgroups of students (Quinn and Cooc 2015; Curran and Kellogg 2016; Morgan
et al. 2016; Curran 2017). Morgan and colleagues used data from the Early Childhood
Longitudinal Study (ECLS-K) to predict science achievement through eighth grade.
They found that a ﬁrst grade general knowledge assessment, which tested science
(among other components), was a stronger predictor of science achievement from third
to eighth grade than measures of mathematics achievement, reading achievement,
or observable student characteristics. Außerdem, among similar covariates, kinder-
garten general knowledge was the strongest predictor of ﬁrst grade general knowledge
(Morgan et al. 2016). These ﬁndings suggest that early science performance predicts
future academic trajectories, serving as a foundation for future science achievement.

Bedauerlicherweise, evidence suggests that these early science trajectories vary signiﬁ-
cantly across racial/ethnic, Geschlecht, and socioeconomic subgroups. Curran and Kellogg
(2016) found that racial/ethnic gaps in science achievement exist in kindergarten, mit
white students outperforming black and Hispanic students by over three quarters of a
Standardabweichung. Work by others conﬁrms that these racial/ethnic science gaps are
present through the upper elementary and middle school years (Kohlhaas, Lin, and Chu
2010; Quinn and Cooc 2015; Morgan et al. 2016). In a similar fashion, large socioeco-
nomic gaps in science achievement are documented as early as kindergarten (Morgan
et al. 2016; Curran 2017). Zum Beispiel, Curran (2017) ﬁnds the gap in science achieve-
ment at kindergarten between families near the 90th percentile of income compared
with those near the 10th percentile is approximately one standard deviation. Though
gender gaps are less pronounced in the kindergarten year, they begin appearing by ﬁrst

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F. Chris Curran

grade and are reported at nearly a quarter of a standard deviation by third grade, mit
boys outperforming girls (Quinn and Cooc 2015; Curran and Kellogg 2016). Zusamenfassend,
the early presence of science achievement gaps and the importance of early science
achievement as a predictor of later science achievement suggests the potential for early
intervention to improve science achievement overall and equity in science achievement
between subgroups.

Science in Early Childhood Education
Preschool education represents one possible mechanism to inﬂuence early science
achievement. Over the last several decades, early childhood education has expanded
dramatically, with a number of states pushing for universal preschool programs (Fitz-
patrick 2008; Curran 2015). Coupled with enrollment in private preschool and the fed-
erally funded Head Start program, mehr als 65 percent of four-year-olds now attend
some form of preschool care, mit fast 40 percent in a state pre-K or Head Start
Programm (Barnett et al. 2016; NCES 2016).

Despite the increasing prevalence of preschool education, little research has ex-
amined the relationship between preschool participation and science achievement.
Trotzdem, a large body of research has demonstrated connections between high-
quality preschool and early academic achievement in other subjects, such as mathe-
matics and reading. Zum Beispiel, targeted programs such as the High/Scope Perry
Preschool Project and the Abecedarian Project have been shown to produce academic
gains in the early years of kindergarten, as well as reduced incarceration and higher
levels of educational attainment later in life (Campbell et al. 2002; Belﬁeld et al. 2006;
Temple and Reynolds 2007). Ähnlich, studies have found positive impacts of state-
sponsored preschool programs and the federally funded Head Start program on aca-
demic outcomes (Henry, Gordon, and Rickman 2006; Fitzpatrick 2008; Gormley,
Phillips, and Gayer 2008; Wong et al. 2008; Camilli et al. 2010; Puma et al. 2010).
At a national level, prior work using the original Early Childhood Longitudinal Study
has documented a positive relationship between center-based preschool participation
and early academic achievement (Magnuson, Ruhm, and Waldfogel 2007a; Claessens,
Engel, and Curran 2014). In addition to overall positive eﬀects, prior work also sug-
gests that preschool may particularly beneﬁt racial minorities and, in manchen Fällen,
students from lower-income households (Magnuson et al. 2004; Magnuson, Ruhm,
and Waldfogel 2007a; Fitzpatrick 2008; Bassok 2010; Weiland and Yoshikawa 2013).
Außerdem, though prior work is mixed, some research demonstrates that the size
of the relationship can vary based on structural components of the preschool envi-
ronment, such as whether the preschool is co-located with a K–12 school or whether
students attend on a part-time or full-time basis (Robin, Frede, and Barnett 2006;
Magnuson, Ruhm, and Waldfogel 2007a, 2007B; Reynolds et al. 2014; Leow and Wen
2016).

Very few of these studies, Jedoch, have examined the impact of preschool partici-
pation on early science outcomes. In one of the few studies that does examine science
outcomes, Henry, Gordon, and Rickman (2006) estimate that participation in the Geor-
gia state preschool program predicted higher teacher-rated science ability in the fall of
kindergarten than students who attended Head Start. Their study, Jedoch, is limited

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Preschool Attendance and Science Achievement

to evidence from a single state’s preschool program and did not include a standardized
science achievement test.

Although there is little evidence on the relationship between preschool attendance
and science outcomes, studies of the prevalence of science instruction in preschool set-
tings, as well as the emphasis on science in preschool state standards, suggest that the
emphasis on science in preschool can vary signiﬁcantly across settings. A recent sur-
vey of state early-learning standards found approximately 94 percent of states had sci-
ence early-learning standards (DeBruin-Parecki and Slutzky 2016). Approximately two
thirds included science as a speciﬁcally named section in the standards, und der andere
third included science learning standards under another content domain (DeBruin-
Parecki and Slutzky 2016). Though science content is almost universal in state early-
learning standards, not all preschool providers are required to adhere to state standards.
The extent to which such standards are required varies signiﬁcantly across preschool
settings. Zum Beispiel, 66 percent of states require that state-funded preschools in pub-
lic school buildings use the standards, compared with 30 percent for other center-
based preschools, und nur 8 percent for parochial preschools (DeBruin-Parecki and
Slutzky 2016). That the requirement to adhere to state science standards varies based
on whether the preschool is a state-funded program in a public school building suggests
the possibility of variation in relationships between preschool attendance and science
outcomes across preschool type and preschool location.

Gleichzeitig, evidence suggests that, in addition to varying across settings,
science instruction is often limited in preschool. In a study of twenty preschool class-
rooms across thirteen Midwestern child care centers, Tu (2006) found that about half
of classrooms had a formal science area but less than 5 percent of time was spent on
formal science instruction and less than 10 percent of time was spent on informal sci-
ence learning. Relatedly, a study of preschools in Oklahoma, a state with a universal
preschool program, found that students in state-funded preschool as well as in Head
Start received approximately the same amount of science instruction (um 17 Prozent
of time), though the frequency of both was about half that of English language arts (24–
30 percent of time; Phillips, Gormley, and Lowenstein 2009). Compared with a broader
sample of state-run and Head Start preschool programs, Jedoch, preschools in Okla-
homa provided students with 30–50 percent more science instruction, suggesting that
national averages are lower (Phillips, Gormley, and Lowenstein 2009). Ähnlich, Ca-
bell et al. (2013) found science instructional time to be much lower than that of social
Studien, literacy, or reading in a sample of both Head Start, school-based, and other
preschools.

Science instruction in preschool may vary across settings depending, in part, on a
number of characteristics of preschool settings. Qualitative work suggests that some
preschool teachers are hesitant to teach science because of a perceived lack of science
content knowledge and science pedagogical knowledge (Timur 2012). Other work, Wie-
immer, suggests that some groups of teachers may not see these as the most salient lim-
itations. In a sample of Head Start teachers, most had positive views toward comfort
of teaching science but cited a lack of preparation time, lack of materials, and a lack
of available instructional time as the largest obstacles to science instruction (Maier,
Greenﬁeld, and Bulotsky-Shearer 2013). That teachers cite a lack of preparation and
instructional time as an obstacle to science instruction suggests the possibility that

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F. Chris Curran

relationships between preschool attendance and science outcomes could vary based on
whether students attend preschool part-time or full-time.

Although science instruction time is limited in many preschool settings, the re-
search nevertheless supports the potential for such instruction to improve school
readiness indicators such as early achievement. In a study of Head Start classrooms,
Fuccillo (2011) found that, compared with mathematics instruction or to circle time,
science instruction prompted more higher-level instructional interactions. The study
demonstrated that the use of higher-level questioning in these contexts was related
to gains in both cognitive ﬂexibility and science outcomes (Fuccillo 2011). In another
Studie, Cabell et al. (2013) utilized data from over three hundred teachers across both
Head Start, public school preschool programs, and other preschool programs to sim-
ilarly examine the relationship between preschool activities and instructional quality.
The results of this study conﬁrmed those of Fuccillo (2011), ﬁnding that the most eﬀec-
tive instructional interactions took place during science instruction. These ﬁndings are
consistent with other work that shows higher-order dialogue when reading informa-
tional science books in preschool (Price, Bradley, and Smith 2012). Although research
on the eﬀectiveness of preschool science instruction is often limited because of a lack
of early science assessments (Greenﬁeld 2015), these ﬁndings suggest the possibility
that attending preschool could improve early science outcomes.

Zusamenfassend, Dann, the evidence is unclear as to whether one should expect positive re-
lationships between preschool attendance and science outcomes. Einerseits, Die
literature points to the potential beneﬁts of science instruction in preschool, yet, on the
andererseits, the evidence suggests that little time is devoted to science instruction in
preschool. Coupled with the variation in science instructional time across preschools,
this body of evidence suggests the importance of exploring the relationship between
preschool attendance and early science outcomes at scale. This study seeks to address
this issue by using nationally representative data to estimate the relationship between
preschool participation and science outcomes in kindergarten, while also exploring dif-
ferential relationships for subgroups of students. Außerdem, given that science in-
struction may vary based on structural components of preschools, this study examines
two such aspects of preschools—their location and part-time/full-time enrollment. In
the next section, I describe the unique data source that allows for exploration of these
Fragen.

3 . DATA
I draw on data from the newly released Early Childhood Longitudinal Study of 2010–
11 (ECLS-K:2011). The ECLS-K:2011 consists of a representative set of kindergartners
from the 2010–11 school year who will be followed through ﬁfth grade. The survey
used a complex multistage sampling strategy to produce nationally representative esti-
mates of public and private school students (Tourangeau et al. 2015A, B). The ECLS-
K:2011 provides the most current evidence on the experiences of elementary school
students.

The ECLS-K:2011 is unique in its inclusion of science achievement scores in the
kindergarten year. Unlike the original ECLS-K, which collected data on kindergartners

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Preschool Attendance and Science Achievement

in the 1998–99 school year and lacked such early science assessments, the new
study allows for the exploration of the relationship between early childhood educa-
tion experiences and subsequent science achievement during the ﬁrst year of formal
schooling.

The ECLS-K:2011 science assessment included questions pertaining to the physi-
cal sciences, life sciences, environmental sciences, and scientiﬁc inquiry (Tourangeau
et al. 2015A, B). The science assessment was developed from commonalities in the 2009
science standards from six states (Arizona, Kalifornien, Florida, New Mexico, Texas, Und
Virginia) as well as from input from a panel of educators and subject area curriculum
specialists (Tourangeau et al. 2015A, B). Folglich, the science assessment has a high
level of validity, reﬂecting both state science standards and expert input. With regard
to reliability, the test items were subjected to pilot ﬁeld tests prior to selection of the
ﬁnal assessment items and had a reliability of 0.75, a lower reliability than for math-
ematics and reading as a result of the wider range of content assessed on the science
achievement test (Tourangeau et al., 2015A, B). The science assessment, given in the
spring of the kindergarten year, included a consistent set of items for all students and
was administered verbally so as not to depend on written responses (Tourangeau et al.
2015A, B). For this study, I used standardized versions of the science theta score, welche
were derived from item response theory measures. Insbesondere, I standardized the
measures within the kindergarten year using sampling weights and survey settings to
account for the complex sampling design of the ECLS-K:2011. This standardized science
achievement score served as the primary dependent variable for this study.

In addition to exploring standardized science achievement, I also used a series
of teacher-rated science ability measures gathered during the fall semester of kinder-
garten. Teacher-rated science ability measures have been used in prior studies of
preschool (Henry, Gordon, and Rickman 2006). As a part of the survey, teachers rated
each student on their proﬁciency on eight diﬀerent science competencies. The com-
petencies included “uses his/her sense to explore and observe,” “forms explanations
based on observations and explorations,” “classiﬁes and compares living and non-
living things in diﬀerent ways,” “makes logical predictions when pursuing scientiﬁc
investigations,” “communicates scientiﬁc information,” “demonstrates understanding
of physical science concepts,” “demonstrates understanding of life science concepts,”
and “demonstrates understanding of earth and space science concepts” (Tourangeau
et al. 2015A, B). Teachers could rate students’ ability in each of these competencies as
“not yet,” “beginning,” “in progress,” “intermediate,” or “proﬁcient.” They also had the
option of specifying that the skill was not applicable or had not yet been taught. After re-
coding “not applicable or skill not yet taught” to missing, I created a composite version
of these eight measures (Cronbach’s alpha of 0.979 for the combined scale) and used
the composite as well as each of the eight original measures as additional dependent
variables of interest.

Because it is true that many kindergarten teachers had not had an opportunity to
evaluate students’ science abilities in the fall semester of kindergarten, the teacher-
rated ability measure is limited to data from teachers who did indicate they had an
opportunity to teach or observe the skill. As a means of assessing the validity of the
fall teacher-rated ability measures in science, I compared their correlations with the

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F. Chris Curran

spring achievement test to that of mathematics, which also had a fall achievement
test. The correlation between the fall teacher-rated science ability composite measure
and the spring science achievement score was similar to that for fall teacher-rated
mathematics ability and spring mathematics standardized achievement scores (0.35
Und 0.40, jeweils). The fall teacher-rated mathematics ability composite, im Gegenzug,
was moderately correlated (0.50) with the fall mathematics achievement test, vorschlagen-
ing that teachers’ fall ratings of student ability are reasonable measures of student
ability.

The primary independent variable of interest was an indicator of whether a student
attended any formal preschool setting with the exclusion of Head Start. The ECLS-K
asked the parents a series of questions regarding the children’s early educational expe-
riences in the year prior to kindergarten. Insbesondere, parents could specify whether
a child was in center-based care, a state-sponsored preschool program, Head Start, oder
whether a child was cared for by relatives or nonrelatives. I followed precedent from
the literature in creating mutually exclusive indicators of early care (Magnuson et al.
2007A). Insbesondere, I coded students as having attended Head Start if the parent indi-
cated that any of the forms of early care were a Head Start program. I coded the student
as having attended state-sponsored child care if the parent indicated that the program
was state-sponsored and that it was not Head Start. Center-based care represented any
formal preschool experience that was not Head Start or a state-sponsored program.
The primary independent variable of interest, preschool, included those students in
center-based care or state-sponsored care. Although I used this measure as the primary
independent variable of interest, I also made use of the disaggregated center-based,
state-sponsored, and Head Start preschool variables in alternative speciﬁcations.

In addition to the primary dependent and independent variables of interest, I used
a number of covariates to mitigate selection bias. My list of control variables included a
robust set of child, family, and neighborhood covariates from the original ECLS-K that
aligns closely with those used by Magnuson and colleagues in a prior study of preschool
(2007A). Insbesondere, I controlled for measures such as child race, child gender, family
Struktur, family income, parental education, parental workforce participation, educa-
tional expectations, access to books and other resources, participation in extracurricular
and enrichment activities, and neighborhood safety, unter anderen. The full list of con-
trol variables along with descriptive statistics on the control variables is provided in
Appendix table A.1.

The primary analytic sample for this study consisted of students with available in-
formation on their preschool participation, as well as an available standardized sci-
ence achievement score from the spring of kindergarten. Although observations were
dropped due to missing data on these variables, in order to maintain representative-
ness, the use of weights to adjust for nonresponse and missing data attempted to ad-
just for these lost observations. Observations missing data on non-key variables, solch
as the control variables, were dealt with through the use of multiple imputation. Mul-
tiple imputation has been shown to have strong properties for handling missing data
(Allison 2009) and allows for the retention of observations with missing data on con-
trol variables. I used thirty-ﬁve imputed datasets and implemented multiple imputa-
tion through the multivariate normal approach in Stata 14 (Schafer 1997; Graham,
Olchowski, and Gilreath 2007). After imputation and the application of survey weights,

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217

Preschool Attendance and Science Achievement

the ﬁnal analytic sample for this study consisted of 10,500 students (rounded to comply
with Institute of Education Sciences restricted data standards).

4 . M E T H O D S
The primary analytic approach involved ordinary least squares regression with a ro-
bust set of student, parent, and neighborhood control variables. Zusätzlich, I in-
cluded school ﬁxed eﬀects as well as, in some speciﬁcations, classroom ﬁxed eﬀects,
implicitly controlling for both observed and unobserved characteristics that are ﬁxed
within schools or classrooms, jeweils. The primary analytic model is shown in
equation 1:

ScienceOutcomeiy = β0 + β1Preschooliy + β2Xiy + γy + eiy,

(1)

where ScienceOutcome is the standardized science test score in the spring of kinder-
garten or the teacher-rated science ability measure in the fall of kindergarten for stu-
dent i in school or classroom y. Preschool is a binary indicator of whether the student
attended preschool (center-based or state-sponsored) oder, in some models, disaggregated
binary indicators of participation in center-based preschool, state-sponsored preschool,
or Head Start. X is a vector of child, family, and contextual control variables, and γ repre-
sents the inclusion of either school or classroom ﬁxed eﬀects depending on the model.
Bei diesem Modell, β1 represents the covariate of interest and can be interpreted as the dif-
ference in standardized science achievement or teacher-rated ability for students who
attended preschool compared with those who did not after controlling for the covariates
and school or classroom ﬁxed eﬀects. Across models, the comparison group is students
who were not in a formal early child care setting (center-based, state-sponsored, or Head
Start). The estimates were weighted to account for the complex sampling design of the
ECLS-K, and standard errors were estimated using Taylor series linearization.

One limitation of the science achievement tests is that they were administered in
the spring semester of the kindergarten year. Folglich, by the time of the test, stu-
dents had varying opportunities throughout the year to augment their science compre-
hension. Given a large body of literature around the “fade out” of preschool eﬀects, eins
would expect the relationship between preschool attendance and science achievement
to be smaller in the spring semester than it would have been at the start of kinder-
garten (Gibbs, Ludwig, and Miller 2011; Claessens, Engel, and Curran 2014; Lipsey, Far-
ran, and Hofer 2015). The models predicting teacher-rated science ability during the fall
of kindergarten partially address this issue by picking up science ability earlier in the
academic year.

In addition to the primary models, I also ﬁt models exploring diﬀerential relation-
ships for subgroups of students deﬁned by race/ethnicity, Geschlecht, and socioeconomic
Status. Insbesondere, I ﬁt versions of the model shown in equation 1 das enthielt
interactions between the preschool variable and dummy variables indicating student
Wettrennen, student gender, or family income quartile. These models take the form shown in
equation 2:

ScienceOutcomeiy = β0 + β1Preschooliy + β2Preschooliy ∗ Subgroup_Indicatoriy

+ β3Xiy + γy + eiy,

(2)

218

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F. Chris Curran

where the variables and covariates are the same as equation 1 except for the interaction
term between preschool and the subgroup indicators (race/ethnicity, Geschlecht, or income
bracket depending on the model). The key coeﬃcient of interest in these models is β2,
which can be interpreted as the diﬀerential relationship between preschool attendance
and science outcomes for each subgroup.

Endlich, I ﬁt models that examined the relationship between structural characteris-
tics of the preschool environment and early science outcomes. These models inform
policy-amenable characteristics of preschools that prior literature suggests may be re-
lated to preschool eﬀects (Robin, Frede, and Barnett 2006; Magnuson, Ruhm, Und
Waldfogel 2007a, B; Maier, Greenﬁeld, and Bulotsky-Shearer 2013; Reynolds et al. 2014;
DeBruin-Parecki and Slutzky 2016; Leow and Wen 2016). Insbesondere, I ﬁt variants
of the primary model (equation 1) in which the preschool indicator was replaced with
measures of whether the preschool attended was located in a K–12 school building or
nicht, or with measures of whether the student attended the preschool full or part-time.
In the ﬁrst of these models, two binary indicators, one representing preschool atten-
dance in a K-12 building and another representing preschool attendance in a non-K-12
building, were included in the model. In the second of these models, an indicator for
full-time enrollment (>20 hours per week) was included along with an indicator for
part-time enrollment (20 or fewer hours per week), a part/full-time distinction used in
prior literature (Magnuson, Ruhm, and Waldfogel 2007a). As with the primary models,
these models included an indicator for Head Start participation, making the compari-
son group those students who did not attend any formal preschool.

Assessing the eﬀects of preschool on early elementary achievement is complicated
by issues of selection. Insbesondere, the students who participated in preschool may dif-
fer systematically from those who did not in ways that would independently inﬂuence
their academic outcomes. Infolge, any attempt to isolate the eﬀects of preschool on
science outcomes must attempt to account for such selection bias. My analytic strategy
addresses a number of potential sources of bias, although it does not entirely elimi-
nate the possibility of confounding variables. Folglich, the results should be in-
terpreted as covariate-adjusted relationships rather than causal estimates.

5 . R E S U LT S
I ﬁnd that participation in preschool is generally predictive of increased teacher-rated
science ability during the fall of kindergarten but is not signiﬁcantly related to standard-
ized science achievement during the spring of kindergarten. I ﬁnd, Jedoch, that the
relationship varies by type of preschool with the positive relationship between preschool
participation and teacher-rated science ability being driven primarily by participation in
center-based preschool as opposed to state-sponsored preschool or Head Start. The rela-
tionship between preschool participation and science ability/achievement is generally
consistent across student race, Geschlecht, and family income, although there is suggestive
evidence of larger impacts for black and male students. Trotzdem, descriptive statis-
tics suggest that white students and more aﬄuent students have diﬀerent patterns of
preschool attendance than their nonwhite or less-aﬄuent peers. Endlich, the relation-
ship between preschool participation and teacher-rated science ability appears largest

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219

Preschool Attendance and Science Achievement

Tisch 1. Means and Standard Errors of Preschool Participation, Science Achievement, and Teacher-Rated Science Ability for Full Sample
by Preschool Status

Spring science achievement (standardized)

Teacher-rated science ability at fall of K

Sense

Explain

Classify

Predict

Communicate

Physical science

Life science

Earth/space science

Composite

Preschool (center-based or state-sponsored)

Center-based preschool

State-sponsored preschool

Head Start

Relative care

Nonrelative care

Parental care

Structural components

Not located in K—12 school

Located in K—12 school
Full time (>20 hrs/week)
Part time ((cid:2)20 hrs/week)

Full
Sample

0.0690
(0.032)

2.843
(0.029)

2.621
(0.027)

2.845
(0.030)

2.653
(0.031)

2.437
(0.032)

2.575
(0.027)

2.814
(0.027)

2.372
(0.035)

2.582
(0.037)

0.556

0.404

0.152

0.153

0.067

0.024

0.200

0.377

0.179

0.246

0.310

10,500

Preschool
(Center-Based or
State-Sponsored)

0.292
(0.026)

2.988
(0.036)

2.788
(0.034)

3.016
(0.035)

2.818
(0.036)

2.583
(0.039)

2.709
(0.035)

2.955
(0.034)

2.542
(0.044)

2.764
(0.047)

1.000

0.727

0.273

0.000

0.678

0.322

0.443

0.557

5,950

Center-
Based
Preschool

0.385
(0.027)

Zustand-
Sponsored
Preschool

Kopf
Start

0.0445
(0.040)

−0.366
(0.044)

NEIN
Formal
Preschool

−0.128
(0.047)

3.036
(0.044)

2.865
(0.041)

3.088
(0.040)

2.869
(0.040)

2.633
(0.046)

2.761
(0.042)

3.003
(0.038)

2.577
(0.051)

2.831
(0.054)

1.000

0.000

0.779

0.221

0.433

0.567

4,430

2.857
(0.046)

2.581
(0.042)

2.822
(0.058)

2.681
(0.055)

2.453
(0.049)

2.577
(0.048)

2.825
(0.054)

2.450
(0.063)

2.590
(0.071)

1.000

0.000

1.000

0.000

0.411

0.589

0.469

0.531

1,520

2.649
(0.052)

2.355
(0.047)

2.588
(0.046)

2.411
(0.051)

2.226
(0.044)

2.359
(0.040)

2.646
(0.043)

2.161
(0.049)

2.404
(0.055)

0.000

1.000

0.000

2.656
(0.032)

2.419
(0.037)

2.642
(0.043)

2.449
(0.040)

2.264
(0.039)

2.426
(0.035)

2.621
(0.032)

2.157
(0.046)

2.328
(0.042)

0.000

0.231

0.083

0.687

0.000

1,560

2,990

Notes: Standard errors of nonbinary variables shown in parentheses. Sample sizes for teacher-rated ability vary due to missing data.

for preschools not located in K–12 buildings. In diesem Abschnitt, I present the results that
support these ﬁndings.

Descriptive Statistics
Participation in some form of preschool child care is common. As shown in table 1, über
70 percent of kindergarten students had taken part in either center-based preschool,
Head Start, or a state-sponsored preschool program. Of these formal child care set-
tings, center-based preschool was the most common, with over 40 percent of the sam-
ple having taken part in a center-based setting that is not Head Start or a state-sponsored
preschool program.

220

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Tisch 2. Means and Standard Errors of Preschool Participation, Science Achievement, and Teacher-Rated Science Ability for Full Sample and
by Student Characteristics

Spring science achievement

(standardized)

Teacher-rated science ability at fall of K

Sense

Explain

Classify

Predict

Communicate

Physical science

Life science

Earth/space science

Composite

Full
Sample

0.0690
(0.032)

2.843
(0.029)

2.621
(0.027)

2.845
(0.030)

2.653
(0.031)

2.437
(0.032)

2.575
(0.027)

2.814
(0.027)

2.372
(0.035)

2.582
(0.037)

White

Black

Hispanic

Asian

Boys

Girls

Higher
Income

Lower
Income

0.408 −0.424 −0.568 −0.0965
(0.055)
(0.023)

(0.065)

(0.046)

0.0834
(0.031)

0.0536
(0.035)

0.360 −0.358
(0.041)
(0.021)

2.987
(0.036)

2.783
(0.035)

3.009
(0.035)

2.810
(0.039)

2.591
(0.039)

2.723
(0.036)

2.936
(0.035)

2.522
(0.046)

2.755
(0.044)

2.664
(0.059)

2.360
(0.069)

2.633
(0.071)

2.429
(0.064)

2.251
(0.053)

2.399
(0.050)

2.718
(0.072)

2.178
(0.066)

2.395
(0.077)

2.527
(0.039)

2.289
(0.035)

2.507
(0.042)

2.318
(0.041)

2.125
(0.041)

2.281
(0.036)

2.548
(0.037)

2.100
(0.041)

2.254
(0.045)

2.871
(0.106)

2.749
(0.088)

2.869
(0.100)

2.721
(0.077)

2.582
(0.126)

2.629
(0.107)

2.829
(0.091)

2.549
(0.139)

2.720
(0.181)

2.812
(0.031)

2.592
(0.033)

2.817
(0.036)

2.649
(0.035)

2.409
(0.036)

2.559
(0.029)

2.789
(0.028)

2.378
(0.039)

2.557
(0.045)

2.877
(0.034)

2.651
(0.033)

2.875
(0.032)

2.656
(0.035)

2.466
(0.035)

2.593
(0.032)

2.841
(0.032)

2.365
(0.040)

2.607
(0.039)

3.007
(0.037)

2.819
(0.035)

3.052
(0.036)

2.856
(0.037)

2.618
(0.040)

2.755
(0.036)

2.977
(0.032)

2.569
(0.049)

2.788
(0.050)

2.602
(0.032)

2.323
(0.028)

2.538
(0.037)

2.348
(0.033)

2.185
(0.032)

2.321
(0.028)

2.577
(0.036)

2.104
(0.033)

2.297
(0.033)

Preschool (center-based or

state-sponsored)

Center-based preschool

State-sponsored preschool

Head Start

Relative care

Nonrelative care

Parental care

Structural components

Not located in K—12 school

Located in K—12 school
Full time (> 20 hrs/week)
Part time ((cid:2) 20 hrs/week)

0.556

0.654

0.376

0.377

0.652

0.560

0.553

0.692

0.357

0.404

0.152

0.153

0.067

0.024

0.200

0.377

0.179

0.246

0.310

10,500

0.509

0.145

0.093

0.055

0.029

0.168

0.470

0.184

0.256

0.398

5,780

0.225

0.152

0.332

0.079

0.016

0.198

0.242

0.134

0.283

0.093

0.207

0.170

0.220

0.094

0.020

0.289

0.188

0.169

0.207

1,200

2,180

0.538

0.113

0.096

0.053

0.006

0.194

0.490

0.160

0.341

0.310

700

0.402

0.158

0.156

0.063

0.022

0.199

0.377

0.183

0.254

0.306

0.407

0.145

0.150

0.072

0.026

0.200

0.378

0.175

0.238

0.314

5,370

5,130

0.545

0.147

0.078

0.050

0.030

0.150

0.500

0.192

0.293

0.399

6,410

0.199

0.158

0.264

0.092

0.015

0.272

0.197

0.159

0.178

4,090

Notes: Standard errors of nonbinary variables shown in parentheses. Sample sizes for teacher-rated ability vary due to missing data.

Despite the high proportion of students taking part in preschool, not all groups
of students took part at the same rate. Insbesondere, there were signiﬁcant diﬀer-
ences across student race/ethnicity and family income in the rate of participation in
preschool, particularly center-based preschool. As shown in table 2, more than half
of white and Asian students took part in a center-based preschool program, wohingegen
less than one quarter of black and Hispanic students were in such a setting. Black and
Hispanic students were, Jedoch, more likely to take part in the federally funded Head
Start program than white students. Ähnlich, students from higher-income households
($40,000 or more) were approximately two and half times more likely to take part in center-based preschool than their peers from lower-income households, and only about l D o w n o a d e d f r o m h t t p : / / Direkte . m i t . F / / e d u e d p a r t i c e – p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d / . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 221 Preschool Attendance and Science Achievement a quarter as likely to take part in Head Start. There were no meaningful diﬀerences in preschool participation across gender. The results shown in tables 1 Und 2 also point to diﬀerences in spring of kinder- garten science achievement across preschool care, across race/ethnicity, and across family income. Students who participated in preschool (other than Head Start) pro- formed almost half a standard deviation higher than those not in preschool. Across student race/ethnicity, in the spring of kindergarten, white students scored over 0.8 of a standard deviation higher than black and Hispanic students in science achievement. Students from higher-income families scored approximately 0.7 standard deviations higher than their peers from lower-income families. Similar trends were observed on the teacher ratings of science ability at the fall of kindergarten. Insbesondere, students having attended preschool were rated approxi- mately 0.4 units higher on the composite scale (0 Zu 4 representing not yet to proﬁcient) of teacher-rated science ability than those who had not attended any formal preschool. A similar diﬀerence was observed when comparing white students with black or His- panic students and when comparing students from higher-income backgrounds with students from lower-income backgrounds. The descriptive results suggest then that there are large diﬀerences in science abil- ity/achievement between students who attended preschool and those who did not. Fur- thermore, gaps were present across student race/ethnicity and family income in science achievement levels, teacher-rated science ability, and participation in preschool. These results suggest the possibility that preschool may contribute to early science outcomes and that diﬀerences in participation across race and family income may explain some of the early science achievement gaps. To further explore this relationship, I turn next to results of regressions that include a robust set of individual and family controls, as well as school and classroom ﬁxed eﬀects. As the standardized achievement test is both likely more reliable and is available for a larger sample of students, I begin with a pre- sentation of results for spring standardized science achievement and then discuss fall of kindergarten teacher-rated science ability. Standardized Science Achievement During Spring of Kindergarten Table 3 shows results of regression models predicting standardized science achieve- ment during the spring of kindergarten from participation in preschool. The upper panel of the table includes regression results from models including a single binary in- dicator of participation in preschool (center-based or state-sponsored) and the lower panel includes disaggregated measures of center-based preschool, state-sponsored preschool, and Head Start. The omitted group in all of the regression models in both panels include students not in formal early childhood care (not in center-based, state- sponsored, or Head Start). Tisch 3 shows results of models that progressively add controls for family income, contextual factors, school ﬁxed eﬀects, and classroom ﬁxed eﬀects. As shown in the up- per panel of column 1, the bivariate regression captures the same relationship shown in the conditional means of table 1—namely, that students who participated in preschool scored almost half a standard deviation higher on the science assessment. When adding 222 l D o w n o a d e d von h t t p : / / Direkte . m i t . F / / e d u e d p a r t i c e – p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d / . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 F. Chris Curran Table 3. Coefficients and Standard Errors from Regressions Predicting Spring of Kindergarten Standardized Science Achieve- ment from Preschool Participation Preschool (center-based or state-sponsored) Center-based preschool State-sponsored preschool Head Start Income controls Child, family, and contextual controls School fixed effects Classroom fixed effects Observations Spring of Kindergarten Science Achievement (Standardized) (1) (2) (3) (4) (5) 0.420** (0.0396) 0.513** (0.0407) 0.173** (0.0560) −0.238** (0.0408) 0.206** (0.0341) 0.263** (0.0348) 0.0839+ (0.0469) −0.117** (0.0389) X 0.0001 (0.0254) 0.0106 (0.0238) 0.00275 (0.0293) 0.0147 (0.0284) −0.0275 (0.0302) −0.106** (0.0288) X X 0.0239 (0.0251) −0.0169 (0.0336) −0.0968** (0.0333) 0.0141 (0.0314) −0.0236 (0.0410) −0.102* (0.0405) X X X X X X 10,500 10,500 10,500 10,500 10,500 Notes: Robust standard errors in parentheses. All estimates account for the complex survey design of Early Childhood Lon- gitudinal Study through the use of survey setting and weighting. The omitted category in all models is students who were not in a formal preschool setting—namely, those who were cared for by relatives, nonrelatives, or parents, and were not in a center-based, state-sponsored, or Head Start program. **P < 0.01; *p < 0.05; +p < 0.1. controls for family income (column 2), however, this relationship was reduced by ap- proximately half. Column 3 accounted for diﬀerences in child, family, and contex- tual factors. As shown, accounting for these factors reduced the relationship between preschool participation and science achievement to near zero. The ﬁxed eﬀects models (columns 4 and 5) implicitly control for all ﬁxed aspects of students in either the school or classroom. The advantage of these models is that they control for both observable and unobservable characteristics common among students attending the same school or classroom. As shown, the relationship between preschool and spring of kindergarten science achievement remains nonsigniﬁcant with the addi- tion of school or classroom ﬁxed eﬀects, suggesting that the robust set of family income and child, family, and contextual controls were already accounting for much of the dif- ferences in students across these settings. Examining results of the models with disaggregated indicators of preschool demon- strates a similar trend (bottom panel of table 3). In particular, the relationship between center-based preschool as well as state-sponsored preschool and science achievement is positive and signiﬁcant in the unadjusted model (column 1). However, this relation- ship becomes statistically nonsigniﬁcant when controlling for the full range of family income and child, family, and contextual controls (column 3). Likewise, models with school and classroom ﬁxed eﬀects (columns 4 and 5) also show no signiﬁcant relation- ship. The relationship between Head Start and standardized science achievement is consistently negative, although given the targeted nature of Head Start, this relation- ship may be driven by unobserved characteristics of the students participating in Head Start. The statistical nonsigniﬁcance observed for standardized science achievement was also observed for mathematics and reading outcomes during the spring of l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d . f / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 223 Preschool Attendance and Science Achievement Table 4. Coefficients and Standard Errors from Regressions Predicting Spring and Fall of Kindergarten Standardized Math and Reading Achievement from Preschool Participation Panel A: Spring of Kindergarten Mathematics and Reading Achievement Spring of Kindergarten Math Achievement (std.) Spring of Kindergarten Reading Achievement (std.) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Preschool (center-based or state-sponsored) 0.376** (0.0315) 0.178** (0.0263) 0.00624 (0.0213) 0.0274 (0.0260) 0.0379 (0.0330) 0.342** (0.0295) 0.180** (0.0265) 0.0162 (0.0208) 0.0327 (0.0245) 0.0279 (0.0299) Income controls Child, family, and contextual controls School fixed effects Classroom fixed effects X X X X X X X X X X X X X X X X X X Observations 10,500 10,500 10,500 10,500 10,500 10,500 10,500 10,500 10,500 10,500 Panel B: Fall of Kindergarten Mathematics and Reading Achievement Fall of Kindergarten Math Achievement (std.) Fall of Kindergarten Reading Achievement (std.) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Preschool (center-based or state-sponsored) 0.514** (0.0417) 0.309** (0.0347) 0.123** (0.0253) 0.0981** (0.0245) 0.0814* (0.0317) 0.483** (0.0356) 0.305** (0.0314) 0.129** (0.0237) 0.122** (0.0246) 0.117** (0.0319) Income controls Child, family, and contextual controls School fixed effects Classroom fixed effects X X X X X X X X X X X X X X X X X X Observations 10,320 10,320 10,320 10,320 10,320 10,340 10,340 10,340 10,340 10,340 Notes: Robust standard errors in parentheses. All estimates account for the complex survey design of Early Childhood Longitudinal Study through the use of survey setting and weighting. The omitted category in all models is students who were not in a formal preschool setting— namely, those who were cared for by relatives, nonrelatives, or parents, and were not in a center-based, state-sponsored, or Head Start program. std = standardized. **p < 0.01; *p < 0.05. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d / f . kindergarten. Panel A of table 4 shows results of similar regression models predict- ing standardized mathematics and reading achievement (basic reading and early lit- eracy skills) in the spring of kindergarten. As shown, estimates with the full set of controls and the ﬁxed eﬀects models were also statistically nonsigniﬁcant for mathe- matics and reading, although the magnitude of such estimates was larger than that for science. Unlike science, the ECLS-K did include standardized achievement tests for mathematics and reading in the fall of kindergarten. Panel B of table 4 shows re- sults from models predicting standardized mathematics and reading achievement in the fall of kindergarten. As shown, preschool participation predicts statistically signiﬁ- cant higher scores (approximately 0.10 standard deviations or SD) in mathematics and reading achievement during the fall of kindergarten even in the fully controlled mod- els. The presence of a signiﬁcant relationship in the fall of kindergarten but not in the spring of kindergarten is consistent with a “fade out” of preschool eﬀects, as docu- mented in the literature (Gibbs, Ludwig, and Miller 2011; Claessens, Engel, and Curran 2014; Lipsey, Farran, and Hofer 2015). To assess whether preschool participation’s rela- tionship with science outcomes might also be stronger in the fall of kindergarten, I turn next to results of models predicting fall of kindergarten teacher-rated science ability. f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 224 F. Chris Curran Table 5. Coefficients and Standard Errors from Regressions Predicting Fall of Kindergarten Teacher-Rated Science Ability from Preschool Participation Sense Explain Classify Predict Communicate Physical Science Life Science Earth/ Space Science Composite (1) (2) (3) (4) (5) (6) (7) (8) (9) Preschool (center-based or state-sponsored) 0.0820* (0.0354) 0.0783+ (0.0445) 0.0921* (0.0406) 0.0644 (0.0412) 0.0887* (0.0447) 0.111** 0.118* (0.0458) (0.0383) 0.0168 −0.0127 (0.0607) (0.0467) 0.130** (0.0434) 0.000221 (0.0553) 0.00790 (0.0552) 0.0546 (0.0446) 0.0140 (0.0532) 0.0465 (0.0513) 0.0348 (0.0517) 0.0894+ (0.0457) 0.0643 (0.0408) 0.0867* (0.0370) 0.0869+ (0.0508) 0.108* (0.0500) 0.0486 (0.0562) 0.0488 (0.0549) 0.0963* (0.0440) −0.00522 (0.0536) 0.112** (0.0402) 0.0975+ (0.0557) 0.0297 (0.0491) 0.0644 (0.0670) 0.00799 (0.0486) 0.0444 (0.0448) 0.0419 (0.0596) 0.133** (0.0510) 0.180** (0.0563) 0.0372 (0.0647) 0.0694 (0.0616) Center-based preschool State-sponsored preschool Head Start Income controls Child, family, and contextual controls Classroom fixed effects X X X X X X X X X X X X X X X X X X X X X X X X X X X Observations 7,500 6,490 6,050 6,320 5,960 6,510 6,770 4,270 3,390 Notes: Robust standard errors in parentheses. All estimates account for the complex survey design of Early Childhood Longitudinal Study through the use of survey setting and weighting. Sample sizes vary across this table as teachers had the option of not answering the question and instead noting they had not had the opportunity to observe the skill. The omitted category in all models is students who were not in a formal preschool setting—namely, those who were cared for by relatives, nonrelatives, or parents, and were not in a center-based, state-sponsored, or Head Start program. **p < 0.01; *p < 0.05; +p < 0.1. Teacher Perceptions of Science Ability A limitation of the science achievement test in the ECLS is that it was administered dur- ing the latter half of the kindergarten year. Given evidence on the fade out of preschool eﬀects (Gibbs, Ludwig, and Miller 2011; Claessens, Engel, and Curran 2014; Lipsey, Far- ran, and Hofer 2015), one would expect smaller relationships at the end of kindergarten than at the beginning. Although a standardized test of science achievement was not available during the fall of kindergarten, teachers did provide their reports of students’ ability within eight diﬀerent science competencies. Results from regressions predicting these ratings show a consistent positive relationship between preschool attendance and teacher-rated science ability during the fall of kindergarten. In particular, as shown in the top panel of table 5, participation in preschool had at least a marginally signiﬁcant (p < 0.10) and positive relationship with all except two of the teacher ratings—namely, predicting and physical science. The relationship between preschool participation and the composite measure (column 9) of teacher-rated science ability was also positive and statistically signiﬁcant. The magnitude, 0.133 units on a 0 to 4 scale ranging from not yet having the skill to proﬁcient at the skill, equates to an approximately 0.06 standard deviation larger composite teacher rating of science ability on the composite scale. When disaggregating the preschool measure into types of preschool attended (bot- tom portion of table 5), the results suggest that the positive relationship observed is driven primarily by participation in center-based preschool as opposed to participation in state-sponsored preschool. In particular, participation in center-based preschool is predictive of higher teacher-rated science ability in each of the eight science competency areas. Likewise, the composite score (column 9) is approximately 0.18 units higher for students who attended center-based preschool than for students who were in no l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d . f / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 225 Preschool Attendance and Science Achievement formal preschool care. The relationship for state-sponsored and Head Start participa- tion lean in the positive direction but are considerably smaller in magnitude and are not statistically distinguishable from zero. Although teacher ratings may be more subject to personal bias or perception, the models shown in table 5 used classroom ﬁxed eﬀects, meaning that the comparisons were restricted to those ratings conducted by the same teacher. In short, any systematic diﬀerences in teacher ratings, such as a teacher who consistently rates students lower or higher, was accounted for by the classroom ﬁxed eﬀect. Student Subgroup Interactions Next, models were estimated in which the binary indicator for preschool was interacted with binary indicators for student race, student gender, and family income. Appendix tables A.2 through A.4 show results of these models for both spring of kindergarten standardized science achievement, as well as fall of kindergarten teacher-rated science ability. In general, the interaction terms are statistically nonsigniﬁcant. Exceptions in- clude a marginally signiﬁcant (p < 0.10) and positive interaction on the standardized science achievement score between preschool attendance and being black, as well as a marginally signiﬁcant negative relationship between the teacher-rated composite and the interaction term between preschool and the indicator for a female student. With the exception of these suggestive results for black and female students, the interaction models results suggest that, after controlling for the wide range of covariates, the pos- itive relationship between preschool attendance and elementary science achievement does not vary systematically for students of diﬀerent race, gender, or family income. Location and Full-Time/Part-Time Attendance Finally, results suggest that the relationship between preschool attendance and early science outcomes may be sensitive to whether the preschool setting is located in a K–12 school as well as to whether students attend full-time or part-time. As shown in Ap- pendix table A.5, I ﬁnd that attendance in a preschool setting not located in a K–12 school predicts signiﬁcantly higher teacher-rated science ability in the fall of kinder- garten, whereas attendance at a preschool setting in a K–12 school does not. As with the primary models, neither attendance at a preschool in or out of a K–12 school is sig- niﬁcantly related to standardized science achievement in the spring of kindergarten. Results of models predicting science outcomes from indicators of full- or part-time at- tendance in preschool are shown in table A.6. As shown, both full- and part-time atten- dance are predictive of higher teacher-rated science ability in the fall of kindergarten, although neither is predictive of signiﬁcantly higher science achievement in the spring of kindergarten. 6 . D I S C U S S I O N This study suggests that attending preschool may result in higher science ability at the fall of kindergarten but that such higher science ability does not persist to measur- able diﬀerences in science achievement in the spring of kindergarten. Furthermore, the results suggest that the relationship between preschool attendance and early sci- ence outcomes tend to be consistent across subgroups of students. Nevertheless, the 226 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d . / f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 F. Chris Curran to potential diﬀerences by type of preschool results point (center-based, state- sponsored, or Head Start) as well as diﬀerences by preschool characteristics such as whether the preschool is located in a K–12 school. The results have important impli- cations for the study of equity in early science achievement. In this section, I put the ﬁndings in context of prior literature while discussing the implications of the ﬁndings. First, the ﬁnding that preschool participation tends to be related to teacher-rated science ability in the fall of kindergarten is consistent with prior work on the posi- tive academic impacts of early childhood education. In particular, prior studies have demonstrated a positive relationship between preschool participation and mathemat- ics and reading achievement in the fall of kindergarten (e.g., Magnuson, Ruhm, and Waldfogel 2007a; Gormley, Phillips, and Gayer 2008), and, though limited to teacher- rated ability rather than standardized achievement, this study demonstrates that these generally positive relationships may extend to the subject of science. In doing so, this study builds on prior work that found a positive relationship between preschool at- tendance and teacher-rated science ability by validating the ﬁndings with a nationally representative dataset (Henry, Gordon, and Rickman 2006). There are several possible mechanisms by which this positive relationship may be working. First, it is possible that participation in preschool oﬀers students more expo- sure to scientiﬁc concepts and processes. A robust body of literature demonstrates the importance of “opportunity to learn,” or the concept that exposure to material is a neces- sary prerequisite for learning that material (Carroll 1963, 1989; Sørensen and Hallinan 1977; Wang 1998; Aguirre-Muñoz and Boscardin 2008; Hong 2012; Claessens, Engel, and Curran 2014; Jez and Wassmer 2015). Preschool participation, therefore, may im- prove early science outcomes by providing an increased opportunity to learn science. Such a mechanism would be consistent with literature that shows science instruction in preschool facilitates higher-order instruction (Fuccillo 2011; Cabell et al. 2013). A sec- ond mechanism, however, is that preschool participation may aﬀect students’ science ability through increased mathematics and reading ability (see, e.g., O’Reilly and Mc- Namara 2007). Increased language skills may oﬀer students the opportunity to interact with materials that, in turn, expand scientiﬁc knowledge, and increased mathematics ability may foster reasoning skills that translate to scientiﬁc domains. The data available in the current study lack details to explore the mechanisms behind the observed rela- tionship, but future research might further explore the relationship between particular components of the preschool experience and science outcomes to further understand the mechanisms at work. Despite the positive relationship with teacher-rated science ability, the results did not indicate a signiﬁcant relationship between preschool attendance and science achievement on a standardized test in the spring of kindergarten. While this lack of relationship could indicate the teacher-rated ability outcomes were not picking up true science knowledge, it is also plausible that any science learning gains attributable to preschool attendance have faded out by the end of kindergarten. Indeed, results for mathematics and reading show nonsigniﬁcant relationships between preschool atten- dance and spring achievement despite positive relationships in the fall of kindergarten. This ﬁnding would be consistent with the broad literature on the fade out of preschool eﬀects (Gibbs, Ludwig, and Miller 2011; Claessens, Engel, and Curran 2014; Lipsey, Far- ran, and Hofer 2015). l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d f / . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 227 Preschool Attendance and Science Achievement In addition to these general ﬁndings, there was also evidence of heterogeneity across types of preschool attended. In particular, the positive relationship between preschool attendance and teacher-rated science ability appears to be driven predominantly by at- tendance in center-based preschool as opposed to state-sponsored preschool or Head Start. Although these diﬀerential relationships suggest the possibility of diﬀerential ef- fects on science outcomes, these relationships must be interpreted cautiously. Head Start and many state-sponsored preschool programs are targeted toward disadvan- taged student groups. Prior literature has noted the complexities of fully accounting for omitted variable bias in correlational studies of these targeted programs (Magnu- son, Ruhm, and Waldfogel 2007a). Given the evidence of plausible positive causal ef- fects of Head Start and state-sponsored programs on other subjects (Gormley, Phillips, and Gayer 2008; Puma et al. 2010) and some evidence of their positive eﬀects on early science ability (Henry, Gordon, and Rickman 2006), these coeﬃcients should not be taken as evidence of negative or null eﬀects of Head Start and state-sponsored programs on science achievement. Instead, the diﬀerences between the estimates for center-based preschool and other preschools suggest the need for future research ex- ploring possible heterogeneity in the impact of each of these settings on early science achievement. In addition to heterogeneity by sector of preschool, the results also point to the im- portance of considering the structural characteristics of preschool programs. The point estimate on full-time preschool was larger than that for part-time attendance (though not statistically so), which suggests that more time-intensive preschool experiences may yield larger beneﬁts. The research has documented that some preschool teach- ers feel a lack of instructional time hinders their ability to teach science in preschool, so a full-time program may alleviate this issue and result in more science instruc- tion (Maier, Greenﬁeld, and Bulotsky-Shearer 2013). Furthermore, the ﬁnding that the positive relationship between preschool attendance and teacher-rated ability appears to be driven more by attendance in preschool settings not located in K–12 school set- tings suggests that preschools in non-K–12 environments may be approaching science instruction diﬀerently than those embedded in K–12 schools. This ﬁnding contrasts with earlier work that found positive relationships between preschools colocating with K–12 environments and academic achievement in other subjects (Magnuson, Ruhm, and Waldfogel 2007a). It is possible that preschools in K–12 settings feel more pressure than those not in such settings to emphasize mathematics and reading at the expense of science instruction through the increased accountability context of K–12 schools (Marx and Harris 2006). Future research could further explore the factors that explain this diﬀerential relationship. Finally, recent literature has drawn attention to disparities in early science achieve- ment, particularly along lines of race/ethnicity and family income (Curran and Kel- logg 2016; Curran 2017). The results of this study inform ways in which policy makers may begin to address and mitigate these disparities. First, though there were some marginally signiﬁcant relationships, the models with race/ethnicity interactions did not show any consistent diﬀerences across race/ethnicity in the relationship between preschool attendance and early science achievement. This suggests, on average, that any gains in early science outcomes produced by participation in preschool do not vary signiﬁcantly by race/ethnicity. Similar null ﬁndings on interactions with student 228 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d . / f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 F. Chris Curran gender and family income suggest no signiﬁcant diﬀerential eﬀects of preschool on science outcomes for these subgroups either. That said, the descriptive statistics point to signiﬁcant diﬀerences across race– ethnicity and family income in aspects of preschool attendance. In particular, white students are over twice as likely to have participated in center-based preschool than their black or Hispanic counterparts. Likewise, students from higher-income families are over two and half times more likely to have participated in center-based preschool than their peers from lower-income families. Although overall rates of participation in some form of preschool (either Head Start, center-based, or state-based preschool) are fairly similar between students of diﬀerent race/ethnicity, the diﬀerences in types of preschool settings attended by students of diﬀerent race/ethnicity suggest the possi- bility that students of diﬀerent race/ethnicity are systematically exposed to diﬀerential preschool experiences with regard to science. Though the data used in the study did not allow for an exploration of the amount or type of science instruction across preschool settings, future studies could explore whether the science instructional components of diﬀerent preschool types account for diﬀerences in science outcomes by race/ethnicity. While students in diﬀerent race/ethnic groups diﬀered largely on the type of formal preschool care attended as opposed to the probability of being in any formal preschool care, students of diﬀerent family income levels experienced not only diﬀerential like- lihood in attending diﬀerent types of care but also diﬀerential likelihood of being in any formal preschool care. In particular, students from lower-income households were almost 25 percent less likely to have participated in center-based preschool, Head Start, or state-sponsored preschool. This diﬀerence suggests a need for increased access to quality care for students from lower-income households. 7 . C O N C L U S I O N S Science and the related STEM ﬁelds (science, technology, engineering, and mathemat- ics) continue to be priority areas for improving student achievement. International ev- idence suggests that our students lag behind many other developed nations in science achievement (Martin et al. 2012; OECD 2013) and evidence from within the United States points to signiﬁcant disparities across racial/ethnic groups in science achieve- ment (Chen and Weko 2009; Kohlhaas, Lin, and Chu 2010; Quinn and Cooc 2015). Given recent evidence that these disparities are present as early as kindergarten (Cur- ran and Kellogg 2016; Morgan et al. 2016), identifying interventions that may im- prove early science achievement overall and mitigate achievement gaps is of particular importance. This study has addressed one such intervention, namely, preschool, and its rela- tionship with early science outcomes and achievement gaps. The ﬁndings suggest that preschool attendance, particularly center-based preschool, may increase academic per- formance in science but that any such gains are not sustained to the end of kinder- garten. The results also highlight systematic diﬀerences in the types of preschool environments experienced by students of diﬀerent racial/ethnic background and fam- ily income. In doing so, this study builds on a very limited set of prior studies that have explored the relationship between preschool and science achievement or science ability by providing evidence from a nationally representative dataset (Henry et al. 2006). The l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d / f . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 229 Preschool Attendance and Science Achievement results of this study point to the need for increased attention to early science achieve- ment and preschool by both policy makers and researchers. Such attention holds the potential to improve early science outcomes for all students, particularly those most in need. 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Educational Evaluation and Policy Analysis 37(3): 376–393. Weiland, Christina, and Hirokazu Yoshikawa. 2013. Impacts of a prekindergarten program on children’s mathematics, language, literacy, executive function, and emotional skills. Child Devel- opment 84(6): 2112–2130. Wong, Vivian C., Thomas D. Cook, W. Steven Barnett, and Kwanghee Jung. 2008. An eﬀectiveness-based evaluation of ﬁve state pre-kindergarten programs. Journal of Policy Analy- sis and Management 27(1): 122–154. A P P E N D I X A : A D D I T I O N A L DATA Table A.1. Control Variables for Full Sample and by Preschool Subgroup Full Sample Any Preschool Center- Based Preschool State- Funded Preschool Family income $5,001 to $10,000 $10,001 to $15,000 $15,001 to $20,000 $20,001 to $25,000 $25,001 to $30,000 $30,001 to $35,000 $35,001 to $40,000 $40,001 to $45,000 $45,001 to $50,000 $50,001 to $55,000 $55,001 to $60,000 $60,001 to $65,000 $65,001 to $70,000 $70,001 to $75,000 $75,001 to $100,000 $100,001 to $200,000 $200,001 or more 0.036 0.058 0.058 0.078 0.049 0.049 0.047 0.034 0.037 0.034 0.032 0.034 0.033 0.041 0.138 0.168 0.044 0.017 0.029 0.031 0.044 0.039 0.041 0.043 0.028 0.036 0.035 0.034 0.036 0.039 0.048 0.179 0.242 0.063 0.014 0.020 0.023 0.033 0.030 0.034 0.035 0.023 0.032 0.033 0.032 0.036 0.040 0.051 0.192 0.283 0.077 0.026 0.052 0.054 0.075 0.062 0.059 0.065 0.043 0.045 0.038 0.040 0.036 0.034 0.042 0.143 0.131 0.025 Head Start 0.080 0.112 0.116 0.146 0.074 0.062 0.047 0.036 0.035 0.029 0.015 0.024 0.019 0.028 0.056 0.048 0.013 No Formal Preschool 0.048 0.085 0.079 0.106 0.056 0.057 0.055 0.042 0.041 0.035 0.037 0.036 0.031 0.032 0.101 0.090 0.025 234 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d f / . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 F. Chris Curran Table A.1. Continued. Primary parent employed full-time Primary parent employed part-time Secondary parent employed full-time Secondary parent employed part-time Child is female Primary parent education level 9th—12th grade High school diploma or equivalent Vocational technical program Some college Bachelor’s degree Some graduate/professional school Master’s degree or higher Second parent education level 9th—12th grade High school diploma or equivalent Vocational technical program Some college Bachelor’s degree Some graduate/professional school Master’s degree or higher Child weight (pounds) Child height (inches) Black Hispanic Asian Hawaiian Native American Two or more races Non-English language used at home Mother or child participated in WIC Number of siblings Two-parent household One parent and one other adult Other guardians Parental expectations for child Graduate from high school Attend vocational or technical school Attend two or more years of college Finish four-year college Earn a master’s degree Earn a doctorate Important child counts (1—5, essential to not important) Important child shares (1—5, essential to not important) Important child uses pencil (1—5, essential to not important) Important child pays attention (1—5, essential to not important) Important child knows letters (1—5, essential to not important) Full Sample Any Preschool Center- Based Preschool State- Funded Preschool 0.418 0.210 0.757 0.075 0.485 0.072 0.200 0.057 0.272 0.219 0.020 0.121 0.085 0.289 0.051 0.213 0.174 0.013 0.126 47.040 (0.150) 44.780 (0.040) 0.122 0.215 0.036 0.003 0.008 0.042 0.225 0.483 1.479 (0.024) 0.716 0.065 0.021 0.043 0.023 0.117 0.480 0.166 0.170 2.031 (0.015) 1.632 (0.010) 1.868 (0.012) 1.859 (0.012) 1.902 (0.016) 0.469 0.226 0.825 0.061 0.482 0.037 0.133 0.048 0.271 0.296 0.026 0.177 0.043 0.228 0.053 0.223 0.236 0.018 0.177 46.860 (0.180) 44.830 (0.042) 0.083 0.146 0.042 0.001 0.007 0.045 0.159 0.327 1.376 (0.024) 0.787 0.053 0.015 0.028 0.019 0.097 0.528 0.182 0.144 2.045 (0.015) 1.590 (0.012) 1.837 (0.015) 1.869 (0.016) 1.889 (0.019) 0.473 0.236 0.848 0.057 0.489 0.021 0.105 0.042 0.258 0.332 0.027 0.207 0.028 0.188 0.049 0.223 0.276 0.019 0.206 46.430 (0.183) 44.830 (0.051) 0.068 0.110 0.048 0.002 0.003 0.046 0.131 0.246 1.366 (0.028) 0.819 0.044 0.011 0.021 0.017 0.083 0.552 0.193 0.133 2.057 (0.017) 1.580 (0.012) 1.838 (0.016) 1.891 (0.016) 1.897 (0.020) 0.457 0.202 0.763 0.072 0.465 0.078 0.205 0.065 0.305 0.200 0.021 0.097 0.084 0.333 0.063 0.222 0.130 0.015 0.100 48.000 (0.289) 44.810 (0.066) 0.122 0.242 0.027 0.000 0.018 0.043 0.235 0.541 1.403 (0.037) 0.702 0.077 0.026 0.048 0.027 0.134 0.462 0.154 0.175 2.014 (0.026) 1.616 (0.021) 1.835 (0.029) 1.810 (0.023) 1.868 (0.029) Head Start 0.410 0.194 0.609 0.101 0.474 0.100 0.327 0.063 0.314 0.073 0.007 0.041 0.166 0.411 0.050 0.182 0.074 0.000 0.040 47.900 (0.343) 44.750 (0.088) 0.264 0.310 0.023 0.003 0.014 0.036 0.300 0.821 1.514 (0.037) 0.491 0.101 0.040 0.072 0.031 0.164 0.366 0.148 0.217 1.967 (0.023) 1.693 (0.016) 1.899 (0.019) 1.837 (0.020) 1.887 (0.022) No Formal Preschool 0.325 0.186 0.705 0.087 0.497 0.124 0.261 0.070 0.253 0.147 0.016 0.055 0.122 0.342 0.048 0.211 0.108 0.009 0.075 46.930 (0.244) 44.690 (0.067) 0.122 0.298 0.031 0.005 0.007 0.038 0.310 0.602 1.657 (0.037) 0.698 0.070 0.023 0.057 0.024 0.130 0.450 0.143 0.193 2.036 (0.024) 1.680 (0.015) 1.911 (0.016) 1.849 (0.014) 1.935 (0.018) l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d f . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 235 Preschool Attendance and Science Achievement Table A.1. Continued. Frequency of activities (1—4, not at all to every day) Sing Art Chores Games Talk about nature Build things Play sports Number of books Frequency use CD player (1—6, never to daily) Read books to child (1—4, not at all to every day) Read picture books (1—4, not at all to every day) Attend PTA/PTO meetings Attended parent advisory group Volunteered at school Participated in fundraising Parent depression scale (1—4) Parent not stressed scale (1—4) Child spanked in last week Eat dinner together (no. days per week) Eat dinner at regular time (no. days per week) Child uses home computer Hours TV watched on weekdays Visited zoo, aquarium, or farm Visited the library Visited art, museum, or historical site Attended play, concert, or show Dance lessons Organized athletic activities Clubs or recreation programs Music lessons Drama classes Art classes or lessons Performing arts programs Craft classes or lessons Neighborhood quality scale (1—3) N Full Sample Any Preschool Center- Based Preschool State- Funded Preschool 3.142 (0.013) 2.779 (0.012) 3.275 (0.017) 2.872 (0.011) 2.314 (0.019) 2.476 (0.013) 2.811 (0.012) 90.770 (2.720) 5.464 (0.026) 3.392 (0.018) 3.318 (0.016) 0.365 0.125 0.595 (0.013) 0.690 (0.008) 1.372 (0.007) 3.061 (0.010) 0.165 5.814 (0.027) 5.495 (0.033) 0.750 1.597 (0.034) 0.455 0.601 0.350 0.413 0.190 0.533 0.130 0.099 0.023 0.089 0.159 0.114 2.780 (0.010) 10,500 3.140 (0.015) 2.772 (0.015) 3.275 (0.017) 2.874 (0.012) 2.333 (0.023) 2.489 (0.015) 2.801 (0.013) 107.500 (3.103) 5.472 (0.031) 3.477 (0.014) 3.383 (0.015) 0.383 0.124 0.687 (0.011) 0.742 (0.010) 1.336 (0.006) 3.057 (0.010) 0.138 5.803 (0.037) 5.523 (0.041) 0.818 1.343 (0.030) 0.447 0.630 0.381 0.445 0.243 0.650 0.159 0.118 0.029 0.105 0.179 0.129 2.825 (0.008) 5,950 3.137 (0.018) 2.775 (0.016) 3.276 (0.019) 2.892 (0.013) 2.342 (0.024) 2.502 (0.016) 2.805 (0.014) 114.100 (3.499) 5.482 (0.035) 3.517 (0.015) 3.420 (0.015) 0.387 0.123 0.730 (0.012) 0.760 (0.010) 1.326 (0.007) 3.058 (0.011) 0.126 5.791 (0.042) 5.548 (0.045) 0.831 1.256 (0.029) 0.461 0.654 0.400 0.457 0.270 0.692 0.167 0.132 0.031 0.111 0.191 0.133 2.846 (0.009) 4,430 3.148 (0.023) 2.763 (0.026) 3.271 (0.027) 2.828 (0.019) 2.307 (0.029) 2.454 (0.031) 2.791 (0.026) 89.710 (3.996) 5.445 (0.055) 3.370 (0.022) 3.285 (0.024) 0.373 0.128 0.571 (0.019) 0.695 (0.020) 1.362 (0.013) 3.054 (0.022) 0.172 5.836 (0.048) 5.456 (0.064) 0.784 1.575 (0.048) 0.411 0.565 0.331 0.415 0.171 0.536 0.137 0.081 0.022 0.090 0.147 0.117 2.768 (0.016) 1,520 Head Start 3.212 (0.027) 2.780 (0.024) 3.300 (0.032) 2.864 (0.023) 2.302 (0.032) 2.430 (0.029) 2.837 (0.028) 62.280 (3.627) 5.392 (0.044) 3.274 (0.024) 3.198 (0.029) 0.347 0.131 0.447 (0.017) 0.610 (0.015) 1.459 (0.012) 3.062 (0.020) 0.225 5.809 (0.043) 5.486 (0.052) 0.644 2.048 (0.058) 0.473 0.580 0.324 0.377 0.108 0.386 0.089 0.071 0.018 0.073 0.146 0.092 2.686 (0.015) 1,560 No Formal Preschool 3.109 (0.018) 2.792 (0.017) 3.261 (0.032) 2.872 (0.022) 2.284 (0.026) 2.477 (0.024) 2.816 (0.020) 73.820 (3.483) 5.488 (0.033) 3.292 (0.029) 3.256 (0.028) 0.339 0.124 0.497 (0.018) 0.634 (0.013) 1.395 (0.012) 3.068 (0.018) 0.184 5.837 (0.034) 5.444 (0.038) 0.676 1.845 (0.050) 0.462 0.559 0.306 0.369 0.132 0.388 0.095 0.077 0.015 0.068 0.127 0.096 2.744 (0.015) 2,990 236 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d . / f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 F. Chris Curran m o r f y t i l i b A e c n e c S i f o s g n i t a R r e h c a e T n e t r a g r e d n K i f o l l a F d n a t n e m e v e h c A i e c n e c S i d e z i d r a d n a t S n e t r a g r e d n K i f o g n i r p S g n i t c d e r P i s n o i s s e r g e R m o r f s r o r r E d r a d n a t S d n a i s t n e c fi f e o C . 2 A . e l b a T e t i s o p m o C ) 0 1 ( * 6 3 1 0 . ) 3 2 6 0 0 ( . 2 5 5 0 0 . ) 0 2 1 0 ( . ) 7 4 9 0 0 ( . 8 4 3 0 0 − . ) 3 8 1 0 ( . 2 5 1 0 − . ) 8 4 9 0 0 ( . + 6 7 1 0 − . ) 6 3 9 0 0 ( . 9 1 1 0 − . 9 0 2 0 . ) 5 6 1 0 ( . X X X / h t r a E e c a p S e c n e i c S ) 9 ( 8 2 7 0 0 . ) 6 1 6 0 0 ( . 0 8 6 0 0 . ) 5 1 1 0 ( . 8 3 1 0 0 . ) 3 5 9 0 0 ( . ) 3 8 1 0 ( . 7 5 1 0 − . * 8 9 1 0 − . ) 5 3 9 0 0 ( . ) 2 3 9 0 0 ( . + 3 8 1 0 − . 4 3 1 0 . ) 2 6 1 0 ( . X X X e f i L e c n e i c S ) 8 ( 2 1 7 0 0 . ) 1 5 4 0 0 ( . 2 9 3 0 0 0 − . ) 5 4 9 0 0 ( . 4 3 3 0 0 . ) 4 3 7 0 0 ( . 1 7 5 0 0 . ) 3 2 1 0 ( . ) 3 6 7 0 0 ( . * * 1 2 2 0 − . ) 3 7 6 0 0 ( . * 6 3 1 0 − . 7 3 1 0 0 . ) 1 1 1 0 ( . X X X l a c i s y h P e c n e i c S ) 7 ( 7 7 3 0 0 . ) 5 9 4 0 0 ( . ) 0 4 9 0 0 ( . 1 2 1 0 . 9 9 3 0 0 . ) 1 5 7 0 0 ( . 6 8 2 0 0 − . ) 6 4 1 0 ( . ) 4 4 7 0 0 ( . * * 3 0 2 0 − . ) 8 0 7 0 0 ( . * 2 7 1 0 − . 2 7 2 0 0 . ) 0 3 1 0 ( . X X X e t a c i n u m m o C t c i d e r P y f i s s a C l l i n a p x E ) 6 ( ) 5 ( ) 4 ( ) 3 ( 6 9 7 0 0 . ) 9 5 5 0 0 ( . 8 9 2 0 0 . ) 5 1 1 0 ( . 2 5 7 0 0 0 . ) 2 4 8 0 0 ( . ) 9 4 1 0 ( . 3 1 1 0 − . * 4 8 1 0 − . ) 2 3 8 0 0 ( . ) 1 1 8 0 0 ( . * 5 9 1 0 − . 9 4 1 0 . ) 0 3 1 0 ( . X X X 1 8 6 0 0 . ) 2 9 4 0 0 ( . 9 7 4 0 0 . ) 8 0 1 0 ( . ) 5 1 8 0 0 ( . 4 4 2 0 0 − . ) 5 3 1 0 ( . 5 9 1 0 − . * 4 9 1 0 − . ) 2 1 8 0 0 ( . ) 7 4 7 0 0 ( . * 6 5 1 0 − . 2 5 1 0 . ) 4 1 1 0 ( . X X X + 9 8 8 0 0 . ) 2 9 4 0 0 ( . 0 1 7 0 0 . ) 1 1 1 0 ( . ) 6 1 8 0 0 ( . 0 3 6 0 0 − . 6 5 9 0 0 0 . ) 6 4 1 0 ( . ) 3 9 8 0 0 ( . * 1 8 1 0 − . ) 4 6 7 0 0 ( . 4 0 1 0 − . 1 6 5 0 0 . ) 0 3 1 0 ( . X X X 9 5 7 0 0 . ) 6 3 5 0 0 ( . 2 6 9 0 0 . ) 7 0 1 0 ( . ) 6 4 8 0 0 ( . 2 2 2 0 0 − . ) 7 3 1 0 ( . 0 4 1 0 − . ) 9 9 8 0 0 ( . * * 2 8 2 0 − . ) 7 7 7 0 0 ( . * 0 0 2 0 − . 5 7 1 0 . ) 7 1 1 0 ( . X X X e s n e S ) 2 ( 1 8 6 0 0 . ) 9 1 4 0 0 ( . 1 0 6 0 0 . ) 1 7 9 0 0 ( . 0 2 2 0 0 . ) 3 2 7 0 0 ( . 9 9 1 0 0 − . ) 3 3 1 0 ( . ) 5 7 7 0 0 ( . * * 9 4 2 0 − . ) 2 7 6 0 0 ( . * * 6 7 1 0 − . 1 8 6 0 0 . ) 7 1 1 0 ( . X X X n e t r a g r e d n K f o i g n i r p S t n e m e v e i h c A e c n e i c S ) d e z i d r a d n a t s ( ) 1 ( e c a R t n e d u t S h t i w d e t c a r e t n I n o i t a p c i i t r a P l o o h c s e r P 5 0 — e 1 2 3 . r o d e s a b - r e t n e c ( l o o h c s e r P ) 7 3 3 0 0 ( . + 7 3 1 0 . ) 1 1 8 0 0 ( . ) 7 5 6 0 0 ( . 2 2 4 0 0 − . 8 9 6 0 0 − . ) 6 1 1 0 ( . ) 0 0 7 0 0 ( . * * 9 3 4 0 − . ) 3 7 5 0 0 ( . * * 3 5 1 0 − . 8 2 9 0 0 − . ) 4 0 1 0 ( . X X X ) d e r o s n o p s - e t a t s l l k c a B * o o h c s e r P i c n a p s i H * o o h c s e r P l l n a i s A * o o h c s e r P i c n a p s i H n a i s A k c a B l s l o r t n o c e m o c n I s l o r t n o c l a u t x e t n o c s t c e f f e d e x fi m o o r s s a C l s n o i t a v r e s b O d n a , y l i m a f , d l i h C 0 9 3 3 , 0 7 2 4 , 0 7 7 6 , 0 1 5 6 , 0 6 9 5 , 0 2 3 6 , 0 5 0 6 , 0 9 4 6 , 0 0 5 7 , 0 0 5 0 1 , s e z i s l e p m a S i . g n i t h g e w d n a g n i t t e s y e v r u s f o e s u e h t h g u o r h t y d u t S l i a n d u t i g n o L d o o h d l i h C y l r a E f o n g i s e d y e v r u s l x e p m o c e h t r o f t n u o c c a s e t a m i t s e l l A . s e s e h t n e r a p n i s r o r r e d r a d n a t s t s u b o R : s e t o N d n a e c a r f o s r o t a c d n i i y r a n b i e d u c n l i s l e d o M . l l i k s e h t e v r e s b o o t y t i n u t r o p p o e h t d a h t o n d a h y e h t g n i t o n d a e t s n i d n a n o i t s e u q e h t g n i r e w s n a t o n f o n o i t p o e h t d a h s r e h c a e t s a l e b a t s i h t s s o r c a y r a v . s t n e d u t s e t i h w r o f l o o h c s e r p d e s a b - r e t n e c n o i t n e c fi f e o c e h t h t i w d e r a p m o c l e b a t e r p r e t n i e r a s m r e t n o i t c a r e t n i l l A . s p u o r g l i a c a r l l a r o f l o o h c s e r p h t i w s n o i t c a r e t n i l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d / . f . . 1 0 < p + ; . 5 0 0 < p * ; . 1 0 0 < p * * f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 237 Preschool Attendance and Science Achievement e t i s o p m o C ) 0 1 ( * * 4 0 2 0 . ) 3 5 6 0 0 ( . ) 7 4 7 0 0 ( . + 1 4 1 0 − . * 0 4 1 0 . ) 4 0 6 0 0 ( . X X X / h t r a E e c a p S e c n e i c S ) 9 ( * 9 4 1 0 . ) 3 3 6 0 0 ( . + 5 2 1 0 − . ) 4 4 7 0 0 ( . + 2 0 1 0 . ) 2 9 5 0 0 ( . X X X e f i L e c n e i c S ) 8 ( * * 8 3 1 0 . ) 4 7 4 0 0 ( . ) 8 6 5 0 0 ( . + 4 0 1 0 − . * * 5 4 1 0 . ) 0 6 4 0 0 ( . X X X l a c i s y h P e c n e i c S ) 7 ( + 6 3 9 0 0 . ) 5 0 5 0 0 ( . ) 2 9 5 0 0 ( . 8 8 5 0 0 − . * * 6 3 1 0 . ) 1 7 4 0 0 ( . X X X e t a c i n u m m o C t c i d e r P y f i s s a C l i l n a p x E ) 6 ( ) 5 ( ) 4 ( ) 3 ( * 0 3 1 0 . ) 9 5 5 0 0 ( . ) 4 5 6 0 0 ( . 2 2 8 0 0 − . * * 2 3 1 0 . ) 5 8 4 0 0 ( . * 6 1 1 0 . ) 5 2 5 0 0 ( . ) 8 0 6 0 0 ( . + 3 0 1 0 − . * 0 1 1 0 . ) 4 9 4 0 0 ( . * 5 1 1 0 . ) 7 3 5 0 0 ( . ) 9 3 6 0 0 ( . 4 5 4 0 0 − . 4 3 8 0 0 . ) 5 1 5 0 0 ( . * 6 1 1 0 . ) 9 5 5 0 0 ( . ) 5 0 6 0 0 ( . 0 5 7 0 0 − . * 1 0 1 0 . ) 3 0 5 0 0 ( . X X X X X X X X X X X X e s n e S ) 2 ( * * 9 1 1 0 . ) 2 4 4 0 0 ( . ) 5 2 5 0 0 ( . 6 3 7 0 0 − . * * 3 1 1 0 . ) 5 2 4 0 0 ( . X X X n e t r a g r e d n K f o i g n i r p S t n e m e v e i h c A e c n e i c S ) d e z i d r a d n a t s ( ) 1 ( 9 6 1 0 0 0 . ) 3 6 3 0 0 ( . 7 1 2 0 0 0 . ) 7 5 4 0 0 ( . ) 0 8 3 0 0 ( . * * 0 0 1 0 − . X X X 0 9 3 3 , 0 7 2 4 , 0 7 7 6 , 0 1 5 6 , 0 6 9 5 , 0 2 3 6 , 0 5 0 6 , 0 9 4 6 , 0 0 5 7 , 0 0 5 0 1 , r o d e s a b - r e t n e c ( l o o h c s e r P ) d e r o s n o p s - e t a t s l l e a m e F * o o h c s e r P s l o r t n o c e m o c n I l e a m e F s l o r t n o c l a u t x e t n o c s t c e f f e d e x fi m o o r s s a C l s n o i t a v r e s b O d n a , y l i m a f , d l i h C m o r f y t i l i b A e c n e c S i f o s g n i t a R r e h c a e T n e t r a g r e d n K i f o l l a F d n a t n e m e v e h c A i i e c n e c S d e z i d r a d n a t S n e t r a g r e d n K i f o g n i r p S g n i t c d e r P i s n o i s s e r g e R m o r f s r o r r E d r a d n a t S d n a i s t n e c fi f e o C . 3 A . e l b a T r e d n e G t n e d u t S h t i w d e t c a r e t n I n o i t a p c i t r a P i l o o h c s e r P 238 s e z i s e p m a S l i . g n i t h g e w d n a g n i t t e s y e v r u s f o e s u e h t h g u o r h t y d u t S l i a n d u t i g n o L d o o h d l i h C y l r a E f o n g i s e d y e v r u s l x e p m o c e h t r o f t n u o c c a s e t a m i t s e l l A . s e s e h t n e r a p n i s r o r r e d r a d n a t s t s u b o R : s e t o N . r e d n e g r o t a c d n i i y r a n b i a e d u c n l i s l e d o M . l l i k s e h t e v r e s b o o t y t i n u t r o p p o e h t d a h t o n d a h y e h t g n i t o n d a e t s n i d n a n o i t s e u q e h t g n i r e w s n a t o n f o n o i t p o e h t d a h s r e h c a e t s a l e b a t s i h t s s o r c a y r a v l a m r o f a n i t o n e r e w o h w s t n e d u t s s i l e b a i r a v l o o h c s e r p e h t r o f y r o g e t a c d e t t i m o e h T . s t n e d u t s l e a m r o f l o o h c s e r p d e s a b - r e t n e c n o i t n e c fi f e o c e h t o t d e r a p m o c l e b a t e r p r e t n i e r a s m r e t n o i t c a r e t n i l l A . m a r g o r p t r a t S d a e H r o , d e r o s n o p s - e t a t s , d e s a b - r e t n e c a n i t o n e r e w d n a , s t n e r a p l r o , s e v i t a e r n o n , s e v i t a e r l y b r o f d e r a c e r e w o h w e s o h t , y l e m a n — – g n i t t e s l o o h c s e r p . . 1 0 < p + ; . 5 0 0 < p * ; . 1 0 0 < p * * l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d f / . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 F. Chris Curran m o r f y t i l i b A e c n e c S i f o s g n i t a R r e h c a e T n e t r a g r e d n K i f o l l a F d n a t n e m e v e h c A i e c n e c S i d e z i d r a d n a t S n e t r a g r e d n K i f o g n i r p S g n i t c d e r P i s n o i s s e r g e R m o r f s r o r r E d r a d n a t S d n a i s t n e c fi f e o C . 4 A . e l b a T t e k c a r B e m o c n I y l i m a F h t i w d e t c a r e t n I n o i t a p c i i t r a P l o o h c s e r P e t i s o p m o C ) 0 1 ( 7 5 1 0 . ) 3 0 1 0 ( . 8 1 9 0 0 − . ) 7 2 1 0 ( . 4 1 1 0 0 . ) 4 2 1 0 ( . 9 8 3 0 0 − . ) 6 2 1 0 ( . 9 0 4 0 0 − . ) 0 2 1 0 ( . 5 5 6 0 0 0 − . ) 4 1 1 0 ( . 3 9 6 0 0 . ) 8 1 1 0 ( . X X X / h t r a E e c a p S e c n e i c S ) 9 ( 4 7 6 0 0 . ) 5 1 1 0 ( . 1 9 5 0 0 . ) 7 3 1 0 ( . 6 7 1 0 0 − . ) 1 3 1 0 ( . 8 9 1 0 0 . ) 5 3 1 0 ( . 7 8 6 0 0 − . ) 6 2 1 0 ( . 2 9 1 0 0 − . ) 8 1 1 0 ( . 0 8 1 0 0 − . ) 3 2 1 0 ( . X X X e f i L e c n e i c S ) 8 ( ) 7 1 8 0 0 ( . 2 1 1 0 . 2 2 9 0 0 − . ) 0 0 1 0 ( . 0 4 1 0 0 . ) 1 8 9 0 0 ( . ) 7 4 9 0 0 ( . 7 6 2 0 0 − . ) 1 4 9 0 0 ( . 1 2 2 0 0 − . ) 9 0 9 0 0 ( . 8 1 5 0 0 − . 0 1 1 0 0 . ) 7 8 8 0 0 ( . X X X l a c i s y h P e c n e i c S ) 7 ( 0 7 2 0 0 . ) 1 7 8 0 0 ( . 2 2 6 0 0 . ) 3 0 1 0 ( . 4 1 3 0 0 . ) 3 0 1 0 ( . 7 6 3 0 0 . ) 6 9 9 0 0 ( . ) 0 1 9 0 0 ( . 9 1 7 0 0 − . ) 2 7 8 0 0 ( . 7 3 3 0 0 − . ) 6 8 8 0 0 ( . 2 6 1 0 0 − . X X X e t a c i n u m m o C t c i d e r P y f i s s a C l l i n a p x E ) 6 ( ) 5 ( ) 4 ( ) 3 ( 5 0 9 0 0 . ) 2 0 1 0 ( . 9 5 3 0 0 − . ) 9 1 1 0 ( . 7 5 1 0 0 − . ) 9 1 1 0 ( . 1 4 3 0 0 . ) 5 1 1 0 ( . ) 4 0 1 0 ( . 4 2 1 0 − . ) 0 0 0 1 0 ( . 8 4 7 0 0 − . 5 1 4 0 0 − . ) 2 0 1 0 ( . X X X 0 9 2 0 0 . ) 5 5 8 0 0 ( . 6 3 4 0 0 . ) 7 0 1 0 ( . 2 0 6 0 0 . ) 4 0 1 0 ( . 4 2 2 0 0 . ) 7 8 9 0 0 ( . ) 8 8 9 0 0 ( . ) 2 3 9 0 0 ( . ) 5 1 9 0 0 ( . 9 8 4 0 0 − . 7 3 1 0 − . 1 6 1 0 − . X X X 5 0 8 0 0 . ) 1 9 8 0 0 ( . 1 6 3 0 0 − . ) 0 1 1 0 ( . 3 3 1 0 0 . ) 7 0 1 0 ( . 1 3 4 0 0 . ) 6 0 1 0 ( . 8 9 6 0 0 0 − . ) 1 1 1 0 ( . 1 8 4 0 0 0 − . ) 3 8 9 0 0 ( . ) 5 8 9 0 0 ( . 3 1 1 0 0 − . X X X 0 1 8 0 0 0 . ) 5 6 8 0 0 ( . 0 7 7 0 0 . ) 4 1 1 0 ( . 3 3 1 0 . ) 5 0 1 0 ( . 8 9 4 0 0 . ) 0 0 1 0 ( . ) 1 0 1 0 ( . 2 6 1 0 − . ) 6 3 9 0 0 ( . + 6 7 1 0 − . ) 2 3 9 0 0 ( . 1 9 8 0 0 − . X X X e s n e S ) 2 ( 0 3 6 0 0 . ) 5 5 7 0 0 ( . 6 8 3 0 0 . ) 9 3 9 0 0 ( . 8 0 3 0 0 . ) 6 3 9 0 0 ( . 5 9 7 0 0 0 . ) 8 5 8 0 0 ( . ) 6 6 8 0 0 ( . 7 8 6 0 0 − . ) 0 2 8 0 0 ( . 1 6 6 0 0 − . ) 1 8 7 0 0 ( . 2 1 1 0 0 − . X X X n e t r a g r e d n K f o i g n i r p S t n e m e v e i h c A e c n e i c S ) d e z i d r a d n a t s ( ) 1 ( 6 1 1 0 0 . ) 8 9 5 0 0 ( . 2 3 7 0 0 . ) 1 9 7 0 0 ( . ) 5 5 7 0 0 ( . 1 0 1 0 0 − . ) 6 0 7 0 0 ( . 0 3 6 0 0 − . ) 5 7 6 0 0 ( . + 1 2 1 0 − . 8 1 2 0 0 . ) 0 6 6 0 0 ( . 1 7 9 0 0 . ) 1 3 6 0 0 ( . X X X 0 9 3 3 , 0 7 2 4 , 0 7 7 6 , 0 1 5 6 , 0 6 9 5 , 0 2 3 6 , 0 5 0 6 , 0 9 4 6 , 0 0 5 7 , 0 0 5 0 1 , r o d e s a b - r e t n e c ( l o o h c s e r P ) d e r o s n o p s - e t a t s 1 e l i t r a u q 2 e l i t r a u q 3 e l i t r a u q l I e m o c n * o o h c s e r P l I e m o c n * o o h c s e r P l I e m o c n * o o h c s e r P 1 e l i t r a u q e m o c n I 2 e l i t r a u q e m o c n I 3 e l i t r a u q e m o c n I s l o r t n o c e m o c n I l a u t x e t n o c d n a , y l i m a f , d l i h C s t c e f f e d e x fi m o o r s s a C l s n o i t a v r e s b O s l o r t n o c s e z i s l e p m a S i . g n i t h g e w d n a g n i t t e s y e v r u s f o e s u e h t h g u o r h t y d u t S l i a n d u t i g n o L d o o h d l i h C y l r a E f o n g i s e d y e v r u s l x e p m o c e h t r o f t n u o c c a s e t a m i t s e l l A . s e s e h t n e r a p n i s r o r r e d r a d n a t s t s u b o R : s e t o N d e r a p m o c l e b a t e r p r e t n i e r a s m r e t n o i t c a r e t n i l l A . l l i k s e h t e v r e s b o o t y t i n u t r o p p o e h t d a h t o n d a h y e h t g n i t o n d a e t s n i d n a n o i t s e u q e h t g n i r e w s n a t o n f o n o i t p o e h t d a h s r e h c a e t s a e b a t l s i h t s s o r c a y r a v , y l e m a n — – g n i t t e s l o o h c s e r p l a m r o f a n i t o n e r e w o h w s t n e d u t s s i l e b a i r a v l o o h c s e r p e h t r o f y r o g e t a c d e t t i m o e h T . ) , + 0 0 0 0 0 1 $ ( e l i t r a u q e m o c n i i t s e h g h e h t n i s t n e d u t s r o f l o o h c s e r p n o t n e c fi f e o c e h t o t i . m a r g o r p t r a t S d a e H r o , d e r o s n o p s - e t a t s , d e s a b - r e t n e c a n i t o n e r e w d n a , s t n e r a p l r o , s e v i t a e r n o n , s e v i t a e r l y b r o f d e r a c e r e w o h w e s o h t . . 1 0 < p + l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d . / f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 239 Preschool Attendance and Science Achievement e t i s o p m o C ) 0 1 ( 2 1 7 0 0 . ) 2 0 6 0 0 ( . * * 3 7 1 0 . ) 1 7 5 0 0 ( . X X X / h t r a E e c a p S e c n e i c S ) 9 ( 3 0 4 0 0 . ) 9 1 6 0 0 ( . * 8 1 1 0 . ) 7 5 5 0 0 ( . X X X e f i L e c n e i c S ) 8 ( 5 5 4 0 0 . ) 1 6 4 0 0 ( . * * 2 1 1 0 . ) 9 9 3 0 0 ( . l a c i s y h P e c n e i c S ) 7 ( 8 4 4 0 0 . ) 1 0 5 0 0 ( . + 3 6 7 0 0 . ) 7 3 4 0 0 ( . X X X X X X e t a c i n u m m o C t c i d e r P y f i s s a C l i l n a p x E ) 6 ( ) 5 ( ) 4 ( ) 3 ( 0 0 8 0 0 . ) 6 3 5 0 0 ( . + 3 5 9 0 0 . ) 9 9 4 0 0 ( . 0 3 5 0 0 . ) 0 1 5 0 0 ( . 4 1 7 0 0 . ) 0 4 4 0 0 ( . 3 9 5 0 0 . ) 1 0 5 0 0 ( . * 1 1 1 0 . ) 6 4 4 0 0 ( . 1 9 2 0 0 . ) 4 7 5 0 0 ( . * 8 0 1 0 . ) 1 6 4 0 0 ( . X X X X X X X X X X X X e s n e S ) 2 ( 2 0 6 0 0 . ) 1 5 4 0 0 ( . * 8 4 9 0 0 . ) 9 7 3 0 0 ( . X X X ) 1 ( ) 7 7 3 0 0 ( . 1 3 3 0 0 − . 2 2 2 0 0 . ) 2 1 3 0 0 ( . X X X 0 9 3 3 , 0 7 2 4 , 0 7 7 6 , 0 1 5 6 , 0 6 9 5 , 0 2 3 6 , 0 5 0 6 , 0 9 4 6 , 0 0 5 7 , 0 9 4 0 1 , l o o h c s 2 1 — K n i t o n l o o h c s e r P l o o h c s 2 1 — K n i l o o h c s e r P s l o r t n o c e m o c n I l a u t x e t n o c d n a , y l i m a f , d l i h C s t c e f f e d e x fi m o o r s s a C l s n o i t a v r e s b O s l o r t n o c n e t r a g r e d n K f o i g n i r p S t n e m e v e i h c A e c n e i c S ) d e z i d r a d n a t s ( n o i t a c o L l o o h c s e r P f o s r o t a c d n i I m o r f l e p m a S i . g n i t h g e w d n a g n i t t e s y e v r u s f o e s u e h t h g u o r h t y d u t S l i a n d u t i g n o L d o o h d l i h C y l r a E f o n g i s e d y e v r u s l x e p m o c e h t r o f t n u o c c a s e t a m i t s e l l A . s e s e h t n e r a p n i s r o r r e d r a d n a t s t s u b o R : s e t o N m o r f y l t h g i l s y r a v s e z i s l e p m a S . l l i k s e h t e v r e s b o o t y t i n u t r o p p o e h t d a h t o n d a h y e h t g n i t o n d a e t s n i d n a n o i t s e u q e h t g n i r e w s n a t o n f o n o i t p o e h t d a h s r e h c a e t s a l e b a t s i h t s s o r c a y r a v s e z i s , y l e m a n — – g n i t t e s l o o h c s e r p l a m r o f a n i t o n e r e w o h w s t n e d u t s s i y r o g e t a c d e t t i m o e h t o s , t r a t S d a e H f o r o t a c d n i i i y r a n b e d u c n l i s l e d o M l . s e b a i r a v n o i t a c o l n o a t a d g n i s s i m o t e u d s l e d o m y r a m i r p . m a r g o r p t r a t S d a e H r o , d e r o s n o p s - e t a t s , d e s a b - r e t n e c a n i t o n e r e w d n a , s t n e r a p l r o , s e v i t a e r n o n , s e v i t a e r l y b r o f d e r a c e r e w o h w e s o h t l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d . f / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 . . 1 0 < p + ; . 5 0 0 < p * ; . 1 0 0 < p * * y t i l i b A e c n e c S i f o s g n i t a R r e h c a e T n e t r a g r e d n K i f o l l a F d n a i i t n e m e v e h c A e c n e c S d e z i d r a d n a t S n e t r a g r e d n K i f o g n i r p S g n i t c d e r P i s n o i s s e r g e R m o r f s r o r r E d r a d n a t S d n a i s t n e c fi f e o C . . 5 A e l b a T 240 F. Chris Curran y t i l i b A e c n e c S i f o s g n i t a R r e h c a e T n e t r a g r e d n K i f o l l i i a F d n a t n e m e v e h c A e c n e c S d e z i d r a d n a t S n e t r a g r e d n K i i f o g n i r p S g n i t c d e r P s n o i s s e r g e R m o r f s r o r r E d r a d n a t S d n a s t n e c fi f e o C i . . 6 A e l b a T l o o h c s e r P n i n o i t a p c i t r a P i e m i T - t r a P d n a - l l u F f o s r o t a c d n i I m o r f e t i s o p m o C ) 0 1 ( * 1 6 1 0 . ) 0 4 6 0 0 ( . * 9 0 1 0 . ) 1 2 5 0 0 ( . X X X / h t r a E e c a p S e c n e i c S ) 9 ( 5 6 7 0 0 . ) 2 2 6 0 0 ( . + 8 5 9 0 0 . ) 0 4 5 0 0 ( . X X X e f i L e c n e i c S ) 8 ( + 2 5 8 0 0 . ) 0 4 4 0 0 ( . * 7 7 8 0 0 . ) 9 9 3 0 0 ( . l a c i s y h P e c n e i c S ) 7 ( + 1 8 8 0 0 . ) 0 7 4 0 0 ( . 7 5 4 0 0 . ) 2 5 4 0 0 ( . X X X X X X e t a c i n u m m o C t c i d e r P y f i s s a C l i l n a p x E ) 6 ( ) 5 ( ) 4 ( ) 3 ( + 0 5 9 0 0 . ) 2 3 5 0 0 ( . + 4 5 8 0 0 . ) 7 9 4 0 0 ( . 7 9 3 0 0 . ) 5 1 5 0 0 ( . + 6 2 8 0 0 . ) 1 4 4 0 0 ( . * 4 1 1 0 . ) 8 9 4 0 0 ( . + 0 5 7 0 0 . ) 8 3 4 0 0 ( . 7 7 7 0 0 . ) 6 5 5 0 0 ( . + 0 9 7 0 0 . ) 5 5 4 0 0 ( . X X X X X X X X X X X X e s n e S ) 2 ( 6 3 5 0 0 . ) 2 3 4 0 0 ( . * * 9 9 9 0 0 . ) 8 7 3 0 0 ( . X X X n e t r a g r e d n K f o i g n i r p S t n e m e v e i h c A e c n e i c S ) d e z i d r a d n a t s ( ) 1 ( 7 8 1 0 0 0 . ) 9 3 3 0 0 ( . 2 1 3 0 0 0 . ) 8 2 3 0 0 ( . X X X e m i t l l u f l o o h c s e r P e m i t t r a p l o o h c s e r P s l o r t n o c e m o c n I s l o r t n o c l a u t x e t n o c s t c e f f e d e x fi m o o r s s a C l d n a , y l i m a f , d l i h C 0 9 3 3 , 0 7 2 4 , 0 7 7 6 , 0 0 5 6 , 0 5 9 5 , 0 2 3 6 , 0 5 0 6 , 0 9 4 6 , 0 0 5 7 , 0 9 4 0 1 , s n o i t a v r e s b O . g n i t h g e w i d n a g n i t t e s y e v r u s f o e s u e h t h g u o r h t y d u t S l i a n d u t i g n o L d o o h d l i h C y l r a E f o n g i s e d y e v r u s l x e p m o c e h t r o f t n u o c c a s e t a m i t s e l l A . s e s e h t n e r a p n i s r o r r e d r a d n a t s t s u b o R : s e t o N y r a v s e z i s l e p m a S . l l i k s e h t e v r e s b o o t y t i n u t r o p p o e h t d a h t o n d a h y e h t g n i t o n d a e t s n i d n a n o i t s e u q e h t g n i r e w s n a t o n f o n o i t p o e h t d a h s r e h c a e t s a l e b a t s i h t s s o r c a y r a v s e z i s l e p m a S l o o h c s e r p l a m r o f a n i t o n e r e w o h w s t n e d u t s s i y r o g e t a c d e t t i m o e h t o s , t r a t S d a e H f o r o t a c d n i i y r a n b i e d u c n l i s l e d o M l . s e b a i r a v e m i t n o a t a d g n i s s i m o t e u d s l e d o m y r a m i r p m o r f y l t h g i l s . m a r g o r p t r a t S d a e H r o , d e r o s n o p s - e t a t s , d e s a b - r e t n e c a n i t o n e r e w d n a , s t n e r a p l r o , s e v i t a e r n o n , s e v i t a e r l y b r o f d e r a c e r e w o h w e s o h t , y l e m a n — – g n i t t e s . . 1 0 < p + ; . 5 0 0 < p * ; . 1 0 0 < p * * l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 4 2 2 1 0 1 6 9 2 7 1 5 e d p _ a _ 0 0 2 4 7 p d . f / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 241 F. 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