Ma, X., & Klinger, D. A. (2000). Hierarchical Linear Modelling of Student and School Effects on Academic Achievement. Canadian Journal Of Education, 25(1), 41-55. <!--Additional Information:
Hierarchical Linear Modelling of Student and School Effects on Academic Achievement
|AUTHOR: ||Xin Ma; Don A. Klinger|
|TITLE: ||Hierarchical Linear Modelling of Student and School Effects on Academic Achievement|
|SOURCE: ||Canadian Journal of Education 25 no1 41-55 2000|
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Hierarchical linear modelling (HLM) and data from the New Brunswick
School Climate Study were used to examine student background, school
context, and school climate effects on Grade 6 student achievement in
mathematics, science, reading, and writing. Gender, socioeconomic status
(SES), and Native ethnicity were significant predictors of academic
achievement. Schools showed the smallest variation in reading, the
largest in mathematics. School mean SES was significant in mathematics,
reading, and writing achievement, as was disciplinary climate in
mathematics, science, and writing. School size and parental involvement
significantly affected only the relationship between mathematics
achievement and individual SES. La modélisation linéaire hiérarchique et
les données provenant d'une étude portant sur le climat scolaire au
Nouveau-Brunswick (New Brunswick School Climate Study) furent utilisées
pour analyser les acquis des élèves, le contexte scolaire et les effets
du climat scolaire sur le rendement d'élèves de 6° année en
mathématique, en sciences, en lecture et en écriture. Le sexe, la
situation socio-économique (SSE) et l'origine autochtone étaient des
prédicteurs importants du rendement scolaire. Les écoles affichent les
plus faibles variations en lecture et les plus fortes, en mathématique.
La SSE moyenne de l'école était un facteur important dans le rendement
en mathématique, en lecture et en écriture, tout comme le climat
disciplinaire pour la mathématique, les sciences et l'écriture. La
taille de l'école et la participation des parents n'avaient une
incidence importante que sur le rapport entre le rendement en
mathématique et la SSE personnelle.
This study examined the influence of student and
school factors on Grade 6 students' performance in mathematics,
science, reading, and writing in New Brunswick. Student characteristics
and school context and climate factors were included in an effort to
fill gaps in the research on effective elementary schools. Increasing
emphasis on academic performance (Council of Ministers of Education,
Canada, 1998; Educational Testing Service, 1999) gives new importance to
investigating factors that contribute to student learning. Because
education systems have a hierarchical structure (students nested within
schools), researchers must examine both student and school
characteristics (Bryk & Raudenbush, 1992). Student characteristics
can be individual characteristics, such as gender, or family
characteristics, such as socioeconomic status (SES). Gender differences
in achievement tend to be subject specific (Hedges & Nowell, 1995;
Manning, 1998; Sammons, West, & Hind, 1997). Males outperform
females in mathematics and science, with larger differences in science
(Beller & Gafni, 1996); females outperform males in reading and
writing, with larger differences in writing (Battistich, Solomon, Kim,
Watson, & Schaps, 1995; Sammons et al., 1997). In general, females
exhibit superior verbal skills and males display superior spatial and
quantitative skills (Hedges & Nowell, 1995).
SES has long been used to explain differences in
student academic achievement (Sammons et al., 1997; Thomas, Sammons,
Mortimore, & Smees, 1997). In 1982, White described the effect as
the most enduring finding in sociological research. Lytton and Pyryt
(1998) have shown that in Canada between 35% and 50% of the variation in
elementary students' academic achievement can be attributed to SES.
Race and ethnicity also affect academic achievement (Sammons et al.,
1997; Strand, 1997). Some researchers attribute the low academic
achievement of certain racial groups to their low SES (for example,
Hull's 1990 discussion of Canadian Native students); others attribute
their underachievement to their unsuccessful incorporation, voluntary or
involuntary, into the dominant culture (Ogbu & Simons, 1998).
Family structure (number of parents and number of siblings) is also said
to influence student academic achievement (Manning, 1998; Pong, 1997,
Teacher satisfaction, principal leadership,
disciplinary climate, academic press (expectations), and parental
involvement often constitute school climate. These factors can be
controlled directly by school staff and influence student academic
achievement (Coyle & Witcher, 1992; Downer, 1991; Willms, 1992;
Zigarelli, 1996). In general, research on effective schools indicates
three important school climate factors (Willms, 1992). Students learn
more and perform better in schools that have strong parental involvement
(Goldring & Shapira, 1996; Ho & Willms, 1996), emphasize
academic success (Lytton & Pyryt, 1998; Zigarelli, 1996), and have a
disciplinary climate conducive to teaching and learning (DeBaryshe,
Patterson, & Capaldi, 1993; Ma & Willms, 1995).
Other school factors, such as size, location,
and mean SES, are contextual and usually beyond the immediate control of
school staff; they too influence academic achievement (Sammons et al.,
1997; Willms, 1992). The average SES of a school has been found to have
as great an effect as an individual student's SES (Caldas &
Bankston, 1997; Ho & Willms, 1996): Students attending a school with
a higher mean SES are more likely to succeed academically, and this
effect is over and above that of individual student SES (Willms, 1992).
School size has not shown a consistent effect on academic achievement
(Griffiths, 1996; Luyten, 1994).
One problem with much previous research is its
inability to accommodate the hierarchical or nested structure of
educational data. Actions and measures at one level affect, and are
affected by, actions and measures at other levels, and this interaction
must be considered in data analysis (Bryk & Raudenbush, 1992).
Research also needs to examine school climate in relation to student
academic achievement (Willms & Raudenbush, 1989). Most previous
studies have focused primarily on student characteristics,
school-context characteristics, or a single school climate factor and so
do not provide adequate knowledge about how school policies and
practices influence student learning outcomes. Finally, most previous
studies of effective schools focused on secondary schools, but
educational problems, especially academic problems, are cumulative.
Students in effective elementary schools are better prepared for
Some recent national and provincial surveys of
education do provide richer descriptions of school climate than earlier
ones. And recently developed statistical techniques such as hierarchical
linear modelling (HLM) allow researchers to analyze multilevel data
such as students nested within schools.
About one-third of New Brunswick's population
speaks French. The province is officially bilingual, and there are
separate English and French school systems. Other than the Mi'kmaq and
Maliseet Native communities, there are few visible minorities. The
entire Grade 6 student population in the English system participated in
the New Brunswick School Climate Study (NBSCS), conducted during the
1995-96 school year (N = 6,883 students from 148 schools). Each student
completed achievement tests in mathematics, science, reading, and
writing as well as a questionnaire. We used the student achievement
scores as dependent measures and the student characteristics and school
context and climate items in the student questionnaire as independent
MEASURES AND VARIABLES
A panel of experienced teachers and subject-area
specialists developed the four NBSCS achievement tests on the basis of
the provincial curriculum. The mathematics test consisted of 39 items
designed to measure numeration, measurement, geometric ability, and data
management, with an emphasis on understanding concepts and solving
problems. Students were encouraged to use manipulatives, and calculators
were permitted. Cronbach's alpha was 0.86. The science test consisted
of 33 items designed to measure knowledge and understanding of
scientific concepts and processes. Cronbach's alpha was 0.79. The
reading test used 35 items in fictional and non-fictional passages to
measure comprehension. Cronbach's alpha was 0.84. The writing assessment
was based on two pieces of student writing, one chosen by the teacher
from regular class work, the other written during the assessment. A
panel of teachers used scoring rubrics and a 6-point scale to grade them
from unrateable to superior. Each student's final writing score was the
sum of the two scores, scaled to have a mean of 0 and a standard
deviation of 1 following the statistical procedures outlined in
Mosteller and Tukey (1977).
The questionnaire consisted of 22 questions,
most containing embedded items, to measure student, family, and school
characteristics. We used the following to obtain information on major
Socioeconomic status. Which of these things do
you have at home for you to use? Books of my own, my own magazine(s), a
dictionary, a computer, a calculator, a musical instrument, a phone, a
specific place to study, and a link to the Internet. Which of these
activities have you done with members of your family over the past year?
Visited parks together, gone shopping, gone to the public library,
attended music concerts, gone skiing, gone on a Canadian holiday outside
of New Brunswick, and gone on a holiday outside of North America.
Ethnicity. The only ethnic group identified was
students from the 11 Native communities in New Brunswick, such as Burnt
Church and St. Mary's.
Number of parents. Most of the time I live with:
my mother, my step-mother, or someone who is like a mother to me; my
father, my step-father, or someone who is like a father to me.
Number of siblings. I have (number) sisters and
(number) brothers (including step-and half-sisters and brothers if any).
Gender, Native ethnicity, and the number of
parents were coded as dichotomous variables. SES was estimated using
students' reports of education-related possessions at home and their
participation in social and cultural activities, rather than parental
income or occupation. The number of siblings was a continuous variable.
School size was based on enrollment in Grade 6,
and school mean SES was derived from the SES of individual students.
Finally, three school climate variables -- disciplinary climate,
academic press, and parental involvement -- were constructed by
averaging scores on 5-point scales for selected items about the school:
Disciplinary climate. Rules at this school seem
to be always changing, students at this school call each other names,
students fool around during class, children at our school know what
"good behavior" means, students behave well in class, students at this
school get into fights, rules at this school are fair, troublemakers
disrupt my teacher's lessons, often the punishment for breaking the
rules is too strict, the rules for behavior at this school are clear to
me, children know what will happen if they break a rule, students are
able to help make the rules here, students agree with the rules at this
school, and kids in this school bully others outside the classroom.
Academic press. How many students in your class:
Think it is important to do well at school, try hard to get good marks
on tests, could do better if they tried harder, find school work too
difficult, usually do their homework on time, think it is more important
to have fun than learn, and feel they can do the work in class if they
try? Our teacher expects all students to do well, most of my school work
is too easy for me, we often have lively discussions in class, the
teacher encourages students to try harder, school work is challenging
for me, doing my homework helps me learn what we are taught in class,
the teacher encourages us to ask questions about the material we are
studying, and I can do well in school if I work hard.
Parental involvement. Since the beginning of
school this past fall, how often have your parents (or guardians) done
the following things? "Helped" you with your homework, talked with you
about how students treat you, limited how much TV you could watch
weekdays, discussed how well you were doing in math, discussed how well
you were doing in reading, talked with you about school projects,
checked your homework for mistakes, said how important school work is,
discussed hurtful things that children might say, helped in the
classroom, and helped with school activities (e.g., field trip).
So constructed, disciplinary climate concerns
mainly rules and compliance. Cronbach's alpha was 0.77 for disciplinary
climate, 0.61 for academic press, and 0.77 for parental involvement.
The effects of student-level and school-level
variables may be represented in various ways. We chose effect size to
make it easier for us to compare the effects of explanatory variables on
the outcome measure (cross-variable comparison) because explanatory
variables were converted to the same scale and for others to compare
their results with ours (cross-study comparison). We standardized
outcome and explanatory variables (converting raw scores into z-scores
for each) so that they had a mean of 0 and a standard deviation of 1.
After fitting a regression model, coefficients associated with
explanatory variables were measures of effect size.
Educational data are often hierarchical or
multilevel (students nested within schools). Failure to consider their
hierarchical nature leads to unreliable estimation of the effectiveness
of school policies and practices (Bryk & Raudenbush, 1992;
Raudenbush & Willms, 1991). Unfortunately, most analyses in
educational research have not taken into account the hierarchical
structure of educational data.
Over the past decade, researchers have developed
hierarchical linear models, multilevel models that can simultaneously
estimate the effects of student-level and school-level variables (Bryk
& Raudenbush, 1992). A separate regression model is fitted for each
school. These regression models yield a mean score adjusted for student
background for each school. They also produce measures of equality: for
example, of males and females or of academic achievement in relation to
social class. Individual school estimates (adjusted mean scores or
measures of equality) then become dependent measures in a model that
attempts to explain variation among schools with measures of school
characteristics (Gamoran, 1991; Lee & Smith, 1993; Willms, 1992).
We used two-level HLM (Bryk & Raudenbush,
1992) to examine the effects of student and school variables on academic
achievement at the student and school (students nested within schools)
levels. Separate HLM analyses were conducted for the achievement measure
in each of mathematics, science, reading, and writing. Each HLM
analysis was done in three stages. At the first stage, the analysis
produced the null model with no independent variables at the student and
school levels. With only the student-level outcome measure, this model
was similar to a random-effect ANOVA model, providing a measure of the
variances within and between schools for each of the four achievement
At the second stage, student variables were
added to the null model, first separately, to determine whether each
variable had a significant absolute effect on academic achievement
measures independently of other variables and whether its relationship
with achievement varied significantly across schools, then in
combination, to determine whether each variable had a significant
relative effect on the academic achievement measures in the presence of
other variables. In other words, the relative effect of the variable was
adjusted for the shared effects of other variables. We examined these
specific effects to find the role of each variable and the
interrelationship between it and others.
Using a similar procedure, at the third stage of
the analysis school variables were added to the student model, first
separately, to examine their absolute effects, then in combination, to
examine their relative effects -- that is, to model average school
academic achievement measures and school variables, and relationships
between academic achievement measures and student variables in relation
to school variables.
Table 1 shows the means and standard deviation
for the outcome (dependent) variables and explanatory (independent)
variables as well as coding information for the dichotomous variables
(gender, Native ethnicity, and number of parents). Means for the
dichotomous variables are proportions of the category coded as 1.
Descriptive statistics are in their original scales; writing
achievement, SES, and school mean SES were available only as z-scores,
with a mean of 0 and a standard deviation of 1. All continuous
variables, with the exception of school size, were standardized to have a
mean of 0 and a standard deviation of 1 at both the student level and
the school level. School size was determined by the number of students
in Grade 6, and we used its original scale. Dichotomous variables were
Most of the variation in achievement was among
students within schools: 0.89 in mathematics, 0.91 in science, 0.95 in
reading, and 0.91 in writing. However, schools differed markedly by
subject for the balance of the variation. The smallest variation (0.05)
suggests that schools were not very different in reading achievement,
the largest (0.11) suggests large differences among students in
The relative and absolute effects for student
and school variables are shown in Table 2. Effect size is the amount of
change in academic achievement, expressed as a proportion of a standard
deviation, associated with one standard deviation increase in an
Absolute effects provided a measure of the
independent effects of student variables. Each student variable had a
significant absolute effect on academic achievement across subject
areas. Gender differences varied greatly in absolute effects across
subject areas, favouring males in mathematics and science, and favouring
females in reading and writing. Males scored 5% of a standard deviation
higher than females in mathematics achievement and 13% of a standard
deviation higher than females in science achievement. To understand the
magnitude of these effect sizes, one may consider a standard achievement
test, such as the Scholastic Aptitude Test (SAT), with a mean of 500
and a standard deviation of 100. If the female average was 500 in both
mathematics and science, then the male average would be 505 (500 + [100 ×
5%]) in mathematics and 513 (500 + [100 × 13%]) in science. Other
effect sizes can be understood in the same manner. In reading and
writing, males scored 19% and 42% of a standard deviation below females.
Individual SES had absolute effects ranging from
13% to 18% of a standard deviation across the four subject areas.
Native students scored below non-Native students in all four subject
areas: 25% of a standard deviation below in mathematics achievements,
39% in science, 36% in reading, and 34% in writing. Students from
single-parent households scored below those from two-parent families:
13% of a standard deviation below in mathematics, 15% in science, 19% in
reading, and 14% in writing. The absolute effects of the number of
siblings were trivial.
Relative effects were adjusted (controlled) for
other variables in the model. Gender differences remained, and gender
gaps did not change much. The effects of individual SES also remained,
and its relative effects were not much different from its absolute
effects. So, gender and SES remain critical in explaining differences in
The Native gap in mathematics achievement
disappeared in the presence of gender and individual SES. However, when
gender and individual SES were controlled for, large Native gaps in
science, reading, and writing achievement remained and were not much
different from the absolute effects. The number of parents no longer had
a significant effect; neither did the number of siblings. The
cumulative relative effects of gender, individual SES, and Native
ethnicity were estimated and found to be substantial. For example, a
Native male whose SES was one standard deviation below the average could
be 34% of a standard deviation below the average in science
achievement, 64% in reading achievement, and 86% in writing achievement.
Average school achievement in each subject area
was independent of school size and parental involvement, neither of
which showed a significant absolute effect. Students in schools with
higher mean SES performed significantly better in mathematics, reading
and writing. And these effects were over and above those of individual
SES. Disciplinary climate and academic press both had significant
absolute effects in mathematics, science, and writing, and the relative
effect of disciplinary climate was quite similar to its absolute effect.
These effects were over and above the effects of student variables, and
in the case of writing achievement, the effect of disciplinary climate
was also over and above the effect of school mean SES.
The relationships (or slopes) between academic
achievement and student variables such as SES may differ across schools.
A shallow slope indicates that a difference in SES does not make a big
difference in academic achievement, a steep slope that the difference in
SES does make a big difference in academic achievement. We examined the
slope between student achievement in each area and each student
variable. The only significant slope was between mathematics achievement
and individual SES: This relationship varied significantly across
schools. When the slope was modelled with the school variables,
individual SES had a greater effect on mathematics achievement in larger
schools (0.01, p < .05) and in schools with stronger parental
involvement (0.03, p < .05).
Most of the variables we examined at the student
and school levels are complex both conceptually and operationally. To
avoid simplistic implications for policies and practices that can
reinforce various social stereotypes, our recommendations are tied to
the measurement of the associated variables.
At the student level, we consider four findings
important. First, the items used to measure SES mean that this variable
was about neither income nor parental occupation but rather
education-related possessions and participation in social-cultural
activities. This measure of SES may underestimate the effect of SES at
the student level but can still generate a reliable estimate of its
effect at the school level (Willms, 1992). The items emphasized
affective elements -- that is, families' attitudes and beliefs about
schooling and learning. Low student academic achievement correlated with
negative family attitudes and beliefs. This finding suggests
opportunities to work with parents and students to improve student
academic achievement. It also illustrates the importance of considering
the social construction of SES: Relating student academic achievement to
family income or parental occupation would lead to a totally different
set of remedial measures.
Second, the effects of family structure (number
of parents and number of siblings) disappeared when SES was considered
(cf. Ma, 1997; Manning, 1998; Sammons et al., 1997). Third, the research
literature in general claims that racial-ethnic differences in academic
achievement disappear once SES is considered (Hull, 1990; Sammons et
al., 1997; Strand, 1997). Our study provides quite different evidence:
When SES was taken into account, the relative effect of Native ethnicity
on science, reading, and writing achievement remained as strong as its
absolute effect. Native ethnicity was the single most important variable
in this study, with more than twice the effect of SES in three out of
four subject areas. Such a result has rarely been observed and suggests
that the underachievement of Native students is not attributable merely
to their SES but, perhaps, to their unsuccessful incorporation into the
mainstream culture (Ogbu & Simons, 1998).
Fourth, gender gaps existed even after
controlling for SES. However, gender differences in mathematics
achievement were so small, in contrast to consistently substantial
gender gaps in other subject areas, that they may indicate a trend
toward gender equity in mathematics education. This hypothesis might
find support in the observations that there was no Native disadvantage
in mathematics achievement and that the smallest SES effect was in
mathematics. Mathematics was clearly the subject area with the greatest
equity in learning outcomes, perhaps the result of decades of emphasis
on equity issues in mathematics education (Gambell & Hunter, 1999).
School mean SES had significant effects over and
above student-level effects in reading and writing but not in
mathematics and science. This result generates further research
questions. It makes sense where there is a large population of
immigrants: Many immigrant children go to low-SES schools, and English
is often more difficult for them than other subjects. However, New
Brunswick's immigrant population is very small. Why does learning
reading and writing seem more sensitive to school SES than learning
mathematics and science?
There was more socioeconomic inequality among
students in large schools, but school size did not affect a school's
average academic achievement. Large elementary schools tend to be
located in urban settings that have more socioeconomic differences.
Large urban schools often offer curricular and extracurricular
activities not available in small schools, and all students benefit. Yet
high-SES students have more resources and can better profit from
opportunities like field trips out of the province. And if large schools
do not develop adequate personal connections with individual students,
an impersonal environment may negatively affect low-SES students.
We found strong correlations between individual
SES and student achievement in schools with strong parental involvement.
The items we used to measure parental involvement assessed mainly the
amount of interaction between parents and children. High-SES parents are
more likely to be involved in schools and to promote their children's
academic success (Stevenson & Baker, 1987). This may explain the
large SES gap in academic achievement among students in schools in our
study with strong parental involvement.
Of the three school climate factors we
investigated, disciplinary climate, which here concerned mainly rules
and compliance, was seen to be the most important determinant of
academic achievement. This is an addition to the inventories of traits
of effective schools reported by Lytton and Pyryt (1998) and Zigarelli
(1996). Some argue that clear reasonable rules and sanctions, active and
proper enforcement, and positive relationships between students and
school staff form the basic elements of a disciplinary climate conducive
to academic success (Ma & Willms, 1995).
Parental involvement is often emphasized, but we
wonder whether frequency of school-home contacts is an unambiguous
measure of parental involvement. Frequent teacher-parent communication
may not be positive, since teachers often contact low-SES parents to
discuss their children's learning or behavioural problems (Ho &
Willms, 1996). Without knowing the nature of the communication, it is
risky to take frequency as a measure of the extent of parental
involvement. Norris (1999) emphasized too that the amount of parental
involvement reported depends on who answers the questions. Teachers
reported less involvement by parents of low-SES children, but no such
differences were found when parents were asked about the amount of
educational support they provided for their children. Different forms of
parental involvement also need to be considered. Ho and Willms (1996)
documented four distinct types: home supervision, home discussion,
home-school communication, and volunteer work.
We believe that HLM is an important statistical
tool for investigating the relationship between student achievement and
school context and climate. By taking into account the hierarchical
nature of educational data, HLM separates variation in schooling
outcomes into between-student and between-school components and then
analyzes each component in relation to the other. Thus HLM can offer
better statistical adjustments and more accurate estimations and promote
better policies and practices.
Xin Ma is a professor in the Faculty of Education at the University of Alberta.
Don A. Klinger obtained his doctorate from the
Faculty of Education at the University of Alberta in the fall of 2000.
Daniel Lawless is a teacher in Okanagan-Skaha School District #67, Pentiction, British Columbia.
The authors are grateful to J. Douglas Willms,
Director of the Canadian Research Institute for Social Policy at the
University of New Brunswick, for providing the data for this study. The
authors also thank the reviewers of this paper, whose insightful
comments helped to refine the research.
TABLE 1 Means and Standard Deviations of Outcome and Explanatory Variables
Variable M SD
Academic achievement (Outcome variables)
Mathematics 17.88 5.87
Science 17.92 5.39
Reading 23.52 6.21
Writing 0.00 1.00
Student characteristics (Explanatory variables)
Gender (0 = male; 1 = female) 0.50 0.50
Socioeconomic status 0.00 1.00
Native ethnicity (0 = non-Native; 1 = Native) 0.01 0.10
Number of parents (0 = two parents; 1 = single parent) 0.13 0.34
Number of siblings 1.75 1.51
School characteristics (Explanatory variables)
School size 39.71 30.73
School mean socioeconomic status 0.00 1.00
Academic press 3.72 0.16
Disciplinary climate 2.96 0.30
Parental involvement 2.27 0.17
Gender, Native ethnicity, and number of parents are dichotomous
variables. Socioeconomic status and writing achievement are standardized
variables (i.e., they are z-scores with a mean of 0 and a standard
deviation of 1) at the student level, and school mean SES is a
standardized variable at the school level.
TABLE 2 HLM Effects of Student and School Variables on Academic Achievement
Absolute Relative Absolute Relative
Variables effect effect effect effect
Gender -0.05(FN*) (0.02) -0.06(FN*) (0.03) -0.13(FN*) (0.03) -0.14(FN*) (0.02)
SES 0.14(FN*) (0.02) -0.09(FN*) (0.02) 0.13(FN*) (0.01) 0.14(FN*) (0.01)
Native ethnicity -0.25(FN*) (0.10) -- -0.39(FN*) (0.12) -0.34(FN*) (0.12)
Number of parents -0.13(FN*) (0.04) -- -0.15(FN*) (0.04) --
Number of siblings -0.02(FN*) (0.01) -- -0.04(FN*) (0.01) --
School size 0.00 (0.00) -- 0.00 (0.00) --
School mean SES 0.05 (0.03) 0.06(FN*) (0.03) 0.05 (0.03) --
Academic press 0.07(FN*) (0.03) -- 0.09(FN*) (0.02) --
Disciplinary climate 0.07(FN*) (0.03) 0.07(FN*) (0.03) 0.10(FN*) (0.03) 0.10(FN*) (0.03)
Parental involvement 0.01(FN*) (0.03) -- 0.01 (0.03) --
Absolute Relative Absolute Relative
Variables effect effect effect effect
Gender 0.19(FN*) (0.03) 0.17(FN*) (0.02) 0.42(FN*) (0.02) 0.40(FN*) (0.02)
SES 0.18(FN*) (0.01) 0.17(FN*) (0.01) 0.16(FN*) (0.01) 0.14(FN*) (0.01)
Native ethnicity -0.36(FN*) (0.09) -0.32(FN*) (0.12) -0.34(FN* (0.11) -0.32(FN*) (0.10)
Number of parents -0.19(FN*) (0.04) -- -0.14(FN*) (0.04) --
Number of siblings -0.04(FN*) (0.01) -- -0.03(FN*) (0.01) --
School size 0.00 (0.00) -- 0.00 (0.00) --
School means SES 0.07(FN*) (0.03) 0.07(FN*) (0.02) 0.10(FN*) (0.03) 0.10(FN*) (0.03)
Academic press 0.03 (0.02) -- 0.09(FN*) (0.03) --
Disciplinary climate 0.03 (0.02) -- 0.06(FN*) (0.03) 0.08(FN*) (0.02)
Parental involvement 0.02 (0.02) -- 0.05 (0.03) --
* p < .05
Note. Relative effects are estimated based on
the final, simplified models. Dashes indicate nonsignificant relative
effects. Values in parentheses are the corresponding standard errors for
the effect sizes.
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