Within-School Social Comparison: How Students Perceive the Standing of Their Class Predicts Academic Self-Concept

Abstract

Results from prior research indicate that a student’s academic self-concept is negatively influenced by the achievement of others in his or her school (a frame of reference effect) and that this negative frame of reference effect is not or only slightly reduced by the quality, standing, or prestige of the track or school attended (a "reflected glory" effect). Going beyond prior studies, the present research used both between-school and within-school approaches to investigate frame of reference and reflected glory effects in education, incorporating students’ own perceptions of the standing of their school and class. Multilevel analyses were performed with data from 3 large-scale assessments with 4,810, 1,502, and 4,247 students, respectively. Findings from all 3 studies showed that, given comparable individual achievement, placement in high-achieving learning groups was associated with comparatively low academic self-concepts. However, students’ academic self-concept was not merely a reflection of their relative position within the class but also substantively associated with their individual and shared perceptions of the class’s standing. Moreover, the negative effects of being placed in high-achieving learning groups were weaker for high-achieving students. Overall, the studies support both educational and social psychology theorizing on social comparison.

Full text

Within-School Social Comparison: How Students Perceive the Standing of
Their Class Predicts Academic Self-Concept
Ulrich Trautwein and Oliver Lu¨dtke
University of Tuebingen and Max Planck Institute for
Human Development
Herbert W. Marsh
Oxford University
Gabriel Nagy
Max Planck Institute for Human Development
Results from prior research indicate that a student’s academic self-concept is negatively influenced by the
achievement of others in his or her school (a frame of reference effect) and that this negative frame of
reference effect is not or only slightly reduced by the quality, standing, or prestige of the track or school
attended (a “reflected glory” effect). Going beyond prior studies, the present research used both
between-school and within-school approaches to investigate frame of reference and reflected glory
effects in education, incorporating students’ own perceptions of the standing of their school and class.
Multilevel analyses were performed with data from 3 large-scale assessments with 4,810, 1,502, and
4,247 students, respectively. Findings from all 3 studies showed that, given comparable individual
achievement, placement in high-achieving learning groups was associated with comparatively low
academic self-concepts. However, students’ academic self-concept was not merely a reflection of their
relative position within the class but also substantively associated with their individual and shared
perceptions of the class’s standing. Moreover, the negative effects of being placed in high-achieving
learning groups were weaker for high-achieving students. Overall, the studies support both educational
and social psychology theorizing on social comparison.
Keywords: social comparison, achievement, frame of reference effect, reflected glory effect
A high evaluation of one’s skills and abilities in important
academic and nonacademic life domains contributes to high self-
esteem and life satisfaction (Taylor & Brown, 1988; Trautwein,
Lu¨dtke, Ko¨ ller, & Baumert, 2006). Furthermore, feeling competent
in a specific area motivates and energizes behavior in that domain
and is associated with favorable long-term outcomes (Bandura,
1997; Marsh, Trautwein, Lu¨ dtke, Ko¨ ller, & Baumert, 2005;
Trautwein, Lu¨dtke, Kastens, & Ko¨ ller, 2006). Not surprisingly, the
sources of such positive self-evaluations have been the subject of
much research. Several studies have shown that the immediate
environment constitutes a salient frame of reference that impacts
people’s self-evaluations (Suls & Wheeler, 2000). In our own
research (e.g., Marsh, 1987; Trautwein, Lu¨dtke, Marsh, Ko¨ ller, &
Baumert, 2006), we have studied frame of reference effects pri-
marily within educational environments, where social comparison
processes are widespread. Frame of reference effects in educa-
tional environments have considerable implications for students’
lives, affecting outcomes such as their long-term educational tra-
jectories (Marsh, 1991; Trautwein & Baeriswyl, 2007) and health-
related behaviors (Trautwein, Gerlach, & Lu¨dtke, 2008). Because
the complex characteristics of educational environments involving
many students and multiple frames of reference pose a challenge
for social comparison theories focusing on individual or dyadic
processes, moreover, research on frame of reference effects in
natural school environments makes an important contribution to
the literature on social comparison processes.
In this article, we examine the possible impact of frame of
reference effects in secondary school. Secondary schools are
known to differ markedly in their student composition and overall
achievement (Marsh, Trautwein, Lu¨dtke, Baumert, & Ko¨ ller,
2007; Trautwein, Lu¨dtke, Marsh, et al., 2006)—factors that are
likely to impact students’ self-evaluations. Results from our prior
research and from several other studies (e.g., Tymms, 2001;
Zeidner & Schleyer, 1999) indicate that a student’s academic
self-concept is strongly influenced by the achievement of others in
his or her school and that this frame of reference effect also applies
to students’ interest, course choice, and educational aspirations
(e.g., Marsh, 1991; Trautwein, Ko¨ller, Lu¨ dtke, & Baumert, 2005;
Trautwein, Lu¨dtke, Marsh, et al., 2006). However, the social
comparison processes underlying this frame of reference effect are
not yet fully understood (Wheeler & Suls, 2007). The present
article makes a fourfold contribution to the literature. First,
whereas most previous research has used between-school designs
to investigate frame of reference effects in education, we also
address within-school differences (i.e., differences between classes
in the same school). Second, in addition to objective information
Ulrich Trautwein and Oliver Lu¨ dtke, Department of Education, Univer-
sity of Tuebingen, Tuebingen, Germany, and Center for Educational Re-
search, Max Planck Institute for Human Development, Berlin, Germany;
Herbert W. Marsh, Department of Education, Oxford University, Oxford,
England; Gabriel Nagy, Center for Educational Research, Max Planck
Institute for Human Development.
Correspondence concerning this article should be addressed to Ulrich
Trautwein, University of Tuebingen, Muenzgasse 22-26, 72070 Tuebin-
gen, Germany. E-mail: ulrich.trautwein@uni-tuebingen.de
Journal of Educational Psychology © 2009 American Psychological Association
2009, Vol. 101, No. 4, 853–866 0022-0663/09/$12.00 DOI: 10.1037/a0016306
853

about the relative standing of a class or school, we investigate
students’ individual and shared perceptions of their class or
school’s standing. To what extent do students agree about the
overall standing of their class or school, and how are these per-
ceptions related to objective achievement? Third, we relate these
perceptions of the standing of the class or school to students’
academic self-concepts, testing whether a positive perception of
class or school quality counteracts the expected negative frame of
reference effect. Fourth, we probe for possible interaction effects
between the average achievement of a class or school and the
perceived standing of the class or school, on the one hand, and
individual achievement, on the other. In other words, we test
whether high-achieving and low-achieving students are differen-
tially affected by class characteristics.
Research Paradigms in Social Comparison Research
Psychological research on social comparison dates back to
James (1890/1963) and Festinger (1954). Disciplines such as so-
cial, developmental, and educational psychology have since seen a
rich history of social comparison research; each discipline has
focused on different phenomena and used different research de-
signs (see Suls & Wheeler, 2000; Wheeler & Suls, 2005; Wood &
Wilson, 2003). In social psychology, there has been an emphasis
on experimental studies on the effects of upward and downward
social comparison, the motives for these comparison processes,
and the preference for and differential impact of specific types of
comparison information. The focus is on the individual as a pro-
cessor of social comparison information. Typically, the respondent
is either presented with a specific target or asked to pick a target.
In either case, the interest is in individual characteristics rather
than in group characteristics.
Results from this body of research suggest that people are
constantly on the lookout for social comparison information that
can be integrated into their self-concepts (Suls & Wheeler, 2000;
for a critical review, see Wood & Wilson, 2003). Perhaps the most
intriguing finding is the compelling evidence for self-enhancing
mechanisms in social comparison processes (e.g., Damisch, Mus-
sweiler, & Plessner, 2006; Mussweiler, 2003; Suls & Wheeler,
2000). Research has shown that— under certain conditions—social
comparison with a target who shows greater proficiency in a
specific domain may result in the comparer developing a higher
self-evaluation through assimilation. Assimilative processes are
especially likely if the comparer and the target share important
characteristics (Mussweiler, 2003; Wheeler & Suls, 2005). In
somewhat simplified terms, social psychology research indicates
that humans are capable of using social comparison processes
adaptively to enhance their self-evaluations.
Research on social comparison processes in educational psy-
chology departs from the paradigms used in social psychology
(e.g., Wheeler & Suls, 2005). One major strand of research has
focused on the impact of achievement differences in naturally
occurring educational environments (e.g., classes, schools) on out-
come variables such as academic self-concept and educational
choices (Marsh & Craven, 2002). In this paradigm, student out-
comes are seen as the consequence of specific characteristics of the
(natural) learning environment. Unlike laboratory experiments in
social psychology, where the experimenter manipulates the avail-
able social comparison information, real-life educational settings
provide a wealth of potentially useful social comparison informa-
tion, and researchers seek to identify the most important sources of
information by relating characteristics of the learning environment
to student outcomes.
An important feature of typical educational settings is their
hierarchical structure: Students are nested within classes, classes
are nested within schools, and schools are nested within larger
units such as school districts, states, or countries. It is imperative
to distinguish between these hierarchical levels for both conceptual
and statistical reasons (Raudenbush & Bryk, 2002). Although
researchers on social comparison processes in educational psy-
chology are well aware of these different levels of analyses, not all
levels have been covered in similar detail, as we describe in more
detail below.
The social comparison paradigm used in educational psychol-
ogy has yielded a fairly consistent body of results (Marsh &
Craven, 2002). However, in contrast to the overall picture emerg-
ing from social psychology research—in which high-achieving
comparison targets often activate assimilation processes with pos-
itive effects on the comparer’s self-concept (see Mussweiler,
2003)—the vast majority of studies in natural learning environ-
ments have found that high-achieving schoolmates have negative
effects on their fellow students’ self-concepts. In the following, we
describe some of the studies and findings most relevant to the
present research.
Imposed Social Comparison: Frame of Reference Effects
in the Classroom
The analytic approach most frequently chosen in studies exam-
ining frame of reference effects in educational environments is
regression based. General or domain-specific academic self-
concept (assessed by items such as “I am smart” or “I am good in
mathematics”) is used as the outcome variable, and individual
student achievement and school-average achievement are used as
the two major predictor variables. Regression analysis is used to
test whether school-average achievement is positively or nega-
tively associated with self-concept when individual achievement is
statistically controlled. In other words, it examines the conse-
quences of placement in high- or low-achieving environments.
Given two students with comparable achievement scores, which
student has a higher academic self-concept: the one placed in a
high-achieving school or the one placed in a low-achieving
school? The large majority of studies have found a negative
regression coefficient of school-average achievement as measured
by standardized achievement tests on academic self-concept (e.g.,
Lu¨dtke, Ko¨ ller, Marsh, & Trautwein, 2005; Marsh & Hau, 2003;
Marsh, Ko¨ller, & Baumert, 2001; see also the review by Marsh &
Craven, 2002), a phenomenon known as the “big-fish-little-pond
effect” (BFLPE; see Marsh, 1987, 1991; Marsh & Hau, 2003).
The empirical support for the BFLPE is compelling. For in-
stance, Marsh and Hau (2003) conducted a large cross-cultural test
of frame of reference effects using data from the Programme for
International Student Assessment (PISA; Organization for Eco-
nomic Cooperation and Development, 2001). Nationally represen-
tative samples of approximately 4,000 students from each of the 26
participating countries (total N⫽103,558 students in 3,851
schools) completed standardized achievement tests and a self-
concept questionnaire. Consistent with a priori predictions, the
854 TRAUTWEIN, LU
¨DTKE, MARSH, AND NAGY

predictive effects of individual student achievement were substan-
tial and positive, whereas the regression coefficients for school-
average achievement were negative.
Some researchers have used track status rather than school-
average achievement to predict self-concept. In a German study,
Schwarzer, Lange, and Jerusalem (1982) examined the effect of
track status on the development of academic self-concept after
transition to secondary school. Students in Germany are tracked on
the basis of their achievement at about age 10. The academic
self-concept of high-achieving students (who were placed in the
high track) tended to decrease after transition to secondary school,
whereas the academic self-concept of low-achieving students (who
were placed in the low track) tended to increase, indicating that the
negative effect of high-achieving classmates was stronger than any
positive effect of high track membership. Similarly, Rheinberg and
Enstrup (1977) compared the academic self-concept, test anxiety,
and achievement motivation of 165 students with mild to moderate
learning disabilities (70 ⬍IQ ⱕ85). When achievement was
controlled, students attending special schools were found to have
higher academic self-concepts and achievement motivation and
lower test anxiety than those enrolled in regular schools.
Counterbalancing Effects: Does the Standing of the
School Predict Self-Concept?
The studies reported thus far indicate that the self-concept of
students who are placed in academically selective schools is neg-
atively affected—a negative BFLPE or contrast effect. However,
might self-perceptions not also be enhanced by membership of
high-achieving or positively valued groups? In the social psychol-
ogy literature, there is sound evidence that people enjoy basking in
the reflected glory of successful others (e.g., Cialdini & Richard-
son, 1980) and that self-perceptions may be enhanced by mem-
bership in groups that are positively valued by the individual
(Diener & Fujita, 1997; Tesser, 1988). Adopting the term reflected
glory effects, Marsh (1984, 1987; Marsh, Kong, & Hau, 2000)
argued that—theoretically speaking—students in academically se-
lective schools might have more positive academic self-concepts
by virtue of being affiliated with a highly selective educational
program. In this sense, placement in a high-achievement group
might be expected to positively affect students’ global and
domain-specific self-concepts by means of “assimilation effects”
(see Marsh et al., 2000; Oakes, 1985; Seaton et al., 2008). From
the theoretical point of view, these reflected glory effects might
weaken or fully counterbalance negative frame of reference ef-
fects.
There are three major approaches to testing the relative strength
of reflected glory and negative frame of reference effects. The first
approach is used when no information other than average school
achievement is available on relevant school characteristics. In this
case—i.e., in the majority of studies on the BFLPE—reflected
glory and negative frame of reference effects are confounded in the
regression coefficient of school-average achievement. Because the
total effect (the regression coefficient of school-average achieve-
ment) is almost always negative (see Marsh, Seaton, et al., 2008),
it is evident that the negative effect is stronger than the positive
effect, although the size of each effect is unknown.
The second approach is used when additional descriptive infor-
mation about a school or a class is available. The best example is
information on within-school or between-school tracking. In
tracked school systems, students are assigned to a specific track on
the basis of their prior achievement, leading to homogenization of
learning groups (see Maaz, Trautwein, Lu¨dtke, & Baumert, 2008).
Students in higher tracks benefit from more cognitively activating
instruction and are more likely to gain access to university
(Becker, Lu¨dtke, Trautwein, Ko¨ ller, & Baumert, 2008; Klusmann,
Kunter, Trautwein, Lu¨dtke, & Baumert, 2008; Maaz et al., 2008).
Hence, membership in a higher track may produce reflected glory
effects. School-average achievement and track level are highly, but
not perfectly, correlated. Accordingly, when track information is
included in the analyses, in addition to school- or class-average
achievement, regression analyses should separate the (negative)
frame of reference effects (as mirrored in school-average achieve-
ment) from the (positive) reflected-glory effects (as expressed in
track status). To date, only a handful of studies have used this
approach. Recently, Trautwein, Lu¨dtke, Marsh, et al. (2006, Study
1) included both track membership and school-average achieve-
ment as predictor variables in a study with more than 14,000 ninth
graders in Germany. When individual achievement and students’
teacher-assigned school grades were controlled, school-average
achievement negatively predicted academic self-concept to a
statistically significant degree, whereas membership in a high or
low track was not associated with self-concept. The authors inter-
preted this finding as indicating that students typically integrate
information about the achievement of other students in their school
into their self-concept, but not information about the achievement
of students in other schools or the prestige of their track.
The third approach to separating the negative and positive
effects of being placed in a selective learning environment uses
student perceptions of the standing of their school or class as an
additional predictor variable. These perceptions can additionally
be aggregated to the class or school level and correlated with
objective achievement and self-concept. This approach thus draws
on both the individual perspective and the shared perceptions of a
group of students. Accordingly, from a psychological point of
view, it has the greatest potential for modeling reflected glory
effects. To our knowledge, however, only a single published study
has used this approach. Marsh et al. (2000) followed a large,
nationally representative sample of Grade 7 students through high
school in Hong Kong (7,997 students, 44 high schools, 4 years).
Although Hong Kong does not have a classical tracked school
system, parents and students are well aware of each school’s
relative standing, and they use this information when selecting
schools. The availability of this information might enable students
in selective high schools to maintain a favorable self-concept
despite their constant exposure to high-achieving fellow students.
Indeed, as expected by the authors, the higher the school-average
achievement, the higher the perceived school status reported by the
students. Consistent with previous findings of negative frame of
reference effects, when individual achievement was controlled,
school-average achievement based on measures collected in Grade
6, prior to the transfer to high school, negatively predicted aca-
demic self-concept in Grade 8 and Grade 9. Most important in the
present context, however, individual students’ perceptions of the
status of their school positively predicted their academic self-
concept, counterbalancing some of the negative effects of being
placed in a selective environment.
855
WITHIN-SCHOOL SOCIAL COMPARISON

The Marsh et al. (2000) study indicates that students’ academic
self-concepts are not fully determined by their relative position in
school, but also reflect their beliefs about the relative standing of
their school. Unfortunately, however, the Marsh et al. study did not
examine whether students within a school had similar perceptions
of the school’s status or whether their perceptions were idiosyn-
cratic. Moreover, the study did not analytically separate the effects
of individual (idiosyncratic) perceptions, on the one hand, and
perceptions shared by the students within a school, on the other.
This distinction is of high theoretical and empirical interest. If
students with higher perceptions of their school’s status have
higher self-concepts, the school status effect reported reflects an
individual-level effect. Alternatively, if the mean academic self-
concept is higher in schools with a relatively high mean perception
of school status, it reflects a school-level effect. Because the Marsh
et al. study did not analytically distinguish between the individual
and school levels, there is no way of telling whether the school
status effect they found documented an effect at the individual
level, the school level, or a mixture of both (Cronbach, 1976;
Lu¨dtke, Robitzsch, Trautwein, & Kunter, 2009).
Do Class Characteristics Interact with Individual
Student Characteristics?
Another important issue in the study of reference group effects
is whether these effects apply to all students in the same way. In
other words, if—when individual ability is controlled—there is a
negative regression coefficient of school/class-average ability on
student self-concept, is this effect the same for all students within
a class? Are high- and low-achieving students within a class
equally affected by a high average ability of their reference group?
From a theoretical perspective, Marsh and colleagues (Marsh,
1987; 1991; Marsh, Trautwein, Lu¨dtke, & Ko¨ ller, 2008) argued
that interactions between school/class-average ability and individ-
ual ability on academic self-concept might be relatively small or
nonsignificant because the frame of reference is established by
school/class-average ability. Accordingly, all students in a high-
ability school/class are predicted to have lower academic self-
concepts than they would if they attended a low-ability school/
class.
From the empirical perspective, the relatively few studies in-
vestigating whether the BFLPE is similar at all ability levels have
yielded nonsignificant results or relatively small effects. More-
over, not even the direction of the small effects was consistent
across studies. For instance, the findings of Marsh, Chessor, Cra-
ven, and Roche (1995) and Marsh and Hau (2003) suggest that the
BFLPE affects all levels of ability in a similar way. Marsh et al.
(2007) tested interaction effects between school-average ability
and individual ability in two samples of college-track high school
students. Whereas there was no evidence for an interaction effect
in the first sample, a negative interaction term in the second sample
suggested that high-achieving students were more strongly af-
fected by placement in high-achieving schools. Conversely, Dai
and Rinn (2008) argued that findings from some studies of gifted
student programs indicate that students in these selective academic
programs may be less affected by negative frame of reference
effects. In sum, although results to date are inconclusive (Coleman
& Fults, 1985; Dai & Rinn, 2008; Marsh et al., 2007; Reuman,
1989), individual difference in ability is a potentially important
BFLPE moderator that warrants further consideration.
Apart from its achievement level, the perceived standing of a
class or school may also interact with individual student achieve-
ment. Believing oneself to be part of a high-quality learning group
may be differentially important for high-or low-achieving students.
For instance, it is conceivable that the self-concept of a low-
achieving student benefits more from the idea of belonging to a
high-quality class or school than does the self-concept of a high-
achieving student. However, empirical studies have yet to test this
hypothesis.
The Present Research
The majority of previous studies on frame of reference effects in
educational settings support the hypothesis that when individual
achievement is controlled, placement in a high-achievement group
is associated with lower academic self-concepts. However, only
one study to date has examined whether student ratings of their
school’s standing influence their self-perceptions. This one excep-
tion, the pioneering study by Marsh et al. (2000), considered
student ratings of school status but did not separate individual- and
school-level effects. Thus, previous research on self-concept in
educational environments strongly supports the hypothesis that the
school is the most salient frame of reference, but very little
attention has been paid to student perceptions of the school or the
track. This paucity of empirical studies stands in marked contrast
to the picture that has emerged from social psychology, where the
bulk of laboratory research portrays humans as active information
seekers who adaptively use the social comparison information
available (Mussweiler, 2003; Suls & Wheeler, 2000) to enhance
their self-concept.
The present research builds on prior research to critically assess
social comparison processes in natural learning environments.
Most important, we included a measure of perceived standing of
the class or school in our analyses, asking students to evaluate the
standing of their mathematics class relative to other mathematics
classes in the school (Studies 1 and 2) and the standing of their
school relative to other schools (Study 3).
In principle, we tested the following set of four questions in all
three studies (in Study 3, we looked at school characteristics rather
than class characteristics): First, we expected to replicate results
from prior research on frame of reference effects, independently of
whether class or school was used as the grouping variable. In other
words, when individual mathematics achievement was controlled,
we expected to find a negative regression weight of class- or
school-average mathematics achievement on mathematics self-
concept. Second, extending the Marsh et al. (2000) study,
we distinguished between students’ individual perceptions of the
standing of their class or school and their shared perceptions of the
standing of their class or school. We expected to find reliable
between-class and between-school differences in students’ evalu-
ations of the standing of their class and school. That is, we
expected students in the same classes or schools to report some
shared perceptions of their class or school’s standing, although
individual members of the same class or school were naturally
expected differ to some degree in their evaluations. Third, we
expected these ratings of the standing of the class or school to be
reflected in students’ mathematics self-concepts, and we made
856 TRAUTWEIN, LU
¨DTKE, MARSH, AND NAGY

parallel predictions for the class or school and the individual
levels. At the class or school level, we expected to find higher
mathematics self-concept in classes in which the overall student
rating of class or school standing was high. Similarly, at the
student level, we expected to find higher mathematics self-concept
in students who reported higher perceptions of their class or
school’s standing. Finally, we probed for possible interaction
effects between two class or school characteristics (the average
achievement of a class or school and the perceived standing of the
class or school), on the one hand, and individual student charac-
teristics (student achievement and perceived class or school stand-
ing), on the other. Hence, four interaction effects in total were
specified in each of the three studies. We were specifically inter-
ested in the interaction effect between class- or school-average
achievement and individual achievement because—as described
above—prior research has yielded inconclusive results.
Study 1
Method
Sample
The data for Study 1 were collected in 156 randomly selected
academic-track secondary schools in the German state of Baden-
Wu¨rttemberg that were representative of the track in that state.
Students graduating from academic-track secondary schools in
Germany are eligible to attend university. Forty students in each
school were randomly selected and invited to participate in the
study; in schools with less than 40 students, all students were
invited to participate. Of the targeted sample of 6,177 students, a
total of N⫽5,016 students ( ⫽81.2%) participated in the study.
Complete data were available from 4,810 students (56% female;
mean age M⫽19.57 years, SD ⫽0.78); these students form the
sample for the present study. Students in the present sample were
in their final year of schooling (i.e., Grade 13); all were enrolled in
a pre-university mathematics class. Students participated voluntar-
ily in the present investigation without any financial reward. Two
trained research assistants administered materials in each school
between February and May 2006.
Instruments
Mathematics self-concept. Mathematics self-concept was as-
sessed using the German adaptation of the Self Description Ques-
tionnaire III, a multidimensional self-concept instrument for late
adolescents and young adults based on the Shavelson, Hubner, and
Stanton (1976; Marsh & Shavelson, 1985) model. In the German
adaptation (Schwanzer, Trautwein, Lu¨dtke, & Sydow, 2005), four
researchers with English as a second language translated all orig-
inal items independently of each other. Subsequently, the most
appropriate translation was chosen (and in some instances refined)
with the assistance of a professional translator. Extensive pilot
testing resulted in a short German instrument with 4 items per
scale and a 4-point response format (from disagree to agree). The
4 items selected per scale emphasized cognitive (e.g., “I’m good at
mathematics”) rather than affective (e.g., “I like mathematics”)
evaluations. Marsh et al. (2007) have provided strong empirical
support for the convergent and discriminant validity of responses
to this mathematics self-concept scale. In the present study, the
internal consistency (Cronbach’s alpha) of the scale score was .90.
Mathematics achievement. The mathematics achievement test
consisted of items from the Third International Mathematics and
Science Study (TIMSS; e.g., Baumert, Bos, & Lehmann, 2000).
Responses were analyzed with item response theory methods and
the ConQuest software (Wu, Adams, & Wilson, 1998), and the
original TIMSS metric was used to generate a total mathematics
achievement score. The reliability of the test scores was .88
(formula by Rost, 1996).
Perceived standing of the mathematics class. Four statements
with an identical item stem (“Relative to other mathematics classes
in my school ___”) tapped students’ ratings of the standing of their
mathematics class (“my mathematics class is considered to be
good,” “we learn a lot in my mathematics class,” “students in my
mathematics class are particularly high achieving,” “my mathe-
matics class has high standing”).
1
A 4-point (from disagree to
agree) response format was used. The internal consistency (Cron-
bach’s alpha) of the scale score was .85. The measure was partly
adapted from the Marsh et al. (2000) study. An exploratory factor
analysis strongly supported a one-factor solution (all factor load-
ings on the first component were ⬎.73).
Statistical Analyses
In most studies conducted in schools, individual student char-
acteristics are confounded with classroom or school characteristics
because individual students are not randomly assigned to groups.
This clustering effect introduces problems related to appropriate
levels of analysis, aggregation bias, and heterogeneity of regres-
sion (Raudenbush & Bryk, 2002). We therefore performed multi-
level regression analyses to predict mathematics self-concept. For
the present investigation, it is particularly important to note that the
meaning of a variable at the student level may not bear any
straightforward relation to its meaning at the classroom level. The
negative frame of reference effect represents a dramatic example
of this problem, in that achievement at the individual level is
positively related to self-concept, whereas achievement at the
class-average level may be unrelated or negatively related to
self-concept. The juxtaposition of the effects of individual achieve-
ment and class-average achievement is inherently a multilevel
issue that cannot be represented properly at either the individual or
the classroom level. Particularly when major variables represent
different levels, it is important to use appropriate multilevel sta-
tistical procedures for data analysis. Multilevel modeling, a gen-
eral form of regression analysis, provides a powerful methodology
for handling hierarchical data, and it was used in this study. A
detailed presentation of multilevel modeling (also referred to as
hierarchical linear modeling [HLM]) is beyond the scope of the
present investigation and is available elsewhere (e.g., Raudenbush
& Bryk, 2002; Snijders & Bosker, 1999).
1
The original German wording of the item stem and the four statements
(items) was as follows: Item stem: “Im Vergleich mit anderen Mathema-
tikkursen an meiner Schule ___”; items: “hat mein Mathematikkurs einen
guten Ruf,” “wird in meinem Mathematikkurs viel gelernt,” “sind Schu¨l-
erinnen und Schu¨ ler in meinem Mathematikkurs besonders leistungsstark,”
“ist mein Mathematikkurs besonders angesehen.”
857
WITHIN-SCHOOL SOCIAL COMPARISON

In the present study, all multilevel analyses were computed
using the HLM 6 computer program (Raudenbush, Bryk, Cheong,
& Congdon, 2004). We specified three-level models, with students
as the first level, classes as the second level, and schools as the
third level. We did not, however, include school-average achieve-
ment as an additional predictor because the very high intercorre-
lation of r⫽.80 between class-average achievement and school-
average achievement would produce unwanted multicollinearity if
both variables were introduced simultaneously, making results
very difficult to interpret.
We specified several sets of multilevel models to test our
hypotheses. As in ordinary regression analyses, one outcome vari-
able was regressed on several predictor variables in each model.
By specifying several consecutive models, researchers are able to
observe the change in the predictive power of one variable when
an additional variable is included. HLM does not report standard-
ized regression coefficients. To enhance the interpretability of the
regression coefficients produced, we standardized (M⫽0, SD ⫽
1) all continuous variables before performing the multilevel anal-
yses. Mathematics achievement was aggregated at the class level
(Level 2) to form an index of the overall level of mathematics
achievement in the class (and was not restandardized). Unless
otherwise indicated, all models reported are random-intercept
models estimated by the full maximum likelihood method.
Centering Level 1 (student-level) predictor variables is a crucial
issue in multilevel modeling (see Enders & Tofighi, 2007). In the
literature on multilevel modeling, two main centering options are
discussed: Level 1 predictor variables can be adjusted to the mean
of the cluster to which the student belongs (centering at the group
mean) or to the mean of the variables in the whole sample (cen-
tering at the grand mean). In line with prior research on frame of
reference effects, students’ individual achievement was centered at
the grand mean. Thus, the predictive effect of class-average math-
ematics achievement on mathematics self-concept is controlled for
individual mathematics achievement. In contrast, perceived class
standing was centered at the group mean. Centering at the group
mean is typically the appropriate option for students’ ratings of
their learning environment (Lu¨dtke et al., 2009): Grand mean
centering would lead to interindividual differences among classes
being controlled in these ratings, thereby eliminating an essential
component of the aggregated ratings (see also Karabenick, 2004).
We assessed model fit using the deviance values provided by
HLM, which can be regarded as a measure of lack of fit between
model and data (Snijders & Bosker, 1999). Deviance values are
not usually interpreted directly; rather, differences in deviance
values are calculated for models applied to the same data set. The
difference in deviance between two models has a chi-square dis-
tribution with degrees of freedom equal to the difference in the
number of parameters estimated. Because we used the full maxi-
mum likelihood method, the chi-square statistic can be used to
evaluate change in model fit when either a fixed or a random effect
is added. Large chi-square values indicate that the model with
more parameters provides a better fit to the data than the more
parsimonious model.
Effect sizes have found increasing use in psychological research
(see Grissom & Kim, 2005). In our study, we used three indicators
of effect size. First, in analogy to the measure of explained vari-
ance in ordinary linear regression models, we report the overall
proportion of variance explained by the predictor variables for
each model. This measure is determined by calculating the de-
crease in the total variance when the predictor variables are intro-
duced into the specific model (see Snijders & Bosker, 1999).
Second, we report easily interpretable regression coefficients for
Level 1 variables. Because we standardized all continuous Level 1
predictor and outcome variables before entering them in our mul-
tilevel models, the coefficients of the continuous Level 1 variables
can be interpreted in almost the same way as the standardized
regression coefficients resulting from ordinary regression analysis.
With reference to Cohen’s (1988) suggestions for correlations, we
consider a regression coefficient of .10 to mark the lower bound
for a meaningful effect (for a similar rationale, see Roberts, Caspi,
& Moffitt, 2003).
Third, in line with most previous multilevel research (e.g.,
Marsh & Hau, 2003), we did not restandardize our Level 2 pre-
dictor variable (class-average mathematics achievement). Hence,
the class-level regression weights show change in the dependent
variable (mathematics self-concept) corresponding to an increase
of one unit in class-average mathematics achievement, expressed
in the metric of mathematics achievement at the student level.
Tymms (2004) proposed that the effect size for continuous Level
2 predictors in multilevel models, which is comparable with Co-
hen’s d, be calculated using the following formula:
⌬⫽2⫻B⫻SDpredictor/␴e,
where Bis the unstandardized regression coefficient in the multi-
level model, SD
predictor
is the standard deviation of the predictor
variable at the class level, and ␴
e
is the residual standard deviation
at the student level. The resulting effect size describes the differ-
ence in the dependent variable between two classes that differ by
two standard deviations on the predictor variable. We suggest that
an effect size of ⌬ⱖ|0.20| can be considered of practical signif-
icance in the present research.
Results and Discussion
Our first hypothesis stated that the typical frame of reference
effect on academic self-concept would also be found when the
class—rather than the school—was used as the grouping variable.
In other words, we expected to find a negative regression weight
for class-average achievement when individual achievement was
controlled. In Model 1, we therefore specified the classical frame
of reference model, including both individual mathematics scores
and class-average mathematics scores as predictor variables. As
documented in Table 1, individual mathematics achievement pos-
itively predicted mathematics self-concept; the regression coeffi-
cient of B⫽0.60 indicates that an increase in mathematics
achievement of one standard deviation was associated with an
increase in mathematics self-concept of more than half a standard
deviation. The regression coefficient for class-average mathemat-
ics achievement was B⫽⫺0.22. We calculated the effect size for
this coefficient using the formula given above. With a standard
deviation in class-average ability of SD ⫽0.59 and a residual
standard deviation at the student level of ␴
e
⫽0.83, we found a
small effect:
⌬⫽2⫻⫺0.22 ⫻0.59/0.83 ⫽⫺0.31.
Hence, in line with our first hypothesis, students with the same
mathematics achievement had higher mathematics self-concepts if
858 TRAUTWEIN, LU
¨DTKE, MARSH, AND NAGY

their class showed low average achievement than if their class
showed high average achievement. The overall proportion of vari-
ance explained in self-concept was 29%. The model fit of Model
1 was statistically significantly better than that of an empty model
(not reported in Table 1) with mathematics self-concept as the
dependent variable, ⌬␹
2
(2, N⫽4,810) ⫽1,615.87, p⬍.001.
Our second hypothesis stated that there would be reliable
between-class differences in students’ perceptions of the standing
of their mathematics classes. How strongly did the perceptions of
students in the same class covary? Consensus (or, more correctly,
reliability of student responses) is easily calculated by means of
the intraclass correlation coefficients (ICC), ICC
1
and ICC
2
(see
Bliese, 2000; Lu¨dtke, Trautwein, Kunter, & Baumert, 2006; Sni-
jders & Bosker, 1999). The ICC
1
indicates the proportion of the
total variance that is located between school classes; given
the same total variance, the higher the ICC
1
, the more similar the
perceptions of the students in the same classes regarding the
standing of their class. In our study, the ICC
1
amounted to .47,
indicating that there were considerable between-class differences
and within-class agreement in how class standing was perceived.
The ICC
2
can be used to evaluate the reliability of the aggregated
student ratings at the class level. It is a function of the ICC
1
and the
number of students per classes. As a rule of thumb, ICC
2
values
above .70 are seen as indicating sufficient reliability (Lu¨dtke et al.,
2006). In the present study, with an average of 8.79 students per
class, the ICC
2
was .88, indicating that the aggregated perceived
class standing score was a reliable indicator of perceived mathe-
matics class standing across classrooms. The aggregated percep-
tion of class standing was positively correlated with class-average
achievement (r⫽.31, p⬍.001); this moderately close association
indicates that perceived class standing reflects more than the
class-average student ability. Taken together, in line with our
hypothesis, we found that classmates reported similar perceptions
of their class’s standing, although individual students within the
same mathematics class differed to some degree in their evalua-
tions.
Our third—and most central— hypothesis stated that these dif-
ferential evaluations of the class standing would also be reflected
in students’ mathematics self-concept at both the class and the
individual level. We specified two additional multilevel models to
address this hypothesis (Models 2 and 3 in Table 1). In Model 2,
we replaced the achievement predictors by perceived class stand-
ing at the individual level. Findings at the individual level showed
that students who had a higher opinion of their class’s standing
reported higher mathematics self-concept than their classmates
who had a lower opinion of their class’s standing. Similarly,
findings at the class level showed that mathematics self-concept
was higher in classes in which the overall students rating of class
standing was high. The effect size for this effect was ⌬⫽2⫻
0.21 ⫻0.74/0.97 ⫽0.25.
In Model 3, we reintroduced the achievement variables at both
levels. Thus, this model examined whether the positive effects of
high perceived class standing would still be observable when
objective differences in standardized achievement were controlled.
As shown in Table 1, all predictor variables were statistically
significantly associated with mathematics self-concept. The beta
coefficients for perceived class standing remained quite stable
from Model 2 to Model 3. At the class level, the regression
coefficient decreased to 0.14; however, with a reduced residual
standard deviation in mathematics self-concept of ␴
e
⫽0.82, the
effect size for class-level perceived prestige remained stable at
⌬⫽0.25. Taken together, in line with Hypothesis 3, and congru-
ent with the idea that people use social comparison processes
adaptively to enhance self-evaluations in natural learning environ-
ments, we found higher mathematics self-concept in classes in
which the overall rating of class standing was high (class-level
effect) as well as in individual students who rated the standing of
their mathematics class more favorably than their classmates
(student-level effect). The theoretical model upon which our pre-
dictions were based posits that the total effect of school-average
ability on self-concept is the net effect of two opposite effects,
namely a positive reflected-glory assimilation effect and a negative
contrast effect. Consistent with these expectations, the introduction
of the perceived standing of the class (Model 3) also resulted in a
somewhat more negative effect of school-average ability.
Finally, we tested whether some individual students were spe-
cifically affected by class characteristics. To this end, a total of
four interaction effects were specified and tested for statistical
significance. In this analysis, class-average achievement was
found to interact with individual achievement. We found a statis-
tically significant regression coefficient of B⫽0.11 ( p⬍.001) for
this interaction term, indicating that—although students at all
levels of achievement were negatively affected by frame of refer-
ence effects— high-achieving students in the present sample were
Table 1
Predicting Mathematics Self-Concept (Study 1): Results From Multilevel Modeling
Fixed effects
Model 1 Model 2 Model 3
B p SE B p SE B p SE
Intercept 0.00 .955 .02 0.00 .946 .02 0.00 .880 .02
Class level
Perceived class standing 0.21 ⬍.001 .02 0.14 ⬍.001 .02
Class-average achievement ⫺0.22 ⬍.001 .03 ⫺0.28 ⬍.001 .03
Individual level
Perceived class standing 0.19 ⬍.001 .02 0.17 ⬍.001 .02
Mathematics achievement 0.60 ⬍.001 .02 0.60 ⬍.001 .02
Variance explained .29 .04 .31
Deviance 11,962.30 13,428.24 11,810.39
Estimated parameters 6 6 8
859
WITHIN-SCHOOL SOCIAL COMPARISON

somewhat less affected than low-achieving students. All other
interaction effects failed to reach conventional levels of statistical
significance (all ps⬎.20).
In sum, the findings of Study 1 confirmed our main hypothesis.
Most importantly, students within a class had similar perceptions
of the standing of their class, and the perceived standing of the
class was positively related to students’ self-concept, offsetting to
some extent the negative effects of class-average ability. Further-
more, as indicated by the significant interaction between class-
average achievement and individual achievement, high-achieving
students were somewhat less affected by the negative frame of
reference effect than were low-achieving students.
Study 2
Method
Sample
Study 2 was essentially a replication of Study 1 with a different
sample of students. The analyses in Study 2 are based on data from
the Initial Achievement and Learning Development study (LAU;
Lehmann, Vieluf, Nikolova, & Ivanov, 2006; Trautwein, Ko¨ller,
Lehmann, & Lu¨dtke, 2007). In this study, all Grade 13 students in
the German state of Hamburg took a mandatory achievement test
in 2005. As an optional part of the study, they were invited to
answer a questionnaire including a self-concept inventory and
questions relating to the perceived standing of their mathematics
classes. Only students who were enrolled in comparable mathe-
matics classes (i.e., general rather than advanced mathematics
classes) and who provided valid data were included in the present
analyses, giving a sample of 1,502 students (58% female, mean
age: M⫽19.8 years, SD ⫽1.10) from 192 general mathematics
classes in 72 schools.
Instruments
We used the same instruments as in Study 1. Internal consis-
tency of the scale scores was .87 for mathematics achievement, .89
for mathematics self-concept, and .87 for perceived mathematics
class standing.
Results and Discussion
We conducted the same set of analyses as in Study 1. Results
from multilevel modeling are reported in Table 2. In Model 1, the
negative frame of reference effect was replicated. Controlling for
individual mathematics achievement, we again found that class-
average mathematics achievement negatively predicted mathemat-
ics self-concept. With a standard deviation in class-average
achievement of SD ⫽0.55 and a residual standard deviation in
mathematics self-concept of ␴
e
⫽0.81, the effect size was a
sizeable ⌬⫽⫺0.63. The model fit of Model 1 was statistically
significantly better, ⌬␹
2
(2, N⫽1,502) ⫽609.10, p⬍.001, than
that of an empty model (␹
2
⫽4,261.56; not reported in Table 2)
with mathematics self-concept as the dependent variable.
We next examined the consistency of classmates’ perceptions of
class standing by calculating the intraclass correlations coeffi-
cients. The ICC
1
was .39 and the ICC
2
was .83, indicating that
there was considerable consistency in perceived class standing
among classmates and justifying the use of this variable as a
class-level construct. The positive association between the class-
average perception of class standing and class-average achieve-
ment was nonsignificant (r⫽.14, p⫽.06).
In Model 2, we used individual and class-average perceptions of
class standing to predict mathematics self-concept. Findings at the
class level showed that students in classes with a high average
perception of the standing of their class reported comparatively
high self-concepts. With a standard deviation in class-average
perceived standing of SD ⫽0.71 and a residual standard deviation
in mathematics self-concept of ␴
e
⫽0.95, the effect size was a
sizeable ⌬⫽0.25. Similarly, at the level of the individual student,
we found comparatively high mathematics self-concept in students
whose evaluations of class standing were higher than those of their
classmates.
We simultaneously introduced all predictor variables in Model
3. Although the beta coefficients of the predictor variables de-
creased slightly, the pattern of results remained virtually the same.
Due to the reduced residual standard deviation of mathematics
self-concept in Model 3 (␴
e
⫽0.79), the effect sizes for class-
average achievement (⌬⫽⫺0.64) and aggregated perceived class
standing (⌬⫽0.27) were almost unchanged.
Table 2
Predicting Mathematics Self-Concept (Study 2): Results From Multilevel Modeling
Fixed effects
Model 1 Model 2 Model 3
B p SE B p SE B p SE
Intercept 0.04 .091 .02 0.00 .955 .02 0.04 .061 .02
Class level
Perceived class standing 0.17 ⬍.001 .03 0.15 ⬍.001 .03
Class-average achievement ⫺0.46 ⬍.001 .06 ⫺0.45 ⬍.001 .05
Individual level
Perceived class standing 0.38 ⬍.001 .04 0.27 ⬍.001 .03
Mathematics achievement 0.65 ⬍.001 .02 0.61 ⬍.001 .02
Variance explained .33 .09 .38
Deviance 3,652.45 4,123.90 3,542.12
Estimated parameters 6 6 8
860 TRAUTWEIN, LU
¨DTKE, MARSH, AND NAGY

Finally, we again specified four interaction terms between class
characteristics and individual student characteristics. In this
random-slope model, we again found a statistically significant
interaction between class-average achievement and individual
achievement (B⫽0.08, p⬍.05), suggesting that high-achieving
students were less affected by the negative frame of reference
effect than were low-achieving students.
Taken together, Study 2 closely replicated the findings of Study
1. Most important, the perceived standing of the mathematics class
predicted mathematics self-concept over and above the predictive
effects of mathematics achievement at both the individual and the
class level. In fact, the effect sizes for the class-level indicators
were somewhat stronger than in Study 1. This result might reflect
the greater diversity of classes in Study 2 (conducted in a city with
strong social disparities) than in Study 1 (conducted in a rather
more homogeneous state). Additionally, we again found high-
achieving students to be less affected by the negative frame of
reference effect.
Study 3
Method
Sample
In Study 3, we focused the school level rather than the class
level. The data for Study 3 were provided by a large, ongoing
German study conducted by the Max Planck Institute for Human
Development, Berlin (see Ko¨ ller, Watermann, Trautwein, &
Lu¨dtke, 2004). The analyses are based on data from 4,247 Grade
13 students (55.5% female, mean age: M⫽19.58 years, SD ⫽.83)
in 149 randomly selected upper secondary schools in the state of
Baden-Wu¨rttemberg. Two trained research assistants administered
materials in each school between February and May 2002. Stu-
dents participated voluntarily, without any financial reward.
2
Instruments
Mathematics achievement and mathematics self-concept. We
again used the instruments administered in Study 1. Internal con-
sistency of the scale scores was .89 for both mathematics achieve-
ment and mathematics self-concept.
Perceived school standing. In contrast to Studies 1 and 2, in
Study 3 we tapped students’ perceptions of the standing of their
school rather than that of their mathematics class. Accordingly, the
item stem read “Relative to other schools ___,” and we replaced
“mathematics class” with “school” in the four items. Other than
this, the items were identical to those used in Studies 1 and 2.
Internal consistency of the scale score (Cronbach’s alpha) was .77.
Statistical Analyses
We again specified a set of multilevel models to predict math-
ematics self-concept, this time using the school as the Level 2 unit.
Accordingly, we computed school-average achievement as well as
an aggregate of students’ perceptions of school standing as school-
level variables to be included in the two-level multilevel models.
Results and Discussion
The results for Study 3 are reported in Table 3. In Model 1, the
negative frame of reference effect was replicated. Controlling for
individual student achievement, we found a statistically negative
predictive effect of school-average achievement, indicating that
students with the same individual achievement levels reported
lower mathematics self-concept if placed in higher achieving
schools. Hence, our first hypothesis was supported. With a stan-
dard deviation in school-average achievement of SD ⫽0.45 and a
residual standard deviation in mathematics self-concept of ␴
e
⫽
0.86, the effect size amounted to ⌬⫽⫺0.31. The model fit of
Model 1 was statistically significantly better, ⌬␹
2
(2, N⫽
4,247) ⫽2,791.86, p⬍.001, than that of an empty model (␹
2
⫽
13,619.50; not reported in Table 3) with mathematics self-concept
as the dependent variable.
We next calculated the reliability of the aggregated school
standing measure. With an ICC
1
of .28, the intraclass correlation of
perceived school standing was somewhat lower than the ICC of the
mathematics class standing measures used in Studies 1 and 2,
indicating somewhat more variation in classmates’ evaluations of
school standing than in their evaluations of class standing. How-
ever, in support of our second hypothesis, because an average of
28.5 students per school participated in the study, the aggregated
school-level standing indicator was highly reliable, with an ICC
2
of .92. The correlation between perceived school standing aggre-
gated at the school level and aggregated mathematics achievement
was not statistically significant (r⫽.13, p⫽.11).
In Model 2, we related perceived school standing to mathemat-
ics self-concept at the school and student levels. Findings at the
student level showed that perceived school standing was positively
associated with mathematics self-concept. Students who evaluated
their school’s standing more favorably than their fellow students
had a higher mathematics self-concept. At the school level, the
association between perceived school standing and mathematics
self-concept was not statistically significant. In other words, al-
though there was agreement among students on the standing of
their school, these shared perceptions were not reflected in their
mathematics self-concepts.
In Model 3, mathematics achievement and perceived school
standing were simultaneously entered in the regression equation.
The association between mathematics achievement and mathemat-
ics self-concept was positive at the student level and negative at
the school level. Furthermore, perceived school standing was
positively associated with mathematics self-concept at the student
level, but not the school level. Hence, somewhat unexpectedly, we
found only partial support for our third research hypothesis in this
study.
Finally, we specified the four interaction terms between school-
average achievement and school-average perception of school
standing, on the on hand, and individual achievement and individ-
ual perception of school standing, on the other. In this random-
slope model, we again found a statistically significant interaction
between school-average achievement and individual achievement
(B⫽0.13, p⬍.05), suggesting that high-achieving students were
less affected by the negative frame of reference effect than were
2
About half of the students in the present sample were also examined in
a study by Marsh et al. (2007), who investigated the long-term stability of
frame of reference effects. However, Marsh et al. did not include the
measure of school standing considered here.
861
WITHIN-SCHOOL SOCIAL COMPARISON

low-achieving students. The other three interaction effects did not
reach conventional levels of statistical significance ( ps⬎.20).
In sum, the findings of Study 3 replicated the negative frame of
reference effect of school-average achievement and again sug-
gested that high-achieving students are less affected by frame of
reference effects than are low-achieving students. Moreover, stu-
dents’ individual perceptions of their school’s standing were as-
sociated with their self-concept, whereas the aggregated indicator
of the school’s standing did not predict self-concept. This finding
indicates that shared beliefs about between-school differences in a
school’s standing are not systematically integrated into students’
self-concepts.
General Discussion
In three large empirical studies, we extended previous research
on the negative frame of reference effects postulated by Marsh
(1987) in educational settings. There were four main findings.
First, given comparable individual achievement, placement in
high-achieving learning groups is associated with comparatively
low academic self-concepts. We found the same pattern of results
for class-average and school-average achievement. Second, there
was substantial agreement across students’ perceptions of the
relative standing of their class or school, yielding a reliable indi-
cator of perceived class or school standing at the class or school
level. Third, the students’ academic self-concepts were not merely
a reflection of their relative position within the class; they were
also substantively associated with their perceptions of their class’s
overall standing. Across all three studies, student-level perceptions
of class or school standing were positively associated with self-
concept; furthermore, class-average student perceptions of class
standing predicted self-concept. Hence, these findings are consis-
tent with the idea that students actively integrate social comparison
information into their self-concept (Suls & Wheeler, 2000). Our
findings thus support key ideas from both educational and social
psychology research on social comparison processes. Fourth, a
statistically significant interaction effect in all three studies
indicated that high-achieving students were less affected by the
negative frame of reference effect than were low-achieving
students.
Frame of Reference Effects: Generalizability and
Moderator Effects
Students’ placement in certain schools and classes can have
major implications for their academic self-concepts. The complex-
ity of real-life educational environments can hardly be modeled in
laboratory experiments; rather, it is important to adopt a multilevel
strategy at both the conceptual and the empirical level (Rauden-
bush & Bryk, 2002). In our studies, the adoption of a multilevel
approach proved fruitful in several respects.
In line with previous educational psychology research on frame
of reference effects (see Marsh & Craven, 2002), achievement
proved to be differentially related to academic self-concept at the
individual level and at the class level. Our studies thus add to the
fairly consistent body of findings showing that placement in high-
achieving learning environments is associated with relatively low
academic self-concepts. The negative frame of reference effect
was found whether the class or the school was used as the aggre-
gate unit. Moreover, we extended prior research by calculating
effect sizes for the frame of reference effects. The effect sizes
observed were of meaningful magnitude, indicating that frame of
reference effects indeed matter. Hence, unlike many social psy-
chology studies highlighting powerful assimilation effects (see
Mussweiler, 2003; Wheeler & Suls, 2005), we found that—when
individual achievement is controlled— high-achieving classrooms
may elicit contrast effects. The observed contrast effect is consis-
tent with Diener and Fujita’s (1997) observation that classrooms
may act as “total environments” whose pervasive impact is not
easily shaken off.
Despite the consistency of the frame of reference effect across
the three studies and its meaningful effect size, we also found some
indication that the total-environment-like nature of the frame of
reference effect does not apply to all students in exactly the same
way. More specifically, we found that the academic self-concepts
of high-achieving students in all three samples were somewhat less
influenced by the negative frame of reference effect than were the
self-concepts of low-achieving students. From a theoretical point
of view, this finding is quite reasonable. Put simply, high-
achieving students may have less reason to be afraid of high-
achieving classmates because they still fare quite well in a socially
competitive arena. Nevertheless, given the inconclusive results of
Table 3
Predicting Mathematics Self-Concept (Study 3): Results From Multilevel Modeling
Fixed effects
Model 1 Model 2 Model 3
B p SE B p SE B p SE
Intercept 0.00 .861 .02 0.00 .899 .02 0.00 .855 .02
School level
Perceived school standing 0.08 .077 .04 0.04 .233 .04
School-average achievement ⫺0.23 ⬍.001 .04 ⫺0.24 ⬍.001 .04
Individual level
Perceived school standing 0.06 .001 .02 0.07 ⬍.001 .02
Mathematics achievement 0.53 ⬍.001 .02 0.53 ⬍.001 .02
Variance explained .25 .00 .25
Deviance 10,827.62 11,999.33 10,804.65
Estimated parameters 5 5 7
862 TRAUTWEIN, LU
¨DTKE, MARSH, AND NAGY

earlier studies probing for this interaction effect, the consistent
empirical support for this positive cross-level interaction across all
three studies was somewhat unexpected (see Marsh, Seaton, et al.,
2008). We can only speculate about possible reasons for the
consistent findings found in our study. The most important factor
might be the characteristics of the sample. Compared with other
BFLPE studies, the students in the present research, who were in
their last year of high school education, were relatively old. More-
over, because only students in the academic track were included
(in Germany, all other students leave school after Grade 10), the
samples were more selective. It seems possible that the interaction
effect that we found is specific to such selective samples. More-
over, it seems important to note that we did not control for any
mediator variables when testing the interaction effects. Including
mediator variables such as school grades or student perceptions of
teaching characteristics might negatively influence the strength of
the interaction effect (e.g., Lu¨dtke et al., 2005; Marsh et al., 2007).
Finally, the overall size of the interaction effect was relatively
small; accordingly, the size of the frame of reference effects was
affected, but not their overall direction. To conclude, more re-
search is warranted on the conditions under which high individual
achievement buffers the impact of class- or school-average
achievement. This research requires not only substantive theoret-
ical hypotheses, but also large sample sizes and the careful spec-
ification and testing of statistical models.
Integrating Class or School Standing in
Self-Concept Research
A large number of studies have yielded evidence for negative
frame of reference effects (see Marsh, Seaton, et al., 2008). It
would be wrong to deny the occurrence of any adaptive social
comparison processes in classroom settings, however. Studies
teasing apart frame of reference effects and reflected glory pro-
cesses have typically relied on “objective” characteristics of the
school, such as track status (e.g., Marsh et al., 2001). Although
they have produced some evidence for reflected glory effects, this
evidence is not conclusive. Reflected glory effects as measured by
a questionnaire scale were first described and analyzed in detail in
the study by Marsh et al. (2000), but this study did not separate
individual and class- or school-level effects. Taking a multilevel
perspective, our study extended this pioneering study and found
support for other information processing processes that led to
differential academic self-concept across classes or students.
Our study adds to the literature on reflected glory effects in two
ways. First, we were able to distinguish between students’ indi-
vidual perceptions of class or school standing and their shared
perceptions of the standing of their learning environment. The
perception of an individual student is an important source of
information in social comparison studies, but individual ratings are
prone to person-specific biases. For this reason, we also used
aggregated individual perceptions as a measure of shared beliefs
about the standing of the class or school. The analyses indicated
that students’ perceptions of the standing of their class or school
are not highly idiosyncratic; rather, they reflect shared beliefs that
distinguish between educational contexts. Social comparison pro-
cesses evidently take place at the individual level and the group
level. Students think about the characteristics of groups of students
and use this information to evaluate their own academic qualities.
Moreover, the students in a class share remarkably similar beliefs
about their own class and other classes. Taken together, by adopt-
ing a multilevel perspective, our research went beyond the classi-
cal research design (Suls & Wheeler, 2000; Wood & Wilson,
2003) in which one perceiver rates or selects one specific target.
As our analyses indicated, the ratings of students in the same class
or school provide a highly reliable indicator of the perceived
standing of the class when aggregated to the class or school level.
Although the scale we used to measure perceived class or school
standing was rather short, it evidenced high psychometric quality.
Factor and reliability analyses confirmed it to be unidimensional
and internally consistent. In addition, the high reliability of the
construct at the class level indicates that the scale taps an aspect of
classroom or school reality that is relevant to students and that is
relatively easy to describe in rating scales.
Still, some questions remain. What exactly does the perceived
class or school standing construct measure? What is the likely
genesis of students’ shared beliefs about the standing of a class or
school? Our four items tap the perceived amount learnt in the class
or school, the overall achievement level of students in the class or
school, and more general evaluations of how the class is perceived
by others. We prefer the term perceived standing to some alterna-
tive candidates,
3
such as class or school prestige or class or school
status (see Marsh et al., 2000). The term prestigious is typically
used to describe selective schools or school tracks that admit
students on the basis of their high achievement or other merits. In
tracked school systems, for instance, the highest tracks have the
most prestige (Trautwein, Lu¨dtke, Marsh, et al., 2006). In our
study, however, all students attended the same (precollege) track;
furthermore, their placement in a specific class or school was not
determined by prior achievement. Hence, prestige or status may
not be the most appropriate terms in the present context. Another
alternative would be perceived achievement. However, perceived
achievement emphasizes achievement at a certain time point,
whereas one of our items emphasizes the learning trajectory.
Moreover, despite the positive correlations between class-average
achievement and class-average perceptions of the standing of the
class, which indicate that students’ shared perceptions reflect true
differences in class achievement, the size of the correlation was
only small to moderate. Whereas perceived achievement might be
a too narrow term, another alternative—perceived class or school
quality—might be too broad, because quality encompasses more
than achievement growth and relative standing. Taken together, we
believe the term perceived standing of the class or school ade-
quately reflects the nature of the construct. However, more re-
search is warranted to explore the predictors of high perceived
class or school standing. Moreover, given that school systems
across the world differ markedly, it is quite possible that studies
conducted in other countries would use constructs that differ from
the one used in the present study.
The second important contribution of our study to the analysis
of reflected glory effects is the finding that perceptions of the
standing of the class or school matter for academic self-concept at
both the individual and the aggregate level. Hence, we found
support for information processing processes leading to differen-
3
We thank one anonymous reviewer for important feedback on the
content and labeling of the perceived class or school standing construct.
863
WITHIN-SCHOOL SOCIAL COMPARISON

tial academic self-concept across classes or students. Our studies
help to distinguish between processes at the individual, class, and
school levels. At the individual level, perceived class or school
standing was statistically significantly related to academic self-
concept in all three studies. At the class level (Studies 1 and 2), we
also found a positive association between perceived class standing
and achievement. At the school level (Study 3), however, this
association was not statistically significant.
Previous studies have found students’ academic self-concepts to
be only slightly associated or not at all associated with the status
of a school (Marsh et al., 2001; Trautwein, Lu¨dtke, Marsh, et al.,
2006; Schwarzer et al., 1982), implying that students do not
systematically integrate social comparison information about the
standing of their school into their self-concept. In line with earlier
research, Study 3 found that students in a school generally per-
ceived to have a high standing do not report higher academic
self-concepts. In contrast, students in mathematics classes collec-
tively perceived to have high standing do report higher academic
self-concepts. Hence, different classes within the same school
seem to constitute important frames of reference for students,
whereas different schools seem to constitute less salient frames of
reference in terms of reflected glory. This does not mean, however,
that an individual student’s perception of school standing is irrel-
evant. In fact, a student whose perception of the standing of his or
her school or class was higher than that of his or her school- or
classmates was likely to report a comparatively high mathematics
self-concept (also see Marsh et al., 2000).
Taken together, students’ self-concepts are likely the product of
a complex net of social comparison information that is partly
person specific and partly the result of shared perceptions. When
students’ self-concepts are studied in natural environments, it is
imperative to distinguish between the various levels of analysis.
The results of our studies indicate that students actively seek out
information about their own standing and the standing of their
class and integrate that information into their academic self-
concepts. Although placement in a high-achieving learning envi-
ronment generally has a negative impact on academic self-concept,
a positive evaluation of that environment’s standing tends to buffer
the negative impact somewhat.
Limitations and Conclusion
Although our investigation was based on a well-established
theoretical model and used three strong data sets, some potential
limitations should be addressed in future studies. First, our studies
were nonexperimental and used a single-measurement design,
meaning that caution is warranted in making causal interpretations.
In nonexperimental studies there is always the possibility that
untested variables affected the pattern of results. Yet, in real-world
situations that can have important implications for students’
achievement, motivation, and educational careers, the possibilities
for true random assignment of students to conditions are severely
limited for ethical and legal reasons. Large studies with random
samples of students and powerful analytical tools provide a strong
alternative to the experimental approach.
Second, generalizability is an issue. It is unclear to what extent
differences across school systems might affect the results. School-
level differences (in contrast to class-level differences) might be
stronger in some school systems than in others. For instance, in
countries in which school achievement scores are published in the
form of ranking charts, students may be more aware of between-
school differences, which in turn may affect their academic self-
concepts. If this were indeed the case, it would constitute a
moderator effect at a rather general level. Hence, we would like to
see future studies replicate our analyses in diverse samples.
Third, our study focused on self-concept as the outcome vari-
able. Given that a host of studies have demonstrated the impor-
tance of domain-specific self-concepts for short-term and long-
term academic motivation (Marsh et al., 2005, 2007), academic
effort (Trautwein & Lu¨dtke, 2007; Trautwein, Lu¨ dtke, Schnyder,
& Niggli, 2006), and academic choices (Watt & Eccles, 2008), this
choice is justified. Nevertheless, additional outcome variables
should be included in future studies.
The present study contributed to a research field of high prac-
tical importance and theoretical interest by taking a multilevel
approach and including indicators of perceived class and school
standing. The results provide further support for the powerful
impact of frame of reference effects in educational environments.
At the same time, our findings indicate that self-concept is not just
the result of individual achievement moderated by a frame of
reference effect, as readers of studies in educational psychology
might be tempted to reason, but the result of a complex social
comparison process involving several sources of information.
References
Bandura, A. (1997). Self-efficacy: The exercise of control. New York:
Freeman.
Baumert, J., Bos, W., & Lehmann, R. (Eds.). (2000). TIMSS/III: Dritte
Internationale Mathematik- und Naturwissenschaftsstudie: Mathema-
tische und naturwissenschaftliche Bildung am Ende der Schullaufbahn
[TIMSS/III: Third international mathematics and science study: Stu-
dents’ knowledge of mathematics and science at the end of secondary
education]. Opladen, Germany: Leske & Budrich.
Becker, M., Lu¨ dtke, O., Trautwein, U., Ko¨ ller, O., & Baumert, J. (2008).
The effect of schooling on psychometric intelligence: Does school qual-
ity make a difference? Manuscript submitted for publication.
Bliese, P. D. (2000). Within-group agreement, non-independence, and
reliability: Implications for data aggregation and analysis. In K. J. Klein
& S. W. Kozlowski (Eds.), Multilevel theory, research, and methods in
organizations (pp. 349 –381). San Francisco: Jossey-Bass.
Cialdini, R. B., & Richardson, K. D. (1980). Two indirect tactics of image
management: Basking and blasting. Journal of Personality and Social
Psychology, 39, 406 – 415.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences
(2nd ed.). Hillsdale, NJ: Erlbaum.
Coleman, J. M., & Fults, B. A. (1985). Special class placement, level of
intelligence, and the self-concept of gifted children: A social comparison
perspective. Remedial and Special Education, 6, 7–11.
Cronbach, L. J. (1976). Research on classrooms and schools: Formula-
tions of questions, design and analysis. Stanford, CA: Stanford Evalu-
ation Consortium.
Dai, D. Y., & Rinn, A. N. (2008). The big-fish-little-pond effect: What do
we know and where do we go from here? Educational Psychology
Review, 20, 283–317.
Damisch, L., Mussweiler, T., & Plessner, H. (2006). Olympic medals as
fruits of comparison? Assimilation and contrast in sequential perfor-
mance judgments. Journal of Experimental Psychology: Applied, 12,
166 –178.
Diener, E., & Fujita, F. (1997). Social comparison and subjective well-
being. In B. P. Buunk & F. X. Gibbons (Eds.), Health, coping, and
864 TRAUTWEIN, LU
¨DTKE, MARSH, AND NAGY

well-being: Perspectives from social comparison theory (pp. 329–358).
Mahwah, NJ: Erlbaum.
Enders, C. K., & Tofighi, D. (2007). Centering predictor variables in
cross-sectional multilevel models: A new look at an old issue. Psycho-
logical Methods, 12, 121–138.
Festinger, L. (1954). A theory of social comparison processes. Human
Relations, 7, 117–140.
Grissom, R. J., & Kim, J. J. (2005). Effect sizes for research: A broad
practical approach. Mahwah, NJ: Erlbaum.
James, W. (1963). The principles of psychology. New York: Holt, Rinehart
& Winston. (Original work published 1890)
Ko¨ ller, O., Watermann, R., Trautwein, U., & Lu¨ dtke, O. (2004). Wege zur
Hochschulreife in Baden-Wu¨ rttemberg. TOSCA – Eine Untersuchung an
allgemein bildenden und beruflichen Gymnasien [Educational pathways
to college in Baden-Wu¨ rttemberg: TOSCA—A study at upper secondary
level of traditional and vocational Gymnasium schools]. Opladen, Ger-
many: Leske & Budrich.
Karabenick, S. A. (2004). Perceived achievement goal structure and col-
lege student help seeking. Journal of Educational Psychology, 96, 569 –
581.
Klusmann, U., Kunter, M., Trautwein, U., Lu¨ dtke, O., & Baumert, J.
(2008). Teachers’ well-being and the quality of instruction: The impor-
tant role of self-regulatory patterns. Journal of Educational Psychology,
100, 702–715.
Lu¨ dtke, O., Ko¨ ller, O., Marsh, H. W., & Trautwein, U. (2005). Teacher
frame of reference and the big-fish-little-pond effect. Contemporary
Educational Psychology, 30, 263–285.
Lu¨ dtke, O., Robitzsch, A., Trautwein, U., & Kunter, M. (2009). Assessing
features of the learning environment: How to use student ratings in
multilevel modeling. Contemporary Educational Psychology, 34, 120 –
131.
Lu¨ dtke, O., Trautwein, U., Kunter, M., & Baumert, J. (2006). Reliability
and agreement of student ratings of the classroom environment: A
reanalysis of TIMSS data. Learning Environments Research, 9, 215–
230.
Lehmann, R. H., Vieluf, U., Nikolova, R., & Ivanov, S. (2006). LAU 13.
Aspekte der Lernausgangslage und Lernentwicklung – Klassenstufe 13
[LAU 13: Aspects of initial achievement and learning development].
Hamburg, Germany: Beho¨ rde fu¨ r Bildung und Sport, Amt fu¨r Bildung.
Maaz, K., Trautwein, U., Lu¨ dtke, O., & Baumert, J. (2008). Educational
transitions and differential learning environments: How explicit
between-school tracking contributes to social inequality. Child Devel-
opment Perspectives, 2, 99 –106.
Marsh, H. W. (1984). Self-concept: The application of a frame of reference
model to explain paradoxical results. Australian Journal of Education,
28, 165–181.
Marsh, H. W. (1987). The big-fish-little-pond effect on academic self-
concept. Journal of Educational Psychology, 79, 280 –295.
Marsh, H. W. (1991). The failure of high-ability high schools to deliver
academic benefits: The importance of academic self-concept and edu-
cational aspirations. American Educational Research Journal, 28, 445–
480.
Marsh, H. W., Chessor, D., Craven, R. G., & Roche, L. (1995). The effects
of gifted and talented programs on academic self-concept: The big fish
strikes again. American Educational Research Journal, 32, 285–319.
Marsh, H. W., & Craven, R. (2002). The pivotal role of frames of reference
in academic self-concept formation: The big-fish-little-pond effect. In F.
Pajares & T. Urdan (Eds.), Adolescence and education (Vol. 2, pp.
83–123). Greenwich, CT: Information Age.
Marsh, H. W., & Hau, K. T. (2003). Big-fish-little-pond effect on academic
self-concept: A crosscultural (26 country) test of the negative effects of
academically selective schools. American Psychologist, 58, 364 –376.
Marsh, H. W., Ko¨ ller, O., & Baumert, J. (2001). Reunification of East and
West German school systems: Longitudinal multilevel modeling study
of the big-fish-little-pond effect on academic self-concept. American
Educational Research Journal, 38, 321–350.
Marsh, H. W., Kong, C.-K., & Hau, K.-T. (2000). Longitudinal multilevel
models of the big-fish-little-pond effect on academic self-concept:
Counterbalancing contrast and reflected-glory effects in Hong Kong
schools. Journal of Personality and Social Psychology, 78, 337–349.
Marsh, H. W., Seaton, M., Trautwein, U., Lu¨ dtke, O., Hau, K. T., O’Mara,
A. J., & Craven, R. G. (2008). The big-fish-little-pond effect stands up
to critical scrutiny: Implications for theory, methodology, and future
research. Educational Psychology Review, 20, 319 –350.
Marsh, H. W., & Shavelson, R. (1985). Self-concept: Its multifaceted,
hierarchical structure. Educational Psychologist, 20, 107–125.
Marsh, H. W., Trautwein, U., Lu¨ dtke, O., Baumert, J., & Ko¨ ller, O. (2007).
Big-fish-little-pond effect: Persistent negative effects of selective high
schools on self-concept after graduation. American Educational Re-
search Journal, 44, 631– 669.
Marsh, H. W., Trautwein, U., Lu¨ dtke, O., & Ko¨ ller, O. (2008). Social
comparison and big-fish-little-pond effects on self-concept and efficacy
perceptions: Role of generalized and specific others. Journal of Educa-
tional Psychology, 100, 510 –524.
Marsh, H. W., Trautwein, U., Lu¨ dtke, O., Ko¨ ller, O., & Baumert, J. (2005).
Academic self-concept, interest, grades and standardized test scores:
Reciprocal effects models of causal ordering. Child Development, 76,
397– 416.
Mussweiler, T. (2003). Comparison processes in social judgment: Mech-
anisms and consequences. Psychological Review, 110, 472– 489.
Oakes, J. (1985). Keeping track: How schools structure inequality. New
Haven, CT: Yale University Press.
Organization for Economic Cooperation and Development (2001). Knowl-
edge and skills for life: First results from the OECD Programme for
International Student Assessment (PISA) 2000. Paris: Author.
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models (2nd
ed.). Thousand Oaks, CA: Sage.
Raudenbush, S. W., Bryk, A. S., Cheong, Y., & Congdon, R. T. (2004).
HLM 6: Hierarchical linear modeling. Chicago: Scientific Software
International.
Reuman, D. A. (1989). How social comparison mediates the relation
between ability-grouping practices and students’ achievement expectan-
cies in mathematics. Journal of Educational Psychology, 81, 178 –189.
Rheinberg, F., & Enstrup, B. (1977). Self-concept of intelligence with
pupils in special and normal schools: A group effect. Zeitschrift fu¨r
Entwicklungspsychologie und Pa¨ dagogische Psychologie, 9, 171–180.
Roberts, B. W., Caspi, A., & Moffitt, T. (2003). Work experiences and
personality development in young adulthood. Journal of Personality and
Social Psychology, 84, 582–593.
Rost, J. (1996). Testtheorie und Testkonstruktion [Test theory and test
construction]. Bern, Switzerland: Huber.
Schwanzer, A. D., Trautwein, U., Lu¨ dtke, O., & Sydow, H. (2005).
Entwicklung eines Instruments zur Erfassung des Selbstkonzepts junger
Erwachsener [Development of a questionnaire on young adults’ self-
concept]. Diagnostica, 51, 183–194.
Schwarzer, R., Lange, B., & Jerusalem, M. (1982). Selbstkonzeptentwick-
lung nach einem Bezugsgruppenwechsel [Self-concept development af-
ter a reference-group change]. Zeitschrift fu¨ r Entwicklungspsychologie
und Pa¨ dagogische Psychologie, 14, 125–140.
Seaton, M., Marsh, H. W., Dumas, F., Huguet, P., Monteil, J. M., Regner,
I., et al. (2008). In search of the big fish: Investigating the coexistence
of the big-fish-little-pond effect with the positive effects of upward
comparison. British Journal of Social Psychology, 47, 73–103.
Shavelson, R. J., Hubner, J. J., & Stanton, G. C. (1976). Validation of
construct interpretations. Review of Educational Research, 46, 407– 441.
Snijders, T. A. B., & Bosker, R. J. (1999). Multilevel analysis: An intro-
duction to basic and advanced multilevel modeling. London: Sage.
865
WITHIN-SCHOOL SOCIAL COMPARISON

Suls, J., & Wheeler, L. (2000). Handbook of social comparison: Theory
and research. New York: Kluwer Academic/Plenum Press.
Taylor, S. E., & Brown, J. D. (1988). Illusion and well-being: A social
psychological perspective on mental health. Psychological Bulletin, 103,
193–210.
Tesser, A. (1988). Toward a self-evaluation maintenance model of social
behavior. In L. Berkowitz (Ed.), Advances in experimental social psy-
chology (Vol. 21, pp. 181–227). San Diego, CA: Academic Press.
Trautwein, U., & Baeriswyl, F. (2007). Wenn leistungsstarke Klassenka-
meraden ein Nachteil sind: Referenzgruppeneffekte bei U
¨bergangsents-
cheidungen [When high-achieving classmates put students at a disad-
vantage: Reference group effects at the transition to secondary
schooling]. Zeitschrift fu¨r Pa¨ dagogische Psychologie/German Journal
of Educational Psychology, 21, 119 –133.
Trautwein, U., Gerlach, E., & Lu¨ dtke, O. (2008). Athletic classmates,
physical self-concept, and free-time physical activity: A longitudinal
study of frame of reference effects. Journal of Educational Psychology,
100, 988 –1001.
Trautwein, U., Ko¨ ller, O., Lu¨ dtke, O., & Baumert, J. (2005). Student
tracking and the powerful effects of opt-in courses on self-concept:
Reflected-glory effects do exist after all. In H. W. Marsh, R. G. Craven,
& D. M. McInerney (Eds.), New frontiers for self research: Vol. 2.
International advances in self research (pp. 307–327). Greenwich, CT:
Information Age.
Trautwein, U., Ko¨ ller, O., Lehmann, R., & Lu¨ dtke, O. (Eds.). (2007).
Schulleistungen von Abiturienten: Regionale, schulformbezogene und
soziale Disparita¨ ten [School achievement of students at Gymnasium
schools: Regional, track-specific, and social disparities]. Mu¨ nster, Ger-
many: Waxmann.
Trautwein, U., & Lu¨ dtke, O. (2007). Students’ self-reported effort and time
on homework in six school subjects: Between-student differences and
within-student variation. Journal of Educational Psychology, 99, 432–
444.
Trautwein, U., Lu¨ dtke, O., Ko¨ ller, O., & Baumert, J. (2006). Self-esteem,
academic self-concept, and achievement: How the learning environment
moderates the dynamics of self-concept. Journal of Personality and
Social Psychology, 90, 334 –349.
Trautwein, U., Lu¨ dtke, O., Kastens, C., & Ko¨ ller, O. (2006). Effort on
homework in Grades 5 through 9: Development, motivational anteced-
ents, and the association with effort on classwork. Child Development,
77, 1094 –1111.
Trautwein, U., Lu¨ dtke, O., Marsh, H. W., Ko¨ ller, O., & Baumert, J. (2006).
Tracking, grading, and student motivation: Using group composition and
status to predict self-concept and interest in ninth grade mathematics.
Journal of Educational Psychology, 98, 788 – 806.
Trautwein, U., Lu¨ dtke, O., Schnyder, I., & Niggli, A. (2006). Predicting
homework effort: Support for a domain-specific, multilevel homework
model. Journal of Educational Psychology, 98, 438 – 456.
Tymms, P. (2001). A test of the big fish in a little pond hypothesis: An
investigation into the feelings of seven-year-old pupils in school. School
Effectiveness & School Improvement, 12, 161–181.
Tymms, P. (2004). Effect sizes in multilevel models. In I. Schagen & K.
Elliot (Eds.), But what does it mean? The use of effect sizes in educa-
tional research (pp. 55– 66). London: National Foundation for Educa-
tional Research.
Watt, H. M. G., & Eccles, J. S. (Eds.). (2008). Explaining gendered
occupational outcomes: Examining individual and social explanations
through school and beyond. Washington, DC: American Psychological
Association.
Wheeler, L., & Suls, J. (2005). Social comparison and self-evaluation of
competence. In A. J. Elliot & C. S. Dweck (Eds.), Handbook of com-
petence and motivation (pp. 566 –578). New York: Guilford Press.
Wheeler, L., & Suls, J. (2007). Assimilation in social comparison: Can we
agree on what it is? Revue Internationale de Psychologie Sociale, 20,
31–51.
Wood, J. V., & Wilson, A. E. (2003). How important is social comparison?
In M. L. Leary & J. P. Tangney (Eds.), Handbook of self and identity
(pp. 344 –366). New York: Guilford Press.
Wu, M. L., Adams, R. J., & Wilson, M. R. (1998). ACER ConQuest:
Generalised item response modelling software manual. Melbourne, Aus-
tralia: Australian Council for Educational Research.
Zeidner, M., & Schleyer, E. J. (1999). The big-fish-little-pond effect for
academic self-concept, test anxiety, and school36 grades in gifted chil-
dren. Contemporary Educational Psychology, 24, 305–329.
Received April 7, 2008
Revision received April 20, 2009
Accepted April 24, 2009 䡲
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