Multilevel Analysis to Evaluate Cross Level Relations in the Big FishLittle Pond Effect BFLPE

Does attending schools with exceptionally bright students increase or decrease academic self-concept? Do the effects of these academically selective schools vary for students differing in academic ability? In this section we describe multilevel modeling approaches to evaluate these issues. In most studies conducted in school settings, individual student characteristics and those associated with groups (day-care centers, classrooms, schools, etc.) are confounded because groups are typically not established according to random assignment. Students within the same group are typically more similar to other students in the same group than they are to students in other groups. Even when students are initially assigned at random, they tend to become more similar to each other over time. Furthermore, the apparently same variable may have a very different meaning when measured at different levels. For example, Marsh's (1987, 1991; Marsh, Chessor, Craven, & Roche, 1995; Marsh & Parker, 1984) research into the BFLPE research suggests that a measure of ability at the student level provides an indicator of a student attribute, whereas school-average ability at the school level becomes a proxy measure of a school's normative environment. Thus, the average ability of a school has an effect on student self-concept above and beyond the effect of the individual student's ability. Multilevel modeling is designed to resolve the confounding of these two effects by facilitating a decomposition of any observed relationship among variables, such as self-concept and ability, into separate within-school and between-school components (see Goldstein, 1995; Rauden-bush & Bryk, 2002; Snijders & Bosker, 1999).

In the theoretical model underlying the BFLPE (Marsh & Parker, 1984), it is hypothesized that students compare their own academic ability with the academic abilities of their peers and use this social comparison impression as one basis for forming their own academic self-concept. A negative BFLPE occurs when equally able students have lower academic self-concepts when they compare themselves to more-able classmates, and higher academic self-concepts when they compare themselves with less-able classmates. In support of this theoretical model, Marsh and Craven (2003) summarized results from a diverse range of studies using different samples and methodological approaches showing that (a) educationally disadvantaged students have higher academic self-concepts in special education classes than in regular mixed-ability (main-streamed) classes, whereas (b) academically gifted students have higher academic self-concepts in regular, mixed-ability classes than in specialized education settings for gifted students. Hence, academic achievement measured at the individual child level has a positive effect on academic self-concept (i.e., one's own high levels of individual achievement lead to high self-concept), whereas the academic achievement measured at the group level has a negative effect (i.e., high average school achievement leads to low self-concept).

Marsh, Roller, and Baumert (2001) evaluated predictions from the BFLPE for East and West German students at the time of the fall of the Berlin Wall. Multilevel longitudinal data (2,778 students, 161 classes) from large cohorts of seventh-grade East and West German students were collected at the start of the reunification of the school systems. Multilevel modeling demonstrated a negative BFLPE; attending classes where class-average achievement was higher led to lower academic self-concepts. West German students had attended schools that were highly stratified in relation to ability before and after the reunification, whereas East German students first attended selective schools after the reunification. Consistent with theoretical predictions based on this difference, the negative BFLPE—the negative effect of class-average achievement—was more negative in West German schools at the start of the reunification. This difference, however, was smaller by the middle of the year and had disappeared by the end of the first postreunification school year. Whereas East and West German results both supported the negative BFLPE, their differences supported theoretical predictions, extended theory, and demonstrated how changes in school policy influence the formation of academic self-concept.

Marsh, Kong, and Hau (2000) conducted longitudinal multilevel path models (7,997 students, 44 high schools, 4 years) to evaluate the effects of school-average achievement and perceived school status on academic self-concept in Hong Kong. Consistent with a priori predictions based on the BFLPE, higher school-average achievements led to lower academic self-concepts (contrast effects) and to higher perceived school status that had a counterbalancing positive effect on self-concept (reflected glory, assimilation effects). Hence, attending a school where school-average achievement was high simultaneously resulted in a more demanding basis of comparison for one's own accomplishments (the stronger, negative contrast effect) and a source of pride (the weaker, positive reflected glory effect). In support of the typically negative effect of school-average ability, the net effect of these two counterbalancing processes (a larger negative contrast effect and a smaller positive assimilation effect) was negative.

Marsh and Hau (2003) conducted the most comprehensive cross-cultural study of the BFLPE, based on nationally representative samples of approximately 4,000, 15-year-olds from each of 26 countries (103,558 students, 3,848 schools, 26 countries), who completed the same self-concept instrument and achievement tests. Consistent with the BFLPE, the effects of school-average achievement were negative in all 26 countries (M = -.20, SD = .08). Results of their three-level multilevel model (Level 1 = students, Level 2 = schools, Level 3 = country) indicated that the effects of individual achievement were positive (linear term = .384, quadratic term = .069), whereas the effects of school-average achievement—the BFLPE—were negative (-.206). The interaction between individual student achievement and school-average achievement was not significant, indicating that the negative effect of school-average achievement was consistent across the range of student achievement levels. Variation in the school-average achievement effect (.007) was small, but highly significant— indicating that there was statistically significant variation from country to country in the size of the BFLPE. In separate analyses of each of the 26 countries, the BFLPE was significantly negative in 24 of 26 countries (-.02 to -.36). In each of the 26 countries, the effect of individual achievement on academic self-concept was significantly positive (.14 to .63; M = .38, SD = .11). The averages across results from the separate two-level models for each of the 26 countries agreed closely with those from the three-level analyses for the total group. Support for the generalizability of the BFLPE across countries suggested that the social comparison processes leading to the BFLPE may approach what Segall et al. (1998, p. 1102) refer to as a "nearly universal psychology, one that has pan-human validity"—one goal of cross-cultural research.

Multilevel modeling demonstrated here is important because the juxtaposition between the effects of individual achievement and class- or school-average achievement is inherently a multilevel problem so that any attempt to model the data at a single level is likely to cause problems. Whereas multilevel modeling is clearly relevant for BFLPE studies, it is also relevant in nearly all research in which individuals are clustered into classes (or other groups). Indeed, it can be argued that nearly all educational psychology research and psychological research more generally could benefit by taking a multilevel perspective, recognizing that social phenomena mostly occur in groups that are not formed randomly and that group members tend to become more similar as they interact with each other. By simultaneously considering data from multiple levels, the researcher opens up new substantive issues related to group-level variables and their interaction with individual-level variables that are typically ignored in studies of individuals.

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