The focus of the study is to understand how and why students’ self-perceptions of academic ability relates to academic achievements, on both individual and school level. For most students, education takes place in social environments, with peers as the main frames of reference for academic achievement. Students tend to compare their academic ability with that of their class and school peers, and this affects how they perceive their own academic ability, which in turn affects their academic achievement (see e.g. Trautwein et al., 2009). This effect, referred to as the big-fish-little-pond effect (BFLPE), tends to be negative. According to the BFLPE model, students with similar abilities have lower self-perceived competencies and lower motivation when attending a high-achieving class or school, than when attending a middle- or low-achieving class or school (Marsh et al., 2015). These effects are argued to be due to processes of social comparisons among students. Even if there are positive effects of attending a high-performing school, they are not as strong as the negative BFLPE (Marsh et al., 2009). Other findings suggest that the relation between academic self-concept and academic achievement is reciprocal, with a negative BFLPE on academic achievement (Marsh & Hau, 2003). In recent research, potential moderating variables have been included in the analyses of the BFLPE such as student age and the characteristics of the reference group (Fang et al., 2018). However, the findings are mixed and the inconsistency in results makes it hard to draw general conclusions.

In the planned study, the effect of schools’ average achievement level for students’ self-concept and self-efficacy will be investigated to test for negative BFLPE when cognitive ability and individual characteristics are controlled for. Although studies have been conducted with regard to the BFLPE, inconsistences exist in the reported effect sizes and there have been difficulties in finding significant moderators (Fang et al., 2018). Some results indicate that the BFLPE is consistent over ability levels (Marsh & Hau, 2003; Marsh & O’Mara, 2008), while other results suggest that high-achieving students are not affected by the BFLPE to the same extent as low-achieving students (Trautwein et al., 2009). In these studies, ability was measured with grades and test scores from international assessments, such as TIMSS and PISA, but few BFLPE studies have controlled for the moderating effect of cognitive ability. Moreover, the BFLPE is generally tested in relation to self-concept, but not in relation to self-efficacy, which is a similar academic self-perception construct.

In many countries, schools have become increasingly market-driven, with education reforms based on choice- and competition models (Levin, 2012). In Sweden, as well as internationally, this trend has resulted in increased school segregation, meaning that the differences in academic achievement between schools have increased (Lubienski, 2005; Yang Hansen & Gustafsson, 2016). This trend further increases the relevance of studying the relation between students’ self-perception of academic ability and schools’ average achievement level, given that the increase of between-school variation in achievement may be expected to affect the students’ frames of reference (National Agency for Education, 2012). Against this background, the purpose of the study is to investigate how the influence of social comparisons and frame of reference groups on class and school level affects students’ self-concept, self-efficacy and academic achievement, with cognitive ability and student characteristics taken into account. The following preliminary hypotheses were formulated:

1. School-level achievement is negatively related to students’ individual self-concept and self-efficacy in Swedish, English and Mathematics.
2. School-level achievement is negatively related to academic achievement on student individual level.
3. High-achieving students are not as strongly affected by the negative BFLPE, compared to low-achieving students.

Data were retrieved from the Swedish longitudinal project Evaluation through Follow-Up (UGU) (Härnqvist, 2000). The sampling was a two-step stratified procedure, where municipalities were selected in the first step and school catchment areas in the second step. The samples are 10 % of the 1992, 1998 and 2004 birth cohorts (N = approximately 10 000) and are nationally representative of their respective population. UGU consists of school administrative data and questionnaire data. The measurement instruments of academic self-concept and self-efficacy will be constructed from existing questionnaire items. Self-concept will be measured by items that refer to a more general form of academic self-perceptions, such as “How good do you think you are in the subject Swedish/English/Mathematics?” Items that measure self-efficacy refer to a more task specific form of academic self-perceptions, such as “How do you think you can manage to spell correctly in Swedish/English?” and “How do you think you can manage to calculate area and perimeter?”. Self-concept and self-efficacy measures will be used from data collections in Grade 6 and 9. Students’ academic achievement will be measured by cognitive ability in Grade 6, and final grades in Swedish, English and Mathematics in Grade 9. School-average achievement will be measured by schools’ grade point average (GPA) in Grade 9. Methods of analysis Descriptive statistics, confirmatory factor analysis (CFA) and structural equation modeling (SEM) will be used as main analytic methods. Self-concept and self-efficacy measurement models will be estimated via CFA. Models will then be constructed, where self-concept and self-efficacy in Grades 6 and 9 are related in a first step. In a second step, school GPA is related to individual students’ self-concept and self-efficacy in Grade 9 and in a third step to final grades. Moderating variables such as cognitive ability, gender, age and family educational background will be included in the analyses. Comparisons will be made between the 1992, 1998 and 2004 birth cohorts in the UGU project. As measures of model fit, the Root Mean Square Error of Approximation (RMSEA), Standardized Root Mean Square Residual (SRMR), Comparative Fit Indices (CFI) and the Tucker-Lewis index (TLI) will be assessed. The data management will be performed in IBM SPSS Statistics 27.0, while the analyses will be conducted in Mplus 8 (Muthén & Muthén, 1998-2017). The analyses will take into account missing data by using full information maximum likelihood missing data modelling, and clustering effects by using multi-level options.

Expected outcomes of the planned study is first and foremost that there will be a negative BFLPE, namely that school-level achievement will relate negatively to individual students’ self-concept and self-efficacy (see e.g. Marsh et al., 2015; Marsh & Hau, 2003). Further hypotheses concern students’ academic achievement, and how this relates to school-average achievement. Marsh (1991) found that in addition to the BFLPE; school-average achievement affected both school grades and standardized test scores negatively. The expected outcomes of the study are thus hypothesized to be similar. The existing research results disagree of whether students are affected differently by the BFLPE, across levels of academic ability (Marsh & Hau, 2003; Trautwein et al., 2009). In the planned study, this will be controlled for with students’ cognitive ability. The expected outcome is that the negative BFLPE is weaker for high-ability students; that is, high-achieving students are not as strongly affected by the negative BFLPE, compared to low-achieving students. Additionally, it is expected that the BFLPE will have a similar relation to students’ self-efficacy as to the more commonly used BFLPE construct self-concept. Lastly, since the BFLPE seems to be consistent across countries and cultures (Fang et al., 2018; Marsh & Hau, 2003), the results from the planned study can, tentatively, be generalized to students outside of Sweden. The paper will be a part of a doctoral project within the research project Student self-concept and school achievement: Bidirectional relations and effects of social comparisons and grading. The research project is funded by the Swedish Research Council (dnr. 2019-04531).

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