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The main objective of this study was to quantify the impact of failing to account for measurement error on school compositional effects. Multilevel structural equation models were incorporated to control for measurement error and/or sampling error. Study 1, a large sample of English primary students in Years 1 and 4, revealed a significantly negative compositional effect associated with school-average achievement that became more negative after controlling for measurement error. Study 2, a large study of Cypriot primary students in Year 4, showed a small, positive but statistically significant compositional effect that became non-significant after controlling for measurement error. Our findings have important methodological, substantive, and theoretical implications for on-going debates on the school compositional effects on students’ outcomes, because nearly all previous research has been based on traditional approaches to multilevel models, which are positively biased, due to the failure to control for measurement error. [ABSTRACT FROM PUBLISHER]

School-average achievement is often reported to have positive effects on individual achievement (peer spillover effect). However, it is well established that school-average achievement has negative effects on academic self-concept (big-fish-little-pond effect [BFLPE]) and that academic self-concept and achievement are positively correlated and mutually reinforcing (reciprocal effects model). We resolve this theoretical paradox based on a large, longitudinal sample (N = 14,985 U.S. children) and improved methodology. More appropriate multilevel modeling that controls for phantom effects (due to measurement error and preexisting differences) makes the BFLPE even more negative, but turns the peer spillover effect from positive to slightly below zero. Thus, attending a high-achieving school has negative effects on academic self-concept and a nonpositive effect on achievement. The results question previous studies and meta-analyses showing a positive peer spillover effect that do not control for phantom effects, along with previous policy and school selection decisions based on this research. [ABSTRACT FROM AUTHOR]