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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. Educational Impact and Implications Statement: Counter to a widely held belief that being in a high-achieving school has a positive effect on student's achievement (peer spillover effect), the present findings suggest that this effect is actually slightly negative. When using stronger, more appropriate statistical methodology, the apparent peer spillover effect disappeared, suggesting that positive effects are a phantom. Furthermore, the negative effect of school-average achievement on academic self-concept (big-fish-little-pond effect) turned out to be even more negative when using more appropriate methodology. Thus, the findings indicate that attending a high-achieving school has a negative effect on self-concept and no positive effect on achievement. These results call into question prior research that did not control for phantom effects, and challenge policy and practice decisions that promote selective schooling.