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The present study uses doubly latent models to estimate the effect of average mathematics achievement at the class level on students' subsequent mathematics achievement (the "Peer Spillover Effect") and mathematics self-concept (the "Big-Fish-Little-Pond-Effect; BFLPE"), controlling for individual differences in prior mathematics achievement. Our data, consisting of 13-year-old students from Canada, the USA, and New Zealand, come from a unique cross-national database with a longitudinal design at the student level: the Second International Mathematics Study (SIMS80). This historical survey was administered by IEA in the 1980s and highly influenced the development of educational policies in the following decades. We replicate a widely cited study based on SIMS80, interrogating the validity of its findings of a positive peer spillover effect. When we adjust for measurement error, using doubly latent models, we observe that originally positive peer spillover effects become less positive or disappear altogether. On the contrary, negative BFLPEs become more negative and remain statistically significant throughout. Our study is the only cross-national study to have evaluated both the BFLPE and the peer spillover effect with controls for a true measure of prior achievement -- and the only study to test the peer spillover effect cross-nationally using doubly latent models. Our findings question the empirical results of past and current research evaluating school- and class-level compositional effects based on sub-optimal models that fail to control for measurement error.

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.

Omitted prior achievement bias is pervasive in international assessment studies and precludes causal inference. For example, reported negative associations between student-oriented teaching strategies and student performance are against expectations and might actually reflect omitted prior achievement bias. Namely, that these teaching strategies are negatively correlated with unobserved prior achievement performance, because teachers offer more support to lower performing students, and not that these strategies "cause" lower performance. This paper examines omitted prior achievement bias in teaching effects with prior achievement data available for students in England participating in the Progress in International Reading Literacy Study. Further, it proposes an analytical approach to account for omitted prior achievement bias in international estimates. The paper argues that the bias is not simply a technical artefact, but reflects educational mechanisms unobserved in international assessment studies, which can be captured with matched assessment data-sets or with evidence from previous studies. Estimates of these mechanisms can be used to postulate scenarios of the bias across education systems and thereby adjust international estimates of teaching effects as if prior achievement were observed. Potentials and limitations of this approach for studying educational effectiveness with international assessment data are discussed.

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.

Omitted prior achievement bias is pervasive in international assessment studies and precludes causal inference. For example, reported negative associations between student-oriented teaching strategies and student performance are against expectations and might actually reflect omitted prior achievement bias. Namely, that these teaching strategies are negatively correlated with unobserved prior achievement performance, because teachers offer more support to lower performing students, and not that these strategiescauselower performance. This paper examines omitted prior achievement bias in teaching effects with prior achievement data available for students in England participating in the Progress in International Reading Literacy Study. Further, it proposes an analytical approach to account for omitted prior achievement bias in international estimates. The paper argues that the bias is not simply a technical artefact, but reflects educational mechanisms unobserved in international assessment studies, which can be captured with matched assessment data-sets or with evidence from previous studies. Estimates of these mechanisms can be used to postulate scenarios of the bias across education systems and thereby adjust international estimates of teaching effects as if prior achievement were observed. Potentials and limitations of this approach for studying educational effectiveness with international assessment data are discussed. [ABSTRACT FROM PUBLISHER]