Contextual-mean effects show little moderation by individual achievement; apparent positive moderation is illusory when the quadratic term is omitted¶

Claim · All claims
Evidence · 1 study (2 entries) · associational r2 · q2
Currency · newest study 2026 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? In the fully specified curvature-adjusted model, the L1 × L2 interaction was small and slightly negative, opposite to the ordinal-standing prediction of a positive attenuating interaction. → Herbert W. Marsh 2026 q2 i? Omitting the quadratic term produced an apparently moderate positive interaction that largely disappeared once curvature was modeled. → Herbert W. Marsh 2026 (2)

Evidence¶

Herbert W. Marsh 2026¶

Herbert W. Marsh. (2026). Four Decades After the Big-Fish–Little-Pond Effect: Critical Boundary Tests and Integrative Models of Mean-Context, Ordinal-Standing, and Distributional-Scaling in 46 Countries. Educational Psychology Review. https://doi.org/10.1007/s10648-026-10200-0

q2 · i? · associational · r2

Multilevel Model 5 (L1, L2, L1², L1 × L2) in the TIMSS 2019 sample: the interaction was "small and slightly negative (β = −0.052, SE = 0.006)", providing little evidence that the contextual effect weakens at higher achievement levels.

"In the fully specified curvature-adjusted model (Model 5), the interaction was small and slightly negative (β = −0.052, SE = 0.006). Figure 1D shows that the contextual-effect profiles remained close to parallel across levels of individual achievement."

Herbert W. Marsh 2026 (2)¶

Herbert W. Marsh. (2026). Four Decades After the Big-Fish–Little-Pond Effect: Critical Boundary Tests and Integrative Models of Mean-Context, Ordinal-Standing, and Distributional-Scaling in 46 Countries. Educational Psychology Review. https://doi.org/10.1007/s10648-026-10200-0

q2 · i? · associational · r2

Model 4 (without L1²) in the same sample produced "an apparently moderate positive interaction (β = 0.153, SE = 0.003)"; the article attributes this to illusory moderation arising from omitted nonlinear terms.

"The importance of modeling curvature is illustrated by Model 4, where omission of the quadratic term produced an apparently moderate positive interaction (β = 0.153, SE = 0.003) and the fan-shaped pattern visible in Fig. 1C. Once the quadratic term was included, however, the apparent moderation largely disappeared."

Discussion¶

Learner Variables¶

• Academic Self-Concept — outcome: instruction changes it

Related Claims¶

• Adding a quadratic achievement term leaves the negative contextual-mean effect essentially unchanged — related
• Integrative models indicate much of the apparent ordinal-rank effect reflects distributionally scaled relative achievement, while contextual means remain the most robust comparative indicator — related
• The negative contextual-mean effect persists for the top-ranked student in each class, constraining rank-sufficiency accounts — related
• Class-average achievement negatively predicts mathematics self-concept after controlling individual achievement (BFLPE replication in TIMSS 2019) — related
• The contextual-mean effect remains negative across every achievement decile and across MSC quantiles, with no systematic attenuation at the top — related
• Measurement error bias inflates peer spillover effects while attenuating the BFLPE; controls strengthen the BFLPE and weaken the spillover effect — related
• Positive class-level peer spillover effects on mathematics achievement fail to replicate once measurement error is controlled with doubly latent models — related