Adding a quadratic achievement term leaves the negative contextual-mean effect essentially unchanged¶

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

Subclaims¶

q2 i? Modest nonlinearity in the achievement–self-concept relation exists, but including L1² does not materially alter the negative class-average effect. → Herbert W. Marsh 2026

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 3 in the same TIMSS 2019 sample added a quadratic achievement term, confirming "modest nonlinearity in the L1–MSC relation (L1² = 0.104, SE = 0.002)" while the contextual effect stayed essentially unchanged (L2 = − 0.660, SE = 0.006).

"Model 3 (Table 1) added a quadratic term for individual achievement and confirmed modest nonlinearity in the L1–MSC relation (L1² = 0.104, SE = 0.002; L1 = 0.577, SE = 0.003). Crucially, however, inclusion of the quadratic term left the contextual effect essentially unchanged (L2 = − 0.660, SE = 0.006, compared with − 0.633 in Model 2)."

Discussion¶

Learner Variables¶

• Academic Self-Concept — outcome: instruction changes it

Related Claims¶

• Contextual-mean effects show little moderation by individual achievement; apparent positive moderation is illusory when the quadratic term is omitted — 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
• Integrative models indicate much of the apparent ordinal-rank effect reflects distributionally scaled relative achievement, while contextual means remain the most robust comparative indicator — a broader claim this one bears on
• Positive class-level peer spillover effects on mathematics achievement fail to replicate once measurement error is controlled with doubly latent models — related
• School-average achievement negatively predicts academic self-concept (BFLPE) and GPA in the comprehensive doubly-latent model — related