In 3 countries, a quadratic-effects-of-x-and-y polynomial explained 7.2% of achievement variance (an 11% increase over the linear model)¶

Claim · All claims
Evidence · 1 study · associational r2 · q2
Currency · newest study 2024 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? Georgia, Malaysia, and Portugal shared the 'Quadratic effects of x and y' family, whose model explained 7.2% of achievement levels, an 11% increase over the linear model. → Núñez-Regueiro 2024

Evidence¶

Núñez-Regueiro 2024¶

Núñez-Regueiro, F. (2024). Cubic Relations of Autonomous and Controlled Motivation to Achievement: A Cross-National Validation of Self-Determination Theory Using Response Surface Analysis. Educational Psychology Review, 36 (3). https://doi.org/10.1007/s10648-024-09905-x

q2 · i? · associational · r2

Group 4 of the TIMSS 2019 analysis: the 'Quadratic effects of x and y' family estimates quadratic effects of autonomy and control while constraining other second- and third-order effects to null. The model "showed excellent fit to the data" with structural invariance across the three countries.

"explaining 7.2% of achievement levels (R2 = .072), representing an increase in explained variance of 11% relative to the linear model (R2 = .065)."

Discussion¶

Related Claims¶

• In 8 countries, a non-parallel asymmetric congruence/incongruence polynomial explained a modest 4.1% of achievement variance yet a 41% increase over the additive model — related
• Across 37 countries, polynomial models with nonlinear or interactive effects of autonomous and controlled motivation on mathematics achievement always fit better than linear additive-only models — a broader claim this one bears on
• The relation of autonomous motivation to grades is curvilinear, with grades accelerating at higher autonomous motivation — related
• Higher grades occur when high autonomous motivation coincides with low controlled motivation (incongruence), not congruence — related