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¶

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? Eight countries (Bahrain, Egypt, Iran, Jordan, Lebanon, Oman, Saudi Arabia, Turkey) shared polynomial family 25, explaining 4.1% of variance, a 41% increase from the additive 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 3 of the TIMSS 2019 analysis, united on the 'Non-parallel asymmetric congruence and incongruence effect' family with equality constraints between interactive-quadratic and cubic effects of control. The article notes the explained variance "was modest (R2 = 4.1%)" but the relative gain large.

"Although the variance in mathematics explained by this model was modest (R2 = 4.1%), it represented a 41% increase from the additive model (R2 = 2.9%), underlining important higher-order effects."

Discussion¶

Related Claims¶

• In 12 countries, a level-dependent incongruence polynomial with free cubic effect of control explained 7.8% of achievement variance (a 30.9% increase over the additive model) — related
• In 14 countries, a cubic effect of autonomous motivation best fit the motivation-achievement relation, explaining 10.7% of achievement variance (an 8.1% increase over the additive model) — related
• In 3 countries, a quadratic-effects-of-x-and-y polynomial explained 7.2% of achievement variance (an 11% increase over the linear 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