A higher ICC(1) of students' ratings and a larger standardized between slope increase power, with opposite effects on the optimal split between classes and students per class¶

Claim · All claims
Evidence · 1 study (2 entries) · theoretical r3 · q2
Currency · newest study 2022 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? Unlike the ICC(1) of student achievement, a higher ICC(1) of students' ratings of classroom management increases the power to detect the between slope. → Steffen Zitzmann 2021 q2 i? A larger standardized between slope decreases the optimal number of classes, increases the optimal number of students per class, and increases power. → Steffen Zitzmann 2021 (2)

Evidence¶

Steffen Zitzmann 2021¶

Steffen Zitzmann, Wolfgang Wagner, Martin Hecht, Christoph Helm, Christian Fischer, Lisa Bardach, Richard Göllner. (2021). How Many Classes and Students Should Ideally be Sampled When Assessing the Role of Classroom Climate via Student Ratings on a Limited Budget? An Optimal Design Perspective. Educational Psychology Review (2022) 34:511–536. https://doi.org/10.1007/s10648-021-09635-4

q2 · i? · theoretical · r3

Numerical optimization results shown in Fig. 2, with the same budget and cost assumptions as Fig. 1. Selecting a higher ICC(1) of the ratings increases the optimal number of classes and decreases the optimal number of students per class while increasing power.

"unlike the ICC(1) of student achievement, a higher ICC(1) of students' ratings of classroom management will increase the power to detect the between slope."

Steffen Zitzmann 2021 (2)¶

Steffen Zitzmann, Wolfgang Wagner, Martin Hecht, Christoph Helm, Christian Fischer, Lisa Bardach, Richard Göllner. (2021). How Many Classes and Students Should Ideally be Sampled When Assessing the Role of Classroom Climate via Student Ratings on a Limited Budget? An Optimal Design Perspective. Educational Psychology Review (2022) 34:511–536. https://doi.org/10.1007/s10648-021-09635-4

q2 · i? · theoretical · r3

Numerical optimization results shown in Fig. 3 for the standardized between slope (standardized according to Marsh et al.'s (2009) formula) under the same fixed budget and cost assumptions.

"the larger this slope is chosen to be, the smaller the optimal number of classes will be, and the larger the optimal number of students per class will be. Moreover, a larger standardized between slope will increase the power to detect the between slope."

Discussion¶

Related Claims¶

• The variability of the between slope estimate in the multilevel latent covariate model decreases with more classes and students, with higher ICC(1) of the ratings and larger slopes, but increases with higher ICC(1) of the outcome — related
• Under a fixed budget, a higher ICC(1) of the outcome variable shifts the optimal design toward more classes and fewer students per class and reduces maximum power — related
• In the PIRLS 2006 teaching-quality example, the optimal fixed-budget design was 395 classes with 12 students per class, and the actual PIRLS design achieved 83% power — a narrower finding that bears on this claim