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¶
Claim · All claims
Evidence · 1 study · theoreticalr3·q2
Currency · newest study 2022 · not yet checked against its sources · not reviewed by a person
Subclaims¶
Reading the evidence codes
q is the design tier, i the impact, n the sample, and the kind with its r
the rigour judged within that kind: what each code means.
This claim: no standardized effect is recorded in observations/ for it yet, so no benchmark reading is possible.
q2 i? The variability of the between slope decreases as the number of classes and the number of students per class increase. → Steffen Zitzmann 2021
q2 i? The ICC(1) of the students' ratings decreases the variability of the between slope, whereas the ICC(1) of the achievement variable increases it. → Steffen Zitzmann 2021
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
Analytical derivation using a first-order Taylor expansion of the variability of the between slope in Lüdtke et al.'s (2008) model, assuming standardized variables. The derivation shows "the variability will decrease when the number of classes (J ) gets larger" and that the two ICC(1) values have opposite effects on variability.
"it shows that the variability is a function of the sample size, which means that the variability will decrease when the number of classes (J ) gets larger and all other quantities are held constant."
Discussion¶
Related Claims¶
- 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 — 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 — related
Page metadata
| Field | Value |
|---|---|
type |
claim |
id |
between-slope-variability-depends-on-iccs-and-slopes |
title |
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 |
description |
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... |
status |
review |
evidence_strength |
weak |
newest_evidence |
2022 |
generated |
by process:wiki-ingest on 2026-10-21 |
trust |
unverified — no one has confirmed this page's content |
sources |
1 — steffen-zitzmann-2021 |
Frontmatter is the page's machine-readable record — see the Schema & Guide.