Closing the Gap: Modeling within-school Variance Heterogeneity in School Effect Studies

Oct 15, 2026

Uploaded by Grenda

The article examines school effectiveness by modeling heterogeneity in within-school achievement variance alongside achievement levels, addressing the tendency of prior school effect studies to focus mainly on mean achievement. Using hierarchical modeling assumptions with TIMSS-R data, it shows how to detect variance heterogeneity, relate within-school variance to school practices, and interpret how achievement homogeneity coexists with practice-driven dispersion differences. Results indicate higher-achievement schools often exhibit more homogeneous achievement dispersion, yet classroom practices still drive variability.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages15

Reading Time38 min

AccessFree to download

Introduction

Data

TIMSS-R overview

Method and Modeling Approach

Hierarchical modeling of within- and between-school variance

Findings and Implications

Achievement level and dispersion relationships

Purpose and Study Goals

Asia Pacific Education Review Copyright 2008 by Education Research Institute 2008, Vol. 9, No.2, 206-220. Closing the Gap: Modeling within-school Variance Heterogeneity in School Effect Studies Junyeop Kim Kilchan Choi Charles Drew University University of California, Los Angeles USA USA Effective schools should be superior in both enhancing students’ achievement levels and reducing the gap between high- and low-achieving students in the school. However, the focus has been placed mainly on schools’ achievement levels in most school effect studies. In this article, we focused our attention upon the school-specific achievement dispersion as well as achievement level in determining effective schools. The achievement dispersion in a particular school can be captured by within-school variance in achievement (σ2) . Assuming heterogeneous within-school variance across schools in hierarchical modeling, it is possible to identify school factors related to high achievement levels and a small gap between high- and low-achieving students. By analyzing data from the TIMMS-R, we illustrated how to detect variance heterogeneity and how to find a systematic relationship between within-school variance and school practice. In terms of our results, we found that schools with a high achievement level tended to be more homogeneous in achievement dispersion, but even among schools with the same achievement level, schools varied in their achievement dispersion, depending on classroom practices. Keywords: school effect, variance heterogeneity, achievement gap, hierarchical modeling, latent variable regression One of the fundamental questions that most school effect studies have continuously addressed is whether schools make a difference in student achievement, and if so, how much of the student achievement can be attributable to schools’ effort. Regarding this question, most researchers have agreed that schools do have a measurable impact on student achievement, even though the source and the Junyeop Kim, Assistant professor at the Charles Drew University, USA; Kilchan Choi, National Center for Research on Evaluation, Standards, and Student Testing, University of California, Los Angeles, USA. Correspondence concerning this article should be addressed to Junyeop Kim, Charles Drew University, 1748 E, 118th Street. Building N, Los Angeles, CA 90059, United States. e-mail: [junyeopkim@cdrewu.edu](junyeopkim@cdrewu.edu) magnitude of the school effect are still heavily debated (Rumberger & Palardy, 2003) . Using a simple Hierarchical Model (HM), one can successfully show how much of the total variation in achievement comes from the student level (within-school variance, σ2) and how much comes from the school level (between-school variance, τ) . Many studies have found that between-school variance is much smaller than within-school variance. For example, using High School and Beyond (HS&B) data, Lee and Bryk (1989) found that about 19% of the total variation in student math achievement was attributable to school differences. More complicated HMs can be used to discover the source of these within- and between-school variances. Because school effect studies are usually focused on identifying effective schools after controlling for student Modeling within-school Variance Heterogeneity background characteristics, or on finding out school practices that are effective in increasing student achievement, between-school variance (τ) plays an important role. Substantial τ is evidence of a school’s contribution to student outcome, indicating the magnitude of variation among schools in their achievement levels (Raudenbush & Bryk, 2002) . On the other hand, there has been little discussion on within-school variance (σ2) in school effect studies. We argue in this article that σ2 can provide valuable information regarding effective schools because school effectiveness can be determined not only by student achievement levels, but also by t

FAQs

How does the article define an effective school beyond average achievement?

It argues effective schools should improve both students’ achievement levels and reduce the achievement gap within the school, meaning they should have higher average achievement and smaller within-school dispersion.

What data source is used to illustrate detecting variance heterogeneity?

The study uses data from TIMSS-R (Third International Mathematics and Science Study-Repeat), focusing on eighth-grade students and their math and science achievement scores.

What modeling approach is used to separate within- and between-school variance?

The article uses hierarchical modeling, where within-school variance (σ²) captures student-level dispersion inside schools and between-school variance (τ) captures differences across schools.

Oct 15, 2026

Uploaded by Grenda