Asia Pacific Education Review

, Volume 9, Issue 2, pp 206–220 | Cite as

Closing the Gap: Modeling within-school variance heterogeneity in school effect studies



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.


school effect variance heterogeneity achievement gap hierarchical modeling latent variable regression 


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  1. Bryk, A. S., & Raudenbush, S. W. (1988). Heterogeneity of variance in experimental studies: A challenge to conventional interpretations.Psychological Bulletin, 104, 396–404.CrossRefGoogle Scholar
  2. Choi, K., & Seltzer, M. (in press). Modeling heterogeneity in relationships between initial status and rates of change: treating latent variable regression coefficients as random coefficients in a three-level hierarchical model.Journal of Educational and Behavioral Statistics. Google Scholar
  3. Eugenio, J. G., & Julie, A. M. (2001).TIMSS 1999 user guide for the international database. Boston: Boston College, Lynch School of Education, International Study Center.Google Scholar
  4. Gelman, A., Carlin, J., Stern, H., & Rubin, D. (1995).Bayesian data analysis. New York, NY: Chapman & Hall.Google Scholar
  5. Kasim, R., & Raudenbush, S. W. (1998). Application of Gibbs sampling to nested variance components models with heterogeneous within-group variance.Journal of Educational and Behavioral Statistics, 23, 93–116.Google Scholar
  6. Kim, J., & Seltzer, M. (2008).Bayesian model checks for complex hierarchical models in quasi-experimental settings. Paper presented at the 2008 annual meeting of American Educational Research Association.Google Scholar
  7. Kim, J., & Seltzer, M. (2006).Examining heterogeneity in residual variance in experimental and quasi-experimental settings. Paper presented at the 2006 annual meeting of American Educational Research Association.Google Scholar
  8. Lee, V. E., & Bryk, A. S. (1989). A multilevel model of the social distribution of high school achievement.Sociology of Education, 62, 172–192.CrossRefGoogle Scholar
  9. Park, D., Park, J., & Kim, S. (2001). The effects of school and student background variables on math and science achievements in middle schools.Journal of Educational Evaluation, 14, 127–149.Google Scholar
  10. Raudenbush, S. W., & Bryk, A. S. (2002).Hierarchical linear models: Applications and data analysis methods (2nd ed.). Newbury Park, CA: Sage.Google Scholar
  11. Raudenbush, S. W., Bryk, A. S., Cheong, Y. F., & Congdon, R. (2004).HLM6: Hierarchical linear and nonlinear modeling. Lincolnwood, IL: Scientific Software International.Google Scholar
  12. Rumberger, R. W., & Palardy, G. J. (2003). Multilevel models for school effectiveness research. In D. Kaplan (Ed.),Handbook of quantitative methodology for the social sciences (pp. 235–258). Thousand Oaks, CA: Sage.Google Scholar
  13. Seltzer, M., Choi, K., & Thum, Y. (2003). Examining relationship between where students start and how rapidly they progress: Using new developments in growth modeling to gain insight into the distribution of achievement within schools.Education Evaluation and Policy Analysis, 25, 263–286.CrossRefGoogle Scholar
  14. Spiegelhalter, D., Thomas, A., Bets, N., & Lunn, D. (2003).WinBUGS: windows version of Bayesian inference using Gibbs sampling, version 1.4, User manual. Cambridge, UK: University of Cambridge, MRC Biostatistics Unit.Google Scholar
  15. Yang, J., & Kim, K. (2003). Effects of middle school organization on academic achievement in Korea: An HLM analysis of TIMSS-R.Korean Journal of Sociology of Education, 13, 165–184.Google Scholar

Copyright information

© Education Research Institute 2008

Authors and Affiliations

  1. 1.Charles Drew UniversityLos AngelesUSA
  2. 2.National Center for Research on Evaluation, Standards, and Student TestingUniversity of CaliforniaLos AngelesUSA

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