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Standard Errors and Sample Sizes for Two-Level Research

Author

Listed:
  • Tom A. B. Snijders
  • Roel J. Bosker

Abstract

The hierarchical linear model approach to a two-level design is considered, some variables at the lower level having fixed and others having random regression coefficients. An approximation is derived to the covariance matrix of the estimators of the fixed regression coefficients (for variables at the lower and the higher level) under the assumption that the sample sizes at either level are large enough. This covariance matrix is expressed as a function of parameters occurring in the model. If a research planner can make a reasonable guess as to these parameters, this approximation can be used as a guide to the choice of sample sizes at either level.

Suggested Citation

  • Tom A. B. Snijders & Roel J. Bosker, 1993. "Standard Errors and Sample Sizes for Two-Level Research," Journal of Educational and Behavioral Statistics, , vol. 18(3), pages 237-259, September.
    • Handle: RePEc:sae:jedbes:v:18:y:1993:i:3:p:237-259
    DOI: 10.3102/10769986018003237
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    Cited by:

    1. Md Abu Manju & Math J. J. M. Candel & Gerard J. P. van Breukelen, 2019. "SamP2CeT: an interactive computer program for sample size and power calculation for two-level cost-effectiveness trials," Computational Statistics, Springer, vol. 34(1), pages 47-70, March.
    2. Satoshi Usami, 2017. "Generalized SAMPLE SIZE Determination Formulas for Investigating Contextual Effects by a Three-Level Random Intercept Model," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 133-157, March.
    3. Martin Hoegl & K. Praveen Parboteeah & Miriam Muethel, 2012. "Cross-National Differences in Managers’ Creativity Promoting Values," Management International Review, Springer, vol. 52(4), pages 565-595, August.
    4. Oberle, Eva & Guhn, Martin & Gadermann, Anne M. & Thomson, Kimberly & Schonert-Reichl, Kimberly A., 2018. "Positive mental health and supportive school environments: A population-level longitudinal study of dispositional optimism and school relationships in early adolescence," Social Science & Medicine, Elsevier, vol. 214(C), pages 154-161.
    5. Morey, Brittany N. & Gee, Gilbert C. & Muennig, Peter & Hatzenbuehler, Mark L., 2018. "Community-level prejudice and mortality among immigrant groups," Social Science & Medicine, Elsevier, vol. 199(C), pages 56-66.
    6. Seok, Jun Ho & Saghaian, Sayed & Reed, Michael R., 2018. "The ‘Signaling Effect’ and the impact of high maximum residue limit standards on U.S. vegetable exports," Economic Analysis and Policy, Elsevier, vol. 59(C), pages 150-159.

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