The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
Standard Errors and Sample Sizes for Two-Level Research
Open accessAbstract
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.
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“Post hoc power analyses using the multilevel power analysis program PinT (Snijders & Bosker, 1993) confirmed that we had sufficient power (>.80) to detect a mediated pathway comprising paths that were of medium effect sizes and to detect a medium effect size for treatment condition as a moderator of the mediated pathways.”
From Respiratory and cognitive mediators of treatment change in panic disorder: Evidence for intervention specificity. (2010) · cites this paper as Snijders & Bosker, 1993
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In the citing paper
“Tyrer et al reported that brief CBT is no more effective than usual care when it comes to preventing repetition of self-harm, 15”
From Cognitive-behavioural intervention for self-harm: Randomised controlled trial (2008) · cites this paper as [15]
Experimental — accuracy not yet measuredThe check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“Furthermore, this study's findings that time-limited CBT decreases self-harm contrasts with the results reported by Tyrer et al . 15”
From Cognitive-behavioural intervention for self-harm: Randomised controlled trial (2008) · cites this paper as [15]
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Citations
Cites
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Flagged first, then by citations
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Cited by
Sorted by citations
Applied Longitudinal Data Analysis for Epidemiology: A Practical Guide
Twisk, J. W. R. (2003) · Cited by 1,244
Multilevel Analysis in Public Health Research
Roux, A. V. D. (2000) · Annual Review of Public Health · doi:10.1146/annurev.publhealth.21.1.171 · Cited by 1,224
“Sample size and power calculations for multilevel hypotheses testing are particularly complex (8, 56, 90).”
BackgroundHox, J. J. (1995) · Utrecht University Repository (Utrecht University) · Cited by 1,179
Building Theoretical and Empirical Bridges Across Levels: Multilevel Research in Management
Hitt, M. A., Beamish, P. W., Jackson, S. E., & Mathieu, J. E. (2007) · Academy of Management Journal · doi:10.5465/amj.2007.28166219 · Cited by 1,138
“Although some software programs allow researchers to make a priori estimates of the power of multilevel designs, these applications are far more complex than their single-level counterparts (cf. Raudenbush, 1997; Snijders & Bosker, 1993).”
BackgroundWestfall, J., Kenny, D. A., & Judd, C. M. (2014) · Journal of Experimental Psychology: General · doi:10.1037/xge0000014 · Cited by 928
“…there is an extensive literature in education and applied statistics on nested designs, commonly referred to as hierarchically nested designs, and this literature has considered issues of power and optimal design (Raudenbush, 1997; Raudenbush & Liu, 2000; Snijders, 2001; Snijders & Bosker, 1993).”
Background
Metadata
- Authors
- Snijders, T. A. B., & Bosker, R. J.
- Affiliations
- University of Groningen (NL)
- University of Twente (NL)
- Venue
- Journal of Educational Statistics
- Published
- 1993-09
- Volume
- 18
- Issue
- 3
- Pages
- 237-259
- ISSN
- 0362-9791 (ISSN-L)
- OpenAlex
- W2097507923
- Cited by
- 487
- References
- 17
- Citations by year
- 2026: 11 · 2025: 13 · 2024: 14 · 2023: 14 · 2022: 14 · 2021: 27 · 2020: 26 · 2019: 34 · 2018: 20 · 2017: 28 · 2016: 22 · 2015: 25 · 2014: 24 · 2013: 35 · 2012: 21
- FWCI
- 1.01
- Type
- journal article
- Language
- en
- Open access
- green
- www.jstor.org
- Locations
- Journal of Educational Statistics (publishedVersion)
- University of Twente Research Information (submittedVersion, other-oa)
- RePEc: Research Papers in Economics (submittedVersion)
- University of Groningen research database (University of Groningen / Centre for Information Technology) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Survey Sampling and Estimation Techniques
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Keywords
- two-level designs, multilevel analysis, standard errors, sample size determination, covariance matrix approximation, multilevel data
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