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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]
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“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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“This approach is essential for ensuring that the conclusions drawn our statistical analyses are not unduly affected by underlying assumptions or anomalies in the data (Snijders and Bosker 1993).”
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“Although we only sampled 11 institutions, studies have also shown that a sample size greater than 10 is sufficient for model identification (Adam 2020), to conduct bootstrap tests (Hox 2002), and to reduce concerns over standard errors and poor statistical power (Snijders & Bosker 1993, p.239).”
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“An a priori power analysis was conducted using the Power In Two-Level Designs v.212 software (Bosker et al., 1996; Snijders & Bosker, 1993) and a sample size calculator for structural equation models (Soper, 2022).”
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“PINT implements the formulae given in Snijders and Bosker (1993) while OD builds on the work in Raudenbush (1997) and Raudenbush and Liu (2001).”
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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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