The DOI matches its Crossref record; 20 of the 21 references it cites were found in a registry or an index.
Sufficient Sample Sizes for Multilevel Modeling
Abstract
Abstract. An important problem in multilevel modeling is what constitutes a sufficient sample size for accurate estimation. In multilevel analysis, the major restriction is often the higher-level sample size. In this paper, a simulation study is used to determine the influence of different sample sizes at the group level on the accuracy of the estimates (regression coefficients and variances) and their standard errors. In addition, the influence of other factors, such as the lowest-level sample size and different variance distributions between the levels (different intraclass correlations), is examined. The results show that only a small sample size at level two (meaning a sample of 50 or less) leads to biased estimates of the second-level standard errors. In all of the other simulated conditions the estimates of the regression coefficients, the variance components, and the standard errors are unbiased and accurate.
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“Based on a simulation study on sufficient sample sizes for multilevel modeling by Maas and Hox (2005), the target sample size was set at 100 participants from both countries.”
From Visualizing Uncertainty to Promote Clinicians’ Understanding of Measurement Error (2023) · cites this paper as Maas and Hox (2005)
In the citing paper
“Here we hope to address pseudoreplication in single-cell analyses by demonstrating what a large and long-standing body of statistical literature already confirms: applying statistical inference to replicates that are not statistically independent without properly accounting for their correlation structure will inflate type 1 error rates and lead to spurious results4–6,9,25–28.”
From A practical solution to pseudoreplication bias in single-cell studies (2021) · cites this paper as [27]
In the citing paper
“As the denominator of most statistical tests (e.g., Wald test) is a function of the variance, not accounting for the positive correlation among sampling units underestimates the true standard error and leads to false positives27,28.”
From A practical solution to pseudoreplication bias in single-cell studies (2021) · cites this paper as [27]
In the citing paper
“Moreover, Maas and Hox (2005) found that, for sample sizes greater than 50, the estimates of the regression coefficients, the variance components, and the standard errors are unbiased and accurate.”
From Moving the Needle: Evidence of an Effective Study Strategy Intervention in a Community College Biology Course (2022) · cites this paper as Maas and Hox (2005)
In the citing paper
“Thus, while our course clusters are only moderate in size and our overall sample size is above 50, both are large enough to carry out the linear mixed models that will yield unbiased estimates of regression coefficients and standard errors.”
From Moving the Needle: Evidence of an Effective Study Strategy Intervention in a Community College Biology Course (2022) · cites this paper as Maas and Hox (2005)
In the citing paper
“However, the negligible school effects meant that two-level modeling (class, student) was sufficient, with the sample size also more than adequate for this approach (Field, 2013;Maas & Hox, 2005).”
From Teacher–Student Dialogue During Classroom Teaching: Does It Really Impact on Student Outcomes? (2019) · cites this paper as Maas & Hox, 2005
In the citing paper
“The design effect for the two outcomes of interest was smaller than 2 (science identity 1.77; research self-efficacy 1.57). Thus, multilevel modeling (individuals nested within cohorts) is not necessary (Satorra and Muthen, 1995; Maas and Hox, 2005).”
From Outcomes and Processes in the Meyerhoff Scholars Program: STEM PhD Completion, Sense of Community, Perceived Program Benefit, Science Identity, and Research Self-Efficacy (2016) · cites this paper as Maas and Hox, 2005
In the citing paper
“Although students were nested within the 16 cohorts, multilevel modeling was not used in this study, because 50 or fewer clusters lead to biased parameter estimates in multilevel analysis (Maas and Hox, 2005).”
From Outcomes and Processes in the Meyerhoff Scholars Program: STEM PhD Completion, Sense of Community, Perceived Program Benefit, Science Identity, and Research Self-Efficacy (2016) · cites this paper as Maas and Hox, 2005
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Metadata
- Authors
- Maas, C. J. M., & Hox, J. J.
- Affiliations
- Utrecht University (NL)
- Venue
- Methodology
- Publisher
- Hogrefe Publishing Group
- Published
- 2005-01
- Volume
- 1
- Issue
- 3
- Pages
- 86-92
- ISSN
- 1614-1881 (ISSN-L)
- 1614-2241
- OpenAlex
- W2112146495
- Cited by
- 3,582
- References
- 21
- Citations by year
- 2026: 292 · 2025: 282 · 2024: 190 · 2023: 220 · 2022: 241 · 2021: 289 · 2020: 293 · 2019: 258 · 2018: 268 · 2017: 248 · 2016: 201 · 2015: 196 · 2014: 157 · 2013: 130 · 2012: 105
- FWCI
- 15.22
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Methodology (publishedVersion)
- 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 › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Keywords
- sample size, multilevel modeling, variance components, intraclass correlation coefficient, estimation bias, regression coefficients, simulation study
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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