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Cited by 3,582Statistical Methods and Bayesian InferenceSurvey Sampling and Estimation TechniquesSpatial and Panel Data Analysis

Sufficient Sample Sizes for Multilevel Modeling

Maas, Cora J. M., Hox, Joop J.·2005·Methodology
DOI 10.1027/1614-2241.1.3.86
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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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Crossref · 10.1027/1614-2241.1.3.86

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20 of 20 references verified0 citation errors · 0 not checkable

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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.

    “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)

  • 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 results.

    “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]

  • Not accounting for the positive correlation among sampling units underestimates the true standard error and leads to false positives.

    “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]

  • For sample sizes greater than 50, estimates of regression coefficients, variance components, and standard errors are unbiased and accurate.

    “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)

  • The overall sample size and course cluster sizes were large enough to carry out linear mixed models yielding unbiased estimates of regression coefficients and standard errors.

    “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)

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Related

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
DOI
10.1027/1614-2241.1.3.86
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

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