The DOI matches its Crossref record; 49 of the 50 references it cites were found in a registry or an index.
Power Analysis and Effect Size in Mixed Effects Models: A Tutorial
Open accessPublished version of a preprint
Abstract
In psychology, attempts to replicate published findings are less successful than expected. For properly powered studies replication rate should be around 80%, whereas in practice less than 40% of the studies selected from different areas of psychology can be replicated. Researchers in cognitive psychology are hindered in estimating the power of their studies, because the designs they use present a sample of stimulus materials to a sample of participants, a situation not covered by most power formulas. To remedy the situation, we review the literature related to the topic and introduce recent software packages, which we apply to the data of two masked priming studies with high power. We checked how we could estimate the power of each study and how much they could be reduced to remain powerful enough. On the basis of this analysis, we recommend that a properly powered reaction time experiment with repeated measures has at least 1,600 word observations per condition (e.g., 40 participants, 40 stimuli). This is considerably more than current practice. We also show that researchers must include the number of observations in meta-analyses because the effect sizes currently reported depend on the number of stimuli presented to the participants. Our analyses can easily be applied to new datasets gathered.
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“Aggregations provide independent observations for non-parametric testing and make it appropriate when dealing with small sample sizes and repeated measures [8].”
From How University Disability Services Professionals Write Image Descriptions for HCI Figures Using Generative AI (2026) · cites this paper as [8]
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Cites
Fitting Linear Mixed-Effects Models Using lme4
Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015) · Journal of Statistical Software · doi:10.18637/jss.v067.i01 · Cited by 86,835 · cited 2×
“Table 2: Outcome of the lmer analysis (Bates et al., 2015) of the Adelman et al.”
BackgroundFaul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007) · Behavior Research Methods · doi:10.3758/bf03193146 · Cited by 65,971
Mixed-effects modeling with crossed random effects for subjects and items
Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008) · Journal of Memory and Language · doi:10.1016/j.jml.2007.12.005 · Cited by 8,540
Estimating the reproducibility of psychological science
Open Science Collaboration (2015) · Science · doi:10.1126/science.aac4716 · Cited by 8,515
Power failure: why small sample size undermines the reliability of neuroscience
Button, K. S., Ioannidis, J. P. A., Mokrysz, C., Nosek, B. A., Flint, J., Robinson, E. S. J., & Munafò, M. R. (2013) · Nature Reviews Neuroscience · doi:10.1038/nrn3475 · Cited by 7,641
Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011) · Psychological Science · doi:10.1177/0956797611417632 · Cited by 6,567 · cited 1×
“What must be avoided, is that authors try out the various options and only report the one that produces a “significant” effect, a phenomenon known as p-hacking (Simmons et al., 2011).”
BackgroundAnalyzing Linguistic Data: A Practical Introduction to Statistics using R
Baayen, R. H. (2008) · doi:10.1017/cbo9780511801686 · Cited by 3,253
The New Statistics: Why and How
Cumming, G. (2014) · Psychological Science · doi:10.1177/0956797613504966 · Cited by 3,200 · cited 1×
“First, p-values show wide sample-to-sample variability, particularly when they are based on studies with small sample sizes (Cumming, 2014; Halsey, Curran-Everett, Vowler, & Drummond, 2015).”
BackgroundSIMR : an R package for power analysis of generalized linear mixed models by simulation
Green, P., & MacLeod, C. J. (2016) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.12504 · Cited by 2,467 · cited 1×
“A particularly interesting R package is simR (Green & MacLeod, 2016; Green, MacLeod, & Alday, 2016).2 2 The authors thank Jason Geller for pointing them to this package.”
BackgroundAnalyzing linguistic data: a practical introduction to statistics using R
Dévière, E. (2009) · Journal of Applied Statistics · doi:10.1080/02664760802366783 · Cited by 2,347 · cited 2×
“Some authors demand the use of transformations to get normal distributions (e.g., Baayen, 2008).”
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Tamaoka, K., Hayakawa, K., Mansbridge, M. P., Xiong, K., Koizumi, M., & Verdonschot, R. G. (2026) · Applied Psycholinguistics · doi:10.1017/s0142716426100769
“…estimates are provided only as approximate contextual benchmarks and do not replace a full simulation-based power analysis for mixed-effects models, especially in designs with crossed random factors such as participants and items (Brysbaert & Stevens, 2018; Lakens, 2022; Westfall et al., 2014).”
Friede, A., Vorstius, C., Inhoff, A. W., & Radach, R. R. (2026) · Journal of Eye Movement Research · doi:10.3390/jemr19040082
“Following Brysbaert and Stevens [26], standardized effect sizes for the factor target position and for interactions of position with individuals’ verbal and spatial abilities were defined as the ratio of the difference between condition means and the summed standard deviations of all random factor…”
InfluentialThe influence of spatial frequencies, orientation, and familiarity on face stimuli integration
Cuomo, M., Federico, G., Capolongo, G. M., Fracasso, A., & Buonocore, A. (2026) · Attention Perception & Psychophysics · doi:10.3758/s13414-026-03312-w
“As an additional check, we conducted simulation-based power analyses (Brysbaert & Stevens, 2017) using the simr package in R (Green & MacLeod, 2016).”
Metadata
- Authors
- Brysbaert, M., & Stevens, M.
- Affiliations
- Ghent University (BE)
- Corresponding author
- Brysbaert, Marc
- ORCID
- Brysbaert, Marc
- Venue
- Journal of Cognition
- Publisher
- Ubiquity Press, Ltd.
- Published
- 2018
- Volume
- 1
- Issue
- 1
- Pages
- 9-9
- ISSN
- 2514-4820 (ISSN-L)
- PMC
- PMC6646942
- OpenAlex
- W2783948250
- Cited by
- 1,420
- References
- 50
- Citations by year
- 2026: 154 · 2025: 290 · 2024: 189 · 2023: 195 · 2022: 195 · 2021: 162 · 2020: 130 · 2019: 73 · 2018: 31
- FWCI
- 82.16
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Journal of Cognition (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, cc-by-sa)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- PsyArXiv (OSF Preprints) (submittedVersion, cc-by)
- PsyArXiv (OSF Preprints) (submittedVersion)
- OSF Preprints (OSF Preprints) (submittedVersion, cc-by)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Psychology Research and Bibliometrics
- Keywords
- power analysis, effect size, mixed models, replication, cognitive psychology, masked priming, reaction time, repeated measures, sample size, meta-analysis, statistical power
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