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Power Analysis and Effect Size in Mixed Effects Models: A Tutorial
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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].”
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BackgroundThe effect of a presumption of guilt on police guilt judgments
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InfluentialPerceptual intake explains variability in statistical word segmentation
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“Effect size (d) was calculated manu - ally according to the approach introduced by Brysbaert and Stevens (2018 ).”
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BackgroundMethodInfluentialImpact of Instructor Generated Guided Reading Questions for University Textbooks on Learning
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“First, our sample is sufficiently powered to detect differences on the STAI but may be limited in power to detect differences on the BDI-II because of varying effect sizes (Brysbaert & Stevens, 2018; P. Green & MacLeod, 2016).”
Cui, L., Hou, D.-Z., Liu, H.-Y., Zheng, X., & Hyönä, J. (2026) · Language, Cognition and Neuroscience · doi:10.1080/23273798.2026.2680022 · Cited by 1
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The Effects of Structured LLM-Generated Feedback on Programming Assignment Performance
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Simultaneous manipulation of emotion and working memory load distorts temporal distance memory
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“…differences between the original Experiments versus the enhanced interaction Experiments in Japanese or English do not converge because selecting trials in Region 3 in which the addressee is seated opposite leaves too few trials for appropriate statistical power (cf. Brysbaert & Stevens, 2018).”
Thematic knowledge survives visual crowding and influences object identification
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Editorial Journal of Psycholinguistic Research
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“A good target is 40 observations per participant per condition (Brysbaert & Stevens, 2018).”
Self-citationLanguage context flexibly modulates language control mechanisms.
Timmer, K., Wolna, A., Szewczyk, J. M., & Wodniecka, Z. (2026) · Cognition · doi:10.1016/j.cognition.2026.106488 · Cited by 1
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Zhang, Q., & Li, X.-S. (2026) · Psychonomic Bulletin & Review · doi:10.3758/s13423-025-02854-8 · Cited by 1
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“We acknowledge that an a priori power analysis on a mixed effects model is a rela - tively uncertain process (Brysbaert & Stevens, 2018 ).”
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“The sample size was calculated based on the number of observations per condition recommended by Brysbaert and Stevens (2018) for studies with mixed-effects models in reaction time experiments.”
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Lázaro, M., Özkan, Z., García, L., & Perea, M. (2026) · Language, Cognition and Neuroscience · doi:10.1080/23273798.2026.2619561 · Cited by 1
“The sample size, comprising 1,715 observations per condition, aligns with the recommendations of Brysbaert and Stevens (2018) for adequately powered statistical analyses.”
Invernizzi, S., Gilis, S., Bodart, A., Lefebvre, L., & Loureiro, I. S. (2026) · Acta Psychologica · doi:10.1016/j.actpsy.2026.106221
Rademacher, M., Espey, L., Ghio, M., & Bechtold, L. (2026) · PLoS ONE · doi:10.1371/journal.pone.0341113 · Cited by 1
“Notably, our sample size and design should have assured a power of > 75% to uncover a medium effect [66] as has been reported for the N400 emotionality effect by previous studies employing lexical decision tasks (e.g., η ² = 0.22 in [19], and ω ² = 0.25 in [20]).”
InfluentialYu, L.-S., & Kong, Q.-Q. (2026) · Frontiers in Psychology · doi:10.3389/fpsyg.2025.1734210 · Cited by 1
Speech onset time at home or in the lab: The role of testing environment and experimenter presence
Piazza, G., Kartushina, N., Souganidis, C., Flege, J., & Martin, C. D. (2026) · Behavior Research Methods · doi:10.3758/s13428-025-02918-6 · Cited by 1
“Briefly, following Brysbaert and Stevens (2018), an effect of ~15 ms would require about 1,600 observations per condition to reach 80% power.”
Whaling, K. M., Veed, G. J., & Loftin, R. L. (2026) · Neurodiversity · doi:10.1177/27546330251408867 · Cited by 2
The Role of Event Number and Duration in Time-Compressed Memory Replay
Leroy, N., & D’Argembeau, A. (2025) · Open Mind · doi:10.1162/opmi.a.276 · Cited by 2
“Our main statistical analyses were conducted using linear mixed-effects models (Brauer & Curtin, 2018), and the targeted sample size was determined using a power analysis based on Monte-Carlo simulations (Brysbaert & Stevens, 2018; DeBruine & Barr, 2021).”
Aoki, N. B., & Zellou, G. (2025) · Language and Speech · doi:10.1177/00238309251390505 · Cited by 1
“Given the lack of within-participant variables, a sufficiently large sample size is especially critical to ensure that any differences between conditions are not merely due to listener idi-osyncrasies (Brysbaert & Stevens, 2018).”
How time shapes letter position flexibility: Testing positional uncertainty and open bigram accounts
Romero-Ortells, I., Perea, M., Baciero, A., Gómez, P., & Marcet, A. (2025) · Psychonomic Bulletin & Review · doi:10.3758/s13423-025-02803-5 · Cited by 1
“This sample size provided 2,000 observations for each type of pseudoword and delay, following Brysbaert and Stevens’ (2018) recommendations for detecting small effects.”
Early access effects in English compound and pseudo-compound words
Spalding, T., Gagné, C., & Taikh, A. (2025) · Memory & Cognition · doi:10.3758/s13421-025-01819-5 · Cited by 1
“Participant and item sample sizes were determined following the guidelines from Brysbaert and Stevens (2018) of a minimum of 40 participants and 40 items (i.e., 1,600 observations) in each cell to detect main effects in priming studies.”
Bimodal Input in Processing and Learning of Novel Vocabulary During Reading: An Eye‐Tracking Study
Tuzcu, A., & Loewen, S. (2025) · Language Learning · doi:10.1111/lang.70017 · Cited by 1
Till, B., Niederkrotenthaler, T., & Naderer, B. (2025) · Journal of Medical Internet Research · doi:10.2196/79917 · Cited by 1
Effect of cone-opponent modulation on visual discomfort from chromatic flicker.
Matsumoto, J., Morita, A., Wilkins, A. J., & Yoshimoto, S. (2025) · Vision Research · doi:10.1016/j.visres.2025.108715 · Cited by 1
Feng, C., Zhai, M.-J., & Qu, Q.-Q. (2025) · Cortex; a journal devoted to the study of the nervous system and behavior · doi:10.1016/j.cortex.2025.10.011 · Cited by 1
Qianzhi, J. N. L., Gordon, G., Forrest, C., Yiend, J., & Martin, A. F. (2025) · Auditory Perception & Cognition · doi:10.1080/25742442.2025.2571366 · Cited by 1
L1 effects on the processing of L2 compounds: an eye-tracking study
El-Dakhs, D., Sonbul, S., & Siyanova-Chanturia, A. (2025) · Journal of Cognitive Psychology · doi:10.1080/20445911.2025.2567401 · Cited by 1
“It should be noted that our sample size could be expanded to meet recent recommendations against underpowered designs (e.g. Brysbaert & Stevens, 2018).”
Developmental differences in L1 and L2 text comprehension: An ERP study
Pérez, A. I. G., Montoro-Membila, N., Ortega, A., Aguirre, C., Togato, G., & Bajo, M. T. (2025) · Brain and Language · doi:10.1016/j.bandl.2025.105644 · Cited by 1
Eye-tracking as a lens into meta-reasoning
Dhengre, S., Ackerman, R., & Rothrock, L. (2025) · Thinking & Reasoning · doi:10.1080/13546783.2025.2558592 · Cited by 1
“We used a typical effect size of d = .40 in cognitive psychology (Brysbaert & Stevens, 2018).”
Labruna, L., Merrick, C. M., Peterchev, A. V., Inglis, B. A., Ivry, R. B., & Sheltraw, D. (2024) · eLife · doi:10.7554/elife.92088 · Cited by 9
“Cohen’s d was calculated based on the methods outlined in Brysbaert and Stevens, 2018 for mixed-effects models.”
Unseen consequences: the effect of activity-based work environments on work recovery
Valgeirsson, H., Halldórsson, F., & Kristinsson, K. (2025) · Current Research in Ecological and Social Psychology · doi:10.1016/j.cresp.2025.100239 · Cited by 3
Liu, B. (2025) · Journal of Speech Language and Hearing Research · doi:10.1044/2025_jslhr-24-00602 · Cited by 1
Capel, L. K., Bowers, E. M., Woolley, M. G., Soileau, K. J., Thomas, G., Levin, M. E., & Twohig, M. P. (2025) · Cognitive and Behavioral Practice · doi:10.1016/j.cbpra.2025.08.001 · Cited by 1
Александрович, А. И., Kotov, A., Guerra, E., Fedoriaieva, A., & Kotova, T. N. (2025) · Cognitive Science · doi:10.1111/cogs.70101 · Cited by 1
No evidence for a targeted memory reactivation effect on word-meaning priming
Ball, L. V., Kimel, E., Keller, V. G., Ward, E., Cairney, S. A., Mak, M. H., Li, L., Rodd, J. M., & Gaskell, M. G. (2025) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2025.109264 · Cited by 3
Reward as a facet of word meaning: Ratings of motivation for 8,601 English words
Giurgea, D.-I., Pexman, P. M., & Binney, R. J. (2025) · Behavior Research Methods · doi:10.3758/s13428-025-02762-8 · Cited by 5
“…coefficient (ICC), with variances estimated via a random effects model with a global intercept and a random intercept per word (Brysbaert, 2019; Brysbaert & Stevens, 2018), and Spearman–Brown corrected split-half reliability (using 100 random splits; splithalf.r function in multicon package…”
Razza, R. A., Zhang, Y., & Edelstein, A. (2025) · School Psychology International · doi:10.1177/01430343251361133 · Cited by 4
“Effect sizes representing Cohen ’ s d were calculated based on the following equation (Brysbaert & Stevens, 2018): Difference between the means…”
Grisetto, F., Roger, C., & Mahé, G. (2025) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2025.106347 · Cited by 1
‘Not my cup of tea’: The effect of proficiency, frequency, and congruency on L2 knowledge of idioms
Farooqui, A., & Sonbul, S. (2025) · Language Teaching Research · doi:10.1177/13621688251351019 · Cited by 1
Stilp, C. E., Adames, I., & Shorey, A. E. (2025) · PLoS ONE · doi:10.1371/journal.pone.0328490 · Cited by 1
“First, we followed the guidelines of Brysbaert and Stevens [43], who recommended 1600 observations in each condition as a target for properly powered experiments that are being analyzed using mixed-effects regressions.”
Brain potentials reveal how emotional arousal affects bilingual language control
Wang, T., Hu, H., Xu, H., Wang, X., Wang, Y., Yin, K., Chen, S., & Yang, Y. (2025) · Journal of Multilingual and Multicultural Development · doi:10.1080/01434632.2025.2526699
“The calculation indicated that a minimum of 19 participants was needed to achieve a medium effect size with a statistical power of 0.95 (Brysbaert and Stevens 2018).”
InfluentialTesting dialects with simulations : the status of pseudo-partitives in US English
Erbach, K., & Gergel, R. (2025) · Linguistica Brunensia · doi:10.5817/lb2025-38532 · Cited by 1
Cui, Y., & Liu, X. (2025) · Multilingua · doi:10.1515/multi-2024-0245 · Cited by 1
On the impact of syntactic and semantic information when processing words in sentences
Vandendaele, A., & Grainger, J. (2025) · Quarterly Journal of Experimental Psychology · doi:10.1177/17470218251350584 · Cited by 1
“This resulted in a total of 1600 observations per condition, as recommended by Brysbaert and Stevens (2018).”
Annoyance and memory performance in the presence of wind turbine sound
Garcia-Guerrero, S., Manohare, M., O’Hora, D. P., & King, E. A. (2025) · Journal of Environmental Psychology · doi:10.1016/j.jenvp.2025.102653 · Cited by 2
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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