Cited by 1,420Statistical Methods and Bayesian InferenceMeta-analysis and systematic reviewsPsychology Research and Bibliometrics

Power Analysis and Effect Size in Mixed Effects Models: A Tutorial

Open access
Brysbaert, Marc, Stevens, Michaël·2018·Journal of Cognition

Published 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.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.5334/joc.10

Cites

49 of 49 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Aggregations provide independent observations for non-parametric testing and make it appropriate when dealing with small sample sizes and repeated measures.

    “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]

    The ‘Traditional F1 and F2 analysis’ section describes averaging repeated observations for each participant before analysis, which supports the aggregation part of the claim. It enters those averages into repeated-measures ANOVA or a paired t-test, not a non-parametric test. The paper does not say that aggregation makes non-parametric testing appropriate for small samples or establishes independent observations. (LLM, conf=0.85)

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

1 of the 50 references couldn’t be matched to a known paper.

Cited by

Sorted by citations

Authors
Brysbaert, M., & Stevens, M.
Affiliations
Ghent University (BE)
Corresponding author
Brysbaert, Marc
Venue
Journal of Cognition
Published
2018
Volume
1
Issue
1
Pages
9-9
ISSN
2514-4820 (ISSN-L)
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 · 2013: 1
FWCI
82.16
Type
journal article
Language
en
Open access
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

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 ›

Are you an author, or do you see a problem with this page? Request a review