Neuroimaging Sample Size Calculator

Registered Report Considerations

Registered reports require pre-specification of sample size with a formal power analysis. For neuroimaging registered reports:

1. Specify the primary analysis (whole-brain vs. ROI) and the corresponding power analysis method
2. Use simulation-based power when possible; if not, use ROI-based power with conservative effect size estimates
3. Pre-specify the multiple comparison correction method and document its impact on required N
4. Include sensitivity analysis: What is the minimum detectable effect size at the planned N?
5. State stopping rules: Pre-register the exact N and analysis plan; sequential analysis requires adjustment (Lakens, 2014)
6. Account for attrition: Specify expected exclusion rate (typically 10-20% for fMRI) and over-recruit

Domain insight: Reviewers will be suspicious of power analyses based on large effect sizes from small pilot studies. Use conservative (deflated) effect size estimates and show power curves across a range of plausible effect sizes.

Practical Workflow for Grant Applications

When Pilot Data Are Available

1. Run fMRIpower or NeuroPowerTools with pilot maps
2. Generate power curves showing power vs. N for the primary contrast and ROI
3. Select N that achieves 80-90% power for the primary analysis
4. Add 15-20% for expected participant exclusions
5. Report: pilot study details, effect size estimates, power tool used, correction method, target power, final N

When No Pilot Data Are Available

1. Search NeuroVault for comparable paradigms; download unthresholded maps
2. Use NeuroPowerTools with the published map
3. Alternatively, estimate ROI-level effect sizes from published papers:

• Extract t-values and convert to Cohen's d
• Apply deflation (multiply by 0.5-0.75; Button et al., 2013)
• Use G*Power for ROI-based power

4. As a last resort, use the benchmark table above with the analysis type closest to your planned study
5. Document all assumptions and state that the power analysis is based on estimated (not measured) effect sizes

Common Pitfalls

1. Using G*Power for whole-brain analyses: Standard power tools compute power for a single test and do not account for multiple comparison correction. This overestimates power by an order of magnitude (Mumford & Nichols, 2008)
2. Trusting pilot study effect sizes: Small pilot studies (N < 20) produce inflated effect sizes. Always deflate by 25-50% (Button et al., 2013)
3. Ignoring the correction method: Power depends critically on whether you use voxelwise FWE, cluster-based, FDR, or permutation-based correction. Power at FDR q < 0.05 can be 2-3x higher than voxelwise FWE p < 0.05 for the same N
4. Conflating within-subject and between-subject power: Within-subject designs (one-sample t-test on contrast maps) are much more powerful than between-subject designs (two-sample t-test) because they eliminate between-subject variance (Mumford & Nichols, 2008)
5. Not accounting for attrition: In fMRI, 10-20% of data may be unusable due to motion, scanner artifacts, or task non-compliance. Over-recruit accordingly
6. Treating all regions equally: Power varies across the brain because effect sizes and noise vary spatially. Power at your primary ROI may be adequate even if whole-brain power is low
7. Assuming published N is adequate: Most published fMRI studies are underpowered (Button et al., 2013). Matching a published study's N does not guarantee adequate power
8. Not reporting sensitivity analysis: Always report the minimum detectable effect size at your planned N, in addition to the power estimate for the expected effect

Minimum Reporting Checklist

• Source of effect size estimate (pilot data, published study, meta-analysis)
• Effect size metric (Cohen's d, r, percent signal change) and value used
• Whether effect size deflation was applied and the correction factor
• Power analysis method (simulation-based, ROI-based analytical, benchmark-based)
• Power analysis tool and version (fMRIpower, NeuroPowerTools, G*Power, custom simulation)
• Number of simulations (for simulation-based approaches)
• Multiple comparison correction method assumed in power analysis
• Statistical threshold used (e.g., CDT p < 0.001, cluster p < 0.05 FWE)
• Target power level (80% or 90%)
• Planned total N and N per group (if applicable)
• Expected attrition rate and over-recruitment plan
• Sensitivity analysis (minimum detectable effect at planned N)

References

• Button, K. S., Ioannidis, J. P. A., Mokrysz, C., et al. (2013). Power failure: Why small sample size undermines the reliability of neuroscience. Nature Reviews Neuroscience, 14(5), 365-376.
• Cox, R. W., Chen, G., Glen, D. R., Reynolds, R. C., & Taylor, P. A. (2017). FMRI clustering in AFNI: False-positive rates redux. Brain Connectivity, 7(3), 152-171.
• Desmond, J. E., & Glover, G. H. (2002). Estimating sample size in functional MRI (fMRI) neuroimaging studies. Journal of Neuroscience Methods, 118(2), 115-128.
• Durnez, J., Degryse, J., Moerkerke, B., et al. (2016). Power and sample size calculations for fMRI studies based on the prevalence of active peaks. bioRxiv, 049429.
• Eklund, A., Nichols, T. E., & Knutsson, H. (2016). Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates. PNAS, 113(28), 7900-7905.
• Joyce, K. E., & Hayasaka, S. (2012). Development of PowerMap: A software package for statistical power calculation in neuroimaging studies. Neuroinformatics, 10(4), 351-365.
• Laird, A. R., Fox, P. M., Price, C. J., et al. (2005). ALE meta-analysis: Controlling the false discovery rate and performing statistical contrasts. Human Brain Mapping, 25(1), 155-164.
• Lakens, D. (2014). Performing high-powered studies efficiently with sequential analyses. European Journal of Social Psychology, 44(7), 701-710.
• Marek, S., Tervo-Clemmens, B., Calabro, F. J., et al. (2022). Reproducible brain-wide association studies require thousands of individuals. Nature, 603(7902), 654-660.
• Mumford, J. A., & Nichols, T. E. (2008). Power calculation for group fMRI studies accounting for arbitrary design and temporal autocorrelation. NeuroImage, 39(1), 261-268.
• Poldrack, R. A., Baker, C. I., Durnez, J., et al. (2017). Scanning the horizon: Towards transparent and reproducible neuroimaging research. Nature Reviews Neuroscience, 18(2), 115-126.
• Salo, T., Yarkoni, T., Nichols, T. E., et al. (2023). NiMARE: Neuroimaging Meta-Analysis Research Environment. NeuroImage, 268, 119862.
• Smith, S. M., Miller, K. L., Salimi-Khorshidi, G., et al. (2011). Network modelling methods for FMRI. NeuroImage, 54(2), 875-891.
• Thirion, B., Pinel, P., Meriaux, S., et al. (2007). Analysis of a large fMRI cohort: Statistical and methodological issues for group analyses. NeuroImage, 35(1), 105-120.
• Turner, B. O., Paul, E. J., Miller, M. B., & Barbey, A. K. (2018). Small sample sizes reduce the replicability of task-based fMRI studies. Communications Biology, 1, 62.
• Yarkoni, T., Poldrack, R. A., Nichols, T. E., Van Essen, D. C., & Wager, T. D. (2011). Large-scale automated synthesis of human functional neuroimaging data. Nature Methods, 8(8), 665-670.

See references/ for worked examples and simulation code templates.