# Cogsci Power Analysis

> Domain-specific statistical power analysis guidance for cognitive and neuroscience research, encoding effect size priors and sample size recommendations by modality

- Skill: `neuroaihub/cogsci-power-analysis` (Agent Skill, multi-file: 3 files)
- Install (CLI): `npx skillmds@latest add neuroaihub/cogsci-power-analysis`
- Raw SKILL.md: https://api.skillmd.com/api/skills/neuroaihub/cogsci-power-analysis/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Research & Search
- Author: neuroaihub (https://skillmd.com/u/neuroaihub)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/neuroaihub/cogsci-power-analysis

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# Cognitive Science Power Analysis

## Purpose

This skill encodes domain-specific knowledge for planning adequately powered studies in cognitive science and neuroscience. It provides:

- **Effect size priors** calibrated to specific paradigms and modalities (behavioral, EEG/ERP, fMRI, clinical/developmental)
- **Sample size recommendations** grounded in empirical meta-analyses rather than arbitrary conventions
- **Power analysis workflow guidance** tailored to the design complexities of cognitive neuroscience (repeated measures, multilevel, neuroimaging-specific tools)

An AI agent needs this because generic power analysis advice (e.g., "use G*Power with d = 0.5") fails to capture the enormous variability in effect sizes across cognitive science paradigms, and because neuroimaging modalities have unique statistical considerations.

## When to Use This Skill

- A researcher is designing a new behavioral, EEG, or fMRI experiment and needs sample size justification
- A grant proposal requires a power analysis section
- A preregistration document needs effect size justification and sample size rationale
- Someone asks "how many participants do I need?" for a cognitive/neuroscience study
- Reviewing whether a published study was adequately powered

## Research Planning Protocol

Before executing the domain-specific steps below, you MUST:

1. **State the research question** — What study is being planned and what effect is being powered for?
2. **Justify the method choice** — Why this design and analysis approach? What alternatives were considered?
3. **Declare expected outcomes** — What is the smallest effect size of interest (SESOI)?
4. **Note assumptions and limitations** — What assumptions does this power analysis make? Where could it mislead?
5. **Present the plan to the user and WAIT for confirmation** before proceeding.

For detailed methodology guidance, see the `research-literacy` skill.


## ⚠️ Verification Notice

This skill was generated by AI from academic literature. All parameters, thresholds, and citations require independent verification before use in research. If you find errors, please [open an issue](https://github.com/HaoxuanLiTHUAI/awesome_cognitive_and_neuroscience_skills/issues).

## Core Workflow

### Step 1: Identify the Research Modality and Design

Determine which modality and design type apply:

| Modality | Common Designs | Key Consideration |
|----------|---------------|-------------------|
| Behavioral | Between-groups, within-subjects, mixed | Effect sizes vary enormously by paradigm |
| EEG/ERP | Within-subjects repeated measures | Trial count matters as much as participant count |
| fMRI (task) | Within-subjects block/event-related | Whole-brain vs. ROI analysis affects power |
| fMRI (individual differences) | Correlational, between-subjects | Requires much larger N than task contrasts |
| Clinical/Developmental | Case-control, longitudinal | Recruitment constraints often limit N; adjust design |

### Step 2: Obtain an Effect Size Prior

**Do not use generic benchmarks** (Cohen's "small/medium/large"). Instead:

1. **Best option**: Use a meta-analytic estimate for the specific paradigm. See `references/effect-sizes.md` for a curated library organized by modality.
2. **Second option**: Use the smallest effect size of interest (SESOI) — the minimum effect that would be theoretically or practically meaningful (Lakens, 2022).
3. **Third option**: Use pilot data, but apply shrinkage correction — pilot studies systematically overestimate effect sizes (Albers & Lakens, 2018).
4. **Last resort**: Use the modality-specific median effect sizes from large-scale meta-analyses (see below).

**Modality-level median effect sizes (use only when paradigm-specific estimates are unavailable):**

| Modality | Median Effect Size | Source |
|----------|--------------------|--------|
| Behavioral (cognitive psychology) | d = 0.40 | Brysbaert, 2019 |
| EEG/ERP component differences | d = 0.50 - 1.00 | Boudewyn et al., 2018; Clayson et al., 2019 |
| fMRI task activation | d = 0.75 - 1.00 (within-subject) | Poldrack et al., 2017 |
| fMRI brain-behavior correlation | r = 0.10 - 0.20 | Marek et al., 2022 |
| Clinical group differences | d = 0.30 - 0.80 | Leucht et al., 2015; Button et al., 2013 |

> **Critical warning**: The median statistical power in neuroscience has been estimated at only **21%** (Button et al., 2013, Nature Reviews Neuroscience). Many published effect sizes are inflated by publication bias. Always apply skepticism to effect sizes from underpowered, unreplicated studies.

### Step 3: Conduct the Power Analysis

Choose method based on design complexity:

#### Simple Designs (t-test, one-way ANOVA, correlation)

Use **analytic solutions** via G*Power or pwr (R):

```
Target: 80% power (minimum) or 90% power (recommended)
Alpha: 0.05 (two-tailed unless directional hypothesis is justified)
```

- Two-sample t-test: `pwr.t.test(d = effect_size, power = 0.80, sig.level = 0.05, type = "two.sample")`
- Within-subjects t-test: `pwr.t.test(d = effect_size_dz, power = 0.80, sig.level = 0.05, type = "paired")`
- Correlation: `pwr.r.test(r = effect_size, power = 0.80, sig.level = 0.05)`

#### Complex Designs (mixed ANOVA, multilevel, mediation)

Use **simulation-based power analysis**:

- **simr** (R package): For linear mixed-effects models (Green & MacLeod, 2016)
- **Superpower** (R/Shiny): For factorial ANOVA designs (Lakens & Caldwell, 2021)
- **Monte Carlo simulation**: For non-standard designs — simulate data under the expected effect, run analysis, repeat 10,000+ times

#### Neuroimaging-Specific

- **fMRIpower**: Power for fMRI group analyses (Mumford & Nichols, 2008)
- **NeuroPowerTools**: Web-based fMRI power calculator (Durnez et al., 2016)
- **For EEG/ERP**: No standard tool; use simulation with expected component amplitudes and noise levels. See `references/sample-size-guide.md` for worked examples.

### Step 4: Apply Modality-Specific Rules of Thumb

Use these as **sanity checks**, not replacements for formal power analysis:

| Modality | Minimum N (per group/condition) | Basis |
|----------|-------------------------------|-------|
| Behavioral (medium effect, d ≈ 0.5) | n = 30-50 per group | Brysbaert, 2019 |
| Behavioral (small effect, d ≈ 0.2) | n = 80-100 per group | Brysbaert, 2019 |
| Behavioral (within-subjects, d_z ≈ 0.4) | n = 50-65 | Brysbaert, 2019 |
| EEG/ERP (within-subjects) | n = 25-40 | Boudewyn et al., 2018 |
| fMRI (task activation, within-subjects) | n = 30-50 | Cremers et al., 2017; Poldrack et al., 2017 |
| fMRI (individual differences / brain-behavior) | n = 100+ (ideally 200+) | Marek et al., 2022 |
| fMRI (clinical group comparison) | n = 30-50 per group | Button et al., 2013 |
| Clinical/patient studies | n = 20-30 per group (minimum) | Leucht et al., 2015 |
| Developmental (cross-sectional age groups) | n = 25-40 per age group | Mills & Tamnes, 2014 |

### Step 5: Document and Report

For preregistration and manuscripts, the power analysis section must include:

1. **Effect size used** and its source (meta-analysis, pilot, SESOI)
2. **Power analysis method** (analytic, simulation-based, tool used)
3. **Target power level** (80% or 90%) and alpha level
4. **Resulting sample size** and any adjustments (attrition, exclusion rate)
5. **Sensitivity analysis**: What is the minimum detectable effect at the planned N?

Template language:

> "Based on the meta-analytic effect size of d = [X] reported by [Author, Year], a power analysis using [tool] indicated that N = [X] participants per group would be needed to detect this effect with [80/90]% power at alpha = .05 (two-tailed). Anticipating a [X]% attrition/exclusion rate, we plan to recruit N = [adjusted X]."

## Common Pitfalls

1. **Using Cohen's generic benchmarks as effect size priors**: Cohen (1988) himself warned these were rough guidelines. Cognitive science effects range from d = 0.1 to d = 3.0+ depending on the paradigm. Always use paradigm-specific estimates (Brysbaert, 2019).

2. **Ignoring the distinction between d and d_z**: Between-subjects Cohen's d and within-subjects d_z are not interchangeable. Within-subjects designs typically yield larger d_z due to reduced error variance. Confusing them leads to incorrect sample size estimates (Lakens, 2013).

3. **Powering for whole-brain fMRI but reporting ROI results (or vice versa)**: Whole-brain analyses with multiple comparison correction require larger effects to survive thresholding. Power calculations must match the planned analysis (Mumford & Nichols, 2008).

4. **Treating pilot effect sizes as population estimates**: Pilot studies with N = 10-20 produce wildly variable effect size estimates. Apply a correction factor or use the lower bound of the CI (Albers & Lakens, 2018).

5. **Ignoring trial count in EEG/ERP power**: For ERP analyses, both participant N and trial count per condition affect statistical power. Insufficient trials per condition reduces signal-to-noise ratio regardless of participant count (Boudewyn et al., 2018; Luck, 2014).

6. **Assuming brain-behavior correlations are large**: Marek et al. (2022) demonstrated that brain-wide association studies require thousands of participants for reliable effects. Planning an fMRI individual-differences study with N = 30 is almost certainly underpowered.

## Quick Reference Decision Table

| Question | Answer | Recommended Action |
|----------|--------|--------------------|
| "How many subjects for a Stroop study?" | Within-subjects Stroop effect is very large (d ≈ 1.0-1.5) | N = 15-25 likely sufficient (Brysbaert, 2019) |
| "How many for an ERP study of N400?" | N400 semantic violation effect d ≈ 0.8-1.5 | N = 20-30 (Boudewyn et al., 2018) |
| "How many for fMRI brain-behavior correlation?" | True r likely 0.10-0.20 | N = 200+ minimum (Marek et al., 2022) |
| "How many for a patient vs. control comparison?" | Effects vary widely (d ≈ 0.3-0.8) | N = 30-80 per group depending on expected effect |
| "Can I use my pilot N=12 effect size?" | Pilot effect is unreliable | Use meta-analytic estimate instead; if unavailable, use lower CI bound of pilot |

## References

- Albers, C., & Lakens, D. (2018). When power analyses based on pilot data are biased. *Journal of Experimental Social Psychology*, 74, 187-195.
- Boudewyn, M. A., Luck, S. J., Farrens, J. L., & Kappenman, E. S. (2018). How many trials does it take to get a significant ERP effect? *Psychophysiology*, 55(6), e13049.
- Brysbaert, M. (2019). How many participants do we really need? *Journal of Cognition*, 2(1), 16.
- Button, K. S., Ioannidis, J. P. A., Mokrysz, C., Nosek, B. A., Flint, J., Robinson, E. S. J., & Munafo, M. R. (2013). Power failure: Why small sample size undermines the reliability of neuroscience. *Nature Reviews Neuroscience*, 14(5), 365-376.
- Clayson, P. E., Carbine, K. A., Baldwin, S. A., & Larson, M. J. (2019). Methodological reporting behavior, sample sizes, and statistical power in studies of event-related potentials. *Psychophysiology*, 56(11), e13437.
- Cremers, H. R., Wager, T. D., & Yarkoni, T. (2017). The relation between statistical power and inference in fMRI. *PLoS ONE*, 12(11), e0184923.
- Green, P., & MacLeod, C. J. (2016). SIMR: An R package for power analysis of generalized linear mixed models by simulation. *Methods in Ecology and Evolution*, 7(4), 493-498.
- Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science. *Frontiers in Psychology*, 4, 863.
- Lakens, D. (2022). Sample size justification. *Collabra: Psychology*, 8(1), 33267.
- Lakens, D., & Caldwell, A. R. (2021). Simulation-based power analysis for factorial ANOVA designs. *Advances in Methods and Practices in Psychological Science*, 4(1).
- Leucht, S., Hierl, S., Kissling, W., Dold, M., & Davis, J. M. (2015). Putting the efficacy of psychiatric and general medicine medication into perspective. *British Journal of Psychiatry*, 200(2), 97-106.
- Luck, S. J. (2014). *An Introduction to the Event-Related Potential Technique* (2nd ed.). MIT Press.
- Marek, S., Tervo-Clemmens, B., Calabro, F. J., et al. (2022). Reproducible brain-wide association studies require thousands of individuals. *Nature*, 603, 654-660.
- Mills, K. L., & Tamnes, C. K. (2014). Methods and considerations for longitudinal structural brain imaging analysis across development. *Developmental Cognitive Neuroscience*, 9, 172-190.
- 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.

See `references/effect-sizes.md` for the full effect size reference library and `references/sample-size-guide.md` for detailed sample size guidance by modality.