analysis(matlab): add per-variation power simulation (powersim.m + power_result.txt)
Add variation_power.m (self-contained Monte-Carlo power for the paper's stim x day interaction, using each folder's own data as ground truth; scores per-animal cluster-honest power + LME power across N=[3..24] and effect multipliers 1/0.5) and make_variation_power.m, which drops powersim.m into every variations/<name>/ folder and runs it, writing power_result.txt beside the existing data.csv/analyze.m/result.txt. Named powersim (not power) to avoid shadowing the MATLAB builtin. All 28 folders processed. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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==============================================================================
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POWER SIMULATION -- naive_boxa_d6_13
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==============================================================================
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model: behavior ~ stim + day + stim:day + (1|rat) (success COUNT; day within-window)
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observed groups: stim n=3, control n=7 nrep=120, alpha=0.05
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ground truth: stim:day=+0.87/day, rat SD=10.75, residual SD=11.53, days=8
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true stim:day interaction = +0.87 (100% of observed)
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N/group | per-animal power | LME power
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------------------------------------------
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3 | 0.07 | 0.11 <- observed
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5 | 0.17 | 0.21
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8 | 0.17 | 0.19
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12 | 0.23 | 0.23
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16 | 0.28 | 0.33
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24 | 0.38 | 0.41
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true stim:day interaction = +0.44 (50% of observed)
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N/group | per-animal power | LME power
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------------------------------------------
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3 | 0.06 | 0.10 <- observed
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5 | 0.05 | 0.08
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8 | 0.07 | 0.11
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12 | 0.06 | 0.08
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16 | 0.07 | 0.07
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24 | 0.16 | 0.15
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Read the per-animal column as the honest power. At the observed N this study
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is typically underpowered; per-animal power reaches ~0.8 only at larger N.
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