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analysis(matlab): add per-variation power simulation (powersim.m + power_result.txt)

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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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Experiments DB Dev
2026-07-23 13:57:25 -04:00
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analysis/matlab/variations/boxa_a2_d0_10/power_result.txt
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==============================================================================
POWER SIMULATION -- boxa_a2_d0_10
==============================================================================
model: behavior ~ stim + day + stim:day + (1|rat) (success COUNT; day within-window)
observed groups: stim n=3, control n=4 nrep=120, alpha=0.05
ground truth: stim:day=+1.20/day, rat SD=0.00, residual SD=13.47, days=11
true stim:day interaction = +1.20 (100% of observed)
N/group | per-animal power | LME power
------------------------------------------
3 | 0.07 | 0.17 <- observed
5 | 0.20 | 0.24
8 | 0.35 | 0.43
12 | 0.62 | 0.67
16 | 0.72 | 0.72
24 | 0.88 | 0.88
true stim:day interaction = +0.60 (50% of observed)
N/group | per-animal power | LME power
------------------------------------------
3 | 0.07 | 0.08 <- observed
5 | 0.05 | 0.07
8 | 0.10 | 0.11
12 | 0.17 | 0.18
16 | 0.29 | 0.30
24 | 0.31 | 0.33
Read the per-animal column as the honest power. At the observed N this study
is typically underpowered; per-animal power reaches ~0.8 only at larger N.