analysis(matlab): add log(day) model + Cohen's f + power to every variation
Add variation_logpower.m (self-contained) + make_variation_logpower.m, dropping logpowersim.m + logpower_result.txt into all 28 variation folders. Matches the paper's power code: models behavior ~ stim + log(day) + stim:log(day) + (1|rat) (log(day+1), since our day 0 = paper Day 1), reports Cohen's f (partial eta^2 of the interaction) and the interaction under residual/Satterthwaite/honest random-slope DF, then runs the Monte-Carlo power sim on the log-day ground truth (per-animal cluster-honest + LME power). Notable: under log(day) the accumulating divergence is captured more sharply, so several full-window scenarios reach honest significance that were n.s. under raw day (e.g. right_only_d0_13 honest p=0.003, unmerge_d0_13 0.021, unmerge_d0_10 0.036); Cohen's f is small-medium (~0.10-0.34). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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==============================================================================
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LOG-DAY MODEL + COHEN'S f + POWER -- right_only_d0_10
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==============================================================================
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model: behavior ~ stim + log(day) + stim:log(day) + (1|rat) (success COUNT)
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log(day) uses 1-indexed training day (our day 0 = paper "Day 1")
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observed groups: stim n=4, control n=3 nrep=120, alpha=0.05
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--- fitted on real data ---
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stim x log(day) interaction: F(1,68)=8.420 p(resid)=0.004998 p(Satt)=0.005011 (df=67)
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honest per-animal random slope (log-day): F(1,22.8)=7.55 p=0.01151
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Cohen's f (interaction, partial eta^2=0.016) = 0.126 (small-medium; f: .10 small, .25 medium, .40 large)
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--- power simulation (log-day ground truth: stim:logday=+11.36, ratSD=4.91, resSD=11.42) ---
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true stim:log(day) = +11.36 (100% of observed)
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N/group | per-animal power | LME power
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------------------------------------------
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3 | 0.43 | 0.79 <- observed
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5 | 0.88 | 0.95
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8 | 0.98 | 1.00
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12 | 1.00 | 1.00
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16 | 1.00 | 1.00
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24 | 1.00 | 1.00
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true stim:log(day) = +5.68 (50% of observed)
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N/group | per-animal power | LME power
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------------------------------------------
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3 | 0.13 | 0.29 <- observed
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5 | 0.30 | 0.42
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8 | 0.65 | 0.62
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12 | 0.78 | 0.82
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16 | 0.93 | 0.93
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24 | 0.99 | 0.99
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Read the per-animal column as the honest power; the LME column matches the
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paper's power code (anova interaction p, observation-level DF) and is optimistic.
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