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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LOG-DAY MODEL + COHEN'S f + POWER -- naive_a2_d0_13
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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=3, control n=7 nrep=120, alpha=0.05
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--- fitted on real data ---
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stim x log(day) interaction: F(1,120)=6.786 p(resid)=0.01035 p(Satt)=0.01039 (df=116)
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honest per-animal random slope (log-day): F(1,5.5)=5.06 p=0.06966
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Cohen's f (interaction, partial eta^2=0.011) = 0.104 (small-medium; f: .10 small, .25 medium, .40 large)
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--- power simulation (log-day ground truth: stim:logday=+9.94, ratSD=8.36, resSD=14.40) ---
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true stim:log(day) = +9.94 (100% of observed)
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N/group | per-animal power | LME power
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------------------------------------------
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3 | 0.27 | 0.71 <- observed
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5 | 0.68 | 0.82
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8 | 0.97 | 0.97
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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) = +4.97 (50% of observed)
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N/group | per-animal power | LME power
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------------------------------------------
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3 | 0.12 | 0.25 <- observed
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5 | 0.27 | 0.31
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8 | 0.51 | 0.57
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12 | 0.62 | 0.68
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16 | 0.80 | 0.85
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24 | 0.92 | 0.93
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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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