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LOG-DAY MODEL + COHEN'S f + POWER -- boxa_a2_d0_5   [metric: success RATE]
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model: behavior ~ stim + log(day) + stim:log(day) + (1|rat)   (behavior = success RATE)
log(day) uses 1-indexed training day (our day 0 = paper "Day 1")
observed groups: stim n=3, control n=4   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,38)=8.750  p(resid)=0.005301  p(Satt)=0.005517 (df=35)
  honest per-animal random slope (log-day): F(1,12.5)=7.35  p=0.01836
Cohen's f (interaction, partial eta^2=0.099) = 0.331  (medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+0.143, ratSD=0.0361, resSD=0.09377) ---

 true stim:log(day) = +0.143 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.41            |  0.80  <- observed
  5        |  0.80            |  0.93
  8        |  0.99            |  1.00
  12       |  1.00            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +0.07149 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.12            |  0.29  <- observed
  5        |  0.33            |  0.42
  8        |  0.50            |  0.58
  12       |  0.72            |  0.72
  16       |  0.86            |  0.87
  24       |  0.95            |  0.97

Read per-animal as the honest power; LME matches the paper's power code (optimistic).
