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LOG-DAY MODEL + COHEN'S f + POWER -- unmerge_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=3   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,32)=10.951  p(resid)=0.002322  p(Satt)=0.00244 (df=30)
  honest per-animal random slope (log-day): F(1,8.5)=8.07  p=0.02043
Cohen's f (interaction, partial eta^2=0.109) = 0.350  (medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+0.1553, ratSD=0.04445, resSD=0.08516) ---

 true stim:log(day) = +0.1553 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.54            |  0.90  <- observed
  5        |  0.93            |  0.97
  8        |  1.00            |  1.00
  12       |  1.00            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +0.07765 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.13            |  0.38  <- observed
  5        |  0.44            |  0.54
  8        |  0.72            |  0.73
  12       |  0.81            |  0.88
  16       |  0.94            |  0.97
  24       |  1.00            |  1.00

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