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LOG-DAY MODEL + COHEN'S f + POWER -- unmerge_d0_13   [metric: # successes (count)]
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model: behavior ~ stim + log(day) + stim:log(day) + (1|rat)   (behavior = # successes (count))
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(1,66)=8.712  p(resid)=0.004373  p(Satt)=0.004357 (df=67)
  honest per-animal random slope (log-day): F(1,12.9)=6.96  p=0.02062
Cohen's f (interaction, partial eta^2=0.015) = 0.124  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+11.06, ratSD=5.676, resSD=11.36) ---

 true stim:log(day) = +11.06 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.53            |  0.91  <- observed
  5        |  0.99            |  1.00
  8        |  1.00            |  1.00
  12       |  1.00            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +5.528 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.18            |  0.38  <- observed
  5        |  0.41            |  0.54
  8        |  0.78            |  0.80
  12       |  0.86            |  0.91
  16       |  0.97            |  0.98
  24       |  0.98            |  0.98

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