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LOG-DAY MODEL + COHEN'S f + POWER -- matched_current_d0_3
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model: behavior ~ stim + log(day) + stim:log(day) + (1|rat)   (success 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(1,20)=7.043  p(resid)=0.01524  p(Satt)=0.0139 (df=24)
  honest per-animal random slope (log-day): F(1,18.5)=7.24  p=0.01475
Cohen's f (interaction, partial eta^2=0.102) = 0.336  (medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+20.79, ratSD=0.00, resSD=9.99) ---

 true stim:log(day) = +20.79 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.39            |  0.77  <- observed
  5        |  0.84            |  0.93
  8        |  0.97            |  0.99
  12       |  1.00            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +10.40 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.11            |  0.23  <- observed
  5        |  0.33            |  0.47
  8        |  0.49            |  0.59
  12       |  0.80            |  0.79
  16       |  0.79            |  0.84
  24       |  0.95            |  0.97

Read the per-animal column as the honest power; the LME column matches the
paper's power code (anova interaction p, observation-level DF) and is optimistic.