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LOG-DAY MODEL + COHEN'S f + POWER -- boxa_a2_d0_5
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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=4   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,38)=4.320  p(resid)=0.04447  p(Satt)=0.04382 (df=42)
  honest per-animal random slope (log-day): F(1,10.2)=3.63  p=0.0853
Cohen's f (interaction, partial eta^2=0.032) = 0.181  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+15.16, ratSD=0.00, resSD=14.15) ---

 true stim:log(day) = +15.16 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.22            |  0.51  <- observed
  5        |  0.55            |  0.68
  8        |  0.81            |  0.85
  12       |  0.95            |  0.97
  16       |  1.00            |  0.99
  24       |  1.00            |  1.00

 true stim:log(day) = +7.58 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.08            |  0.23  <- observed
  5        |  0.17            |  0.23
  8        |  0.24            |  0.27
  12       |  0.42            |  0.47
  16       |  0.55            |  0.58
  24       |  0.85            |  0.85

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.