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LOG-DAY MODEL + COHEN'S f + POWER -- boxa_b2_d0_10   [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=4, control n=3   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,68)=5.859  p(resid)=0.01817  p(Satt)=0.0182 (df=67)
  honest per-animal random slope (log-day): F(1,21.8)=5.17  p=0.03322
Cohen's f (interaction, partial eta^2=0.013) = 0.115  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+10.4, ratSD=5.517, resSD=12.53) ---

 true stim:log(day) = +10.4 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.32            |  0.62  <- observed
  5        |  0.78            |  0.87
  8        |  0.93            |  0.97
  12       |  1.00            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +5.199 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.10            |  0.20  <- observed
  5        |  0.17            |  0.31
  8        |  0.45            |  0.53
  12       |  0.57            |  0.60
  16       |  0.86            |  0.85
  24       |  0.93            |  0.93

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