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LOG-DAY MODEL + COHEN'S f + POWER -- boxa_a2_d6_10
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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(1,26)=0.252  p(resid)=0.6199  p(Satt)=0.6202 (df=24)
  honest per-animal random slope (log-day): F(1,6.0)=0.19  p=0.6783
Cohen's f (interaction, partial eta^2=0.004) = 0.065  (small; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+9.52, ratSD=6.32, resSD=8.30) ---

 true stim:log(day) = +9.52 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.02            |  0.06  <- observed
  5        |  0.09            |  0.13
  8        |  0.12            |  0.12
  12       |  0.11            |  0.17
  16       |  0.14            |  0.16
  24       |  0.32            |  0.34

 true stim:log(day) = +4.76 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.06            |  0.10  <- observed
  5        |  0.07            |  0.07
  8        |  0.05            |  0.07
  12       |  0.09            |  0.10
  16       |  0.09            |  0.12
  24       |  0.12            |  0.15

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.