==============================================================================
LOG-DAY MODEL + COHEN'S f + POWER -- boxa_b2_d6_10
==============================================================================
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=4, control n=2   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,26)=0.850  p(resid)=0.365  p(Satt)=0.3657 (df=24)
  honest per-animal random slope (log-day): F(1,6.0)=0.67  p=0.4431
Cohen's f (interaction, partial eta^2=0.014) = 0.118  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+18.32, ratSD=6.21, resSD=8.20) ---

 true stim:log(day) = +18.32 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.06            |  0.17
  5        |  0.17            |  0.26
  8        |  0.27            |  0.36
  12       |  0.41            |  0.42
  16       |  0.57            |  0.63
  24       |  0.75            |  0.78

 true stim:log(day) = +9.16 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.07            |  0.11
  5        |  0.10            |  0.12
  8        |  0.07            |  0.13
  12       |  0.16            |  0.15
  16       |  0.20            |  0.20
  24       |  0.31            |  0.31

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.