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LOG-DAY MODEL + COHEN'S f + POWER -- right_only_d0_13
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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=4, control n=3   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,80)=13.182  p(resid)=0.0004969  p(Satt)=0.0004951 (df=81)
  honest per-animal random slope (log-day): F(1,18.9)=11.35  p=0.003237
Cohen's f (interaction, partial eta^2=0.017) = 0.131  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+12.18, ratSD=5.40, resSD=10.82) ---

 true stim:log(day) = +12.18 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.68            |  0.97  <- observed
  5        |  1.00            |  1.00
  8        |  1.00            |  1.00
  12       |  1.00            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +6.09 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.25            |  0.47  <- observed
  5        |  0.53            |  0.69
  8        |  0.84            |  0.87
  12       |  0.93            |  0.96
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

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.