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LOG-DAY MODEL + COHEN'S f + POWER -- right_only_d0_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=4, control n=3   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,68)=8.420  p(resid)=0.004998  p(Satt)=0.005011 (df=67)
  honest per-animal random slope (log-day): F(1,22.8)=7.55  p=0.01151
Cohen's f (interaction, partial eta^2=0.016) = 0.126  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+11.36, ratSD=4.91, resSD=11.42) ---

 true stim:log(day) = +11.36 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.43            |  0.79  <- observed
  5        |  0.88            |  0.95
  8        |  0.98            |  1.00
  12       |  1.00            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +5.68 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.13            |  0.29  <- observed
  5        |  0.30            |  0.42
  8        |  0.65            |  0.62
  12       |  0.78            |  0.82
  16       |  0.93            |  0.93
  24       |  0.99            |  0.99

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.