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LOG-DAY MODEL + COHEN'S f + POWER -- naive_a2_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=3, control n=7   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,120)=6.786  p(resid)=0.01035  p(Satt)=0.01039 (df=116)
  honest per-animal random slope (log-day): F(1,5.5)=5.06  p=0.06966
Cohen's f (interaction, partial eta^2=0.011) = 0.104  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+9.94, ratSD=8.36, resSD=14.40) ---

 true stim:log(day) = +9.94 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.27            |  0.71  <- observed
  5        |  0.68            |  0.82
  8        |  0.97            |  0.97
  12       |  1.00            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +4.97 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.12            |  0.25  <- observed
  5        |  0.27            |  0.31
  8        |  0.51            |  0.57
  12       |  0.62            |  0.68
  16       |  0.80            |  0.85
  24       |  0.92            |  0.93

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.