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LOG-DAY MODEL + COHEN'S f + POWER -- naive_a2_d6_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=6   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,61)=0.405  p(resid)=0.5267  p(Satt)=0.5268 (df=58)
  honest per-animal random slope (log-day): F(1,8.2)=0.20  p=0.663
Cohen's f (interaction, partial eta^2=0.002) = 0.047  (small; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+9.35, ratSD=9.78, resSD=11.90) ---

 true stim:log(day) = +9.35 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.07            |  0.10  <- observed
  5        |  0.19            |  0.19
  8        |  0.17            |  0.19
  12       |  0.25            |  0.25
  16       |  0.30            |  0.32
  24       |  0.42            |  0.42

 true stim:log(day) = +4.68 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.05            |  0.09  <- observed
  5        |  0.05            |  0.07
  8        |  0.07            |  0.10
  12       |  0.11            |  0.09
  16       |  0.07            |  0.07
  24       |  0.17            |  0.17

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.