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LOG-DAY MODEL + COHEN'S f + POWER -- naive_boxa_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=7   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,69)=0.239  p(resid)=0.6263  p(Satt)=0.6264 (df=65)
  honest per-animal random slope (log-day): F(1,9.1)=0.07  p=0.8013
Cohen's f (interaction, partial eta^2=0.001) = 0.034  (small; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+6.70, ratSD=10.78, resSD=11.38) ---

 true stim:log(day) = +6.70 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.05            |  0.07  <- observed
  5        |  0.13            |  0.15
  8        |  0.11            |  0.17
  12       |  0.15            |  0.12
  16       |  0.23            |  0.25
  24       |  0.23            |  0.24

 true stim:log(day) = +3.35 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.05            |  0.08  <- observed
  5        |  0.04            |  0.07
  8        |  0.06            |  0.10
  12       |  0.05            |  0.05
  16       |  0.06            |  0.07
  24       |  0.12            |  0.11

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.