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LOG-DAY MODEL + COHEN'S f + POWER -- naive_boxa_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=8   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,134)=4.865  p(resid)=0.02911  p(Satt)=0.02918 (df=129)
  honest per-animal random slope (log-day): F(1,7.9)=3.22  p=0.1109
Cohen's f (interaction, partial eta^2=0.007) = 0.083  (small; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+8.27, ratSD=8.74, resSD=14.51) ---

 true stim:log(day) = +8.27 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.21            |  0.55  <- observed
  5        |  0.51            |  0.65
  8        |  0.88            |  0.90  <- observed
  12       |  0.97            |  1.00
  16       |  0.98            |  0.98
  24       |  1.00            |  1.00

 true stim:log(day) = +4.13 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.08            |  0.17  <- observed
  5        |  0.19            |  0.27
  8        |  0.42            |  0.42  <- observed
  12       |  0.47            |  0.51
  16       |  0.64            |  0.68
  24       |  0.76            |  0.78

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.