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LOG-DAY MODEL + COHEN'S f + POWER -- unmerge_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=2   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,30)=3.007  p(resid)=0.09315  p(Satt)=0.0931 (df=30)
  honest per-animal random slope (log-day): F(1,12.8)=2.47  p=0.1406
Cohen's f (interaction, partial eta^2=0.025) = 0.161  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+22.97, ratSD=7.14, resSD=7.81) ---

 true stim:log(day) = +22.97 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.47            |  0.64  <- observed
  5        |  0.79            |  0.90
  8        |  0.96            |  0.99
  12       |  0.99            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +11.49 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.12            |  0.22  <- observed
  5        |  0.26            |  0.36
  8        |  0.41            |  0.47
  12       |  0.53            |  0.58
  16       |  0.71            |  0.74
  24       |  0.90            |  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.