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LOG-DAY MODEL + COHEN'S f + POWER -- unmerge_d0_10
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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=3   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,57)=6.230  p(resid)=0.01548  p(Satt)=0.01528 (df=61)
  honest per-animal random slope (log-day): F(1,15.0)=5.28  p=0.0363
Cohen's f (interaction, partial eta^2=0.017) = 0.131  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+11.60, ratSD=0.00, resSD=12.93) ---

 true stim:log(day) = +11.60 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.34            |  0.69  <- observed
  5        |  0.82            |  0.92
  8        |  0.97            |  0.97
  12       |  1.00            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +5.80 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.10            |  0.25  <- observed
  5        |  0.26            |  0.40
  8        |  0.53            |  0.58
  12       |  0.61            |  0.72
  16       |  0.90            |  0.90
  24       |  0.97            |  0.97

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.