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LOG-DAY MODEL + COHEN'S f + POWER -- unmerge_d0_5
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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(1,32)=4.849  p(resid)=0.03498  p(Satt)=0.03414 (df=36)
  honest per-animal random slope (log-day): F(1,7.2)=3.65  p=0.09636
Cohen's f (interaction, partial eta^2=0.039) = 0.200  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+16.48, ratSD=0.00, resSD=13.58) ---

 true stim:log(day) = +16.48 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.33            |  0.64  <- observed
  5        |  0.66            |  0.78
  8        |  0.93            |  0.97
  12       |  0.99            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +8.24 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.09            |  0.24  <- observed
  5        |  0.21            |  0.29
  8        |  0.28            |  0.38
  12       |  0.47            |  0.59
  16       |  0.69            |  0.69
  24       |  0.90            |  0.92

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.