==============================================================================
LOG-DAY MODEL + COHEN'S f + POWER -- unmerge_d6_10
==============================================================================
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(1,21)=0.581  p(resid)=0.4545  p(Satt)=0.4549 (df=20)
  honest per-animal random slope (log-day): F(1,5.0)=0.44  p=0.5382
Cohen's f (interaction, partial eta^2=0.011) = 0.106  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+16.98, ratSD=6.08, resSD=8.72) ---

 true stim:log(day) = +16.98 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.06            |  0.11  <- observed
  5        |  0.17            |  0.23
  8        |  0.22            |  0.31
  12       |  0.33            |  0.33
  16       |  0.47            |  0.50
  24       |  0.63            |  0.66

 true stim:log(day) = +8.49 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.07            |  0.11  <- observed
  5        |  0.09            |  0.11
  8        |  0.06            |  0.09
  12       |  0.12            |  0.14
  16       |  0.17            |  0.17
  24       |  0.26            |  0.26

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.