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LOG-DAY MODEL + COHEN'S f + POWER -- boxa_b2_d0_5   [metric: # successes (count)]
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model: behavior ~ stim + log(day) + stim:log(day) + (1|rat)   (behavior = # successes (count))
log(day) uses 1-indexed training day (our day 0 = paper "Day 1")
observed groups: stim n=4, control n=3   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,38)=3.165  p(resid)=0.08322  p(Satt)=0.08246 (df=42)
  honest per-animal random slope (log-day): F(1,9.4)=2.59  p=0.1407
Cohen's f (interaction, partial eta^2=0.026) = 0.163  (small-medium; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+13.68, ratSD=0, resSD=14.91) ---

 true stim:log(day) = +13.68 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.18            |  0.42  <- observed
  5        |  0.43            |  0.59
  8        |  0.68            |  0.75
  12       |  0.81            |  0.88
  16       |  0.96            |  0.97
  24       |  0.98            |  0.99

 true stim:log(day) = +6.838 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.07            |  0.14  <- observed
  5        |  0.12            |  0.19
  8        |  0.17            |  0.19
  12       |  0.31            |  0.39
  16       |  0.43            |  0.49
  24       |  0.70            |  0.75

Read per-animal as the honest power; LME matches the paper's power code (optimistic).