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LOG-DAY MODEL + COHEN'S f + POWER -- boxa_a2_d0_10   [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=3, control n=4   nrep=120, alpha=0.05

--- fitted on real data ---
stim x log(day) interaction: F(1,68)=3.821  p(resid)=0.05474  p(Satt)=0.05451 (df=72)
  honest per-animal random slope (log-day): F(1,14.6)=3.22  p=0.09348
Cohen's f (interaction, partial eta^2=0.009) = 0.097  (small; f: .10 small, .25 medium, .40 large)

--- power simulation (log-day ground truth: stim:logday=+8.69, ratSD=2.979e-15, resSD=13.42) ---

 true stim:log(day) = +8.69 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.23            |  0.47  <- observed
  5        |  0.57            |  0.72
  8        |  0.83            |  0.87
  12       |  0.98            |  0.99
  16       |  0.99            |  1.00
  24       |  1.00            |  1.00

 true stim:log(day) = +4.345 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.07            |  0.12  <- observed
  5        |  0.11            |  0.19
  8        |  0.30            |  0.38
  12       |  0.34            |  0.40
  16       |  0.62            |  0.64
  24       |  0.75            |  0.78

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