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POWER SIMULATION -- boxa_a2_d0_5
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model: behavior ~ stim + day + stim:day + (1|rat)   (success COUNT; day within-window)
observed groups: stim n=3, control n=4   nrep=120, alpha=0.05
ground truth: stim:day=+4.68/day, rat SD=0.00, residual SD=12.01, days=6

 true stim:day interaction = +4.68 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.23            |  0.54  <- observed
  5        |  0.57            |  0.70
  8        |  0.85            |  0.88
  12       |  0.98            |  0.99
  16       |  0.99            |  0.99
  24       |  1.00            |  1.00

 true stim:day interaction = +2.34 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.08            |  0.20  <- observed
  5        |  0.17            |  0.23
  8        |  0.26            |  0.32
  12       |  0.44            |  0.52
  16       |  0.56            |  0.60
  24       |  0.82            |  0.84

Read the per-animal column as the honest power. At the observed N this study
is typically underpowered; per-animal power reaches ~0.8 only at larger N.