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POWER SIMULATION -- unmerge_d0_10
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model: behavior ~ stim + day + stim:day + (1|rat)   (success COUNT; day within-window)
observed groups: stim n=3, control n=3   nrep=120, alpha=0.05
ground truth: stim:day=+1.56/day, rat SD=5.35, residual SD=12.51, days=11

 true stim:day interaction = +1.56 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.15            |  0.31  <- observed
  5        |  0.44            |  0.56
  8        |  0.59            |  0.66
  12       |  0.88            |  0.90
  16       |  0.93            |  0.95
  24       |  0.99            |  1.00

 true stim:day interaction = +0.78 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.11            |  0.11  <- observed
  5        |  0.09            |  0.13
  8        |  0.22            |  0.23
  12       |  0.32            |  0.32
  16       |  0.47            |  0.47
  24       |  0.63            |  0.60

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.