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POWER SIMULATION -- unmerge_d6_13
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model: behavior ~ stim + day + stim:day + (1|rat)   (success COUNT; day within-window)
observed groups: stim n=3, control n=2   nrep=120, alpha=0.05
ground truth: stim:day=+2.27/day, rat SD=7.12, residual SD=7.73, days=8

 true stim:day interaction = +2.27 (100% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.46            |  0.62  <- observed
  5        |  0.77            |  0.90
  8        |  0.95            |  0.99
  12       |  1.00            |  1.00
  16       |  1.00            |  1.00
  24       |  1.00            |  1.00

 true stim:day interaction = +1.13 (50% of observed)
  N/group  | per-animal power | LME power
  ------------------------------------------
  3        |  0.12            |  0.20  <- observed
  5        |  0.27            |  0.38
  8        |  0.41            |  0.47
  12       |  0.54            |  0.62
  16       |  0.72            |  0.74
  24       |  0.91            |  0.93

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.