analysis(matlab): rate + count outputs, variation batch 5

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

analysis/matlab/variations/unmerge_d6_13/logpower_result_rate.txt

@@ -0,0 +1,35 @@
+==============================================================================
+LOG-DAY MODEL + COHEN'S f + POWER -- unmerge_d6_13   [metric: success RATE]
+==============================================================================
+model: behavior ~ stim + log(day) + stim:log(day) + (1|rat)   (behavior = success RATE)
+log(day) uses 1-indexed training day (our day 0 = paper "Day 1")
+observed groups: stim n=3, control n=2   nrep=120, alpha=0.05
+
+--- fitted on real data ---
+stim x log(day) interaction: F(1,30)=1.838  p(resid)=0.1853  p(Satt)=0.1853 (df=30)
+  honest per-animal random slope (log-day): F(1,3.6)=0.01  p=0.9233
+Cohen's f (interaction, partial eta^2=0.016) = 0.129  (small-medium; f: .10 small, .25 medium, .40 large)
+
+--- power simulation (log-day ground truth: stim:logday=+0.1165, ratSD=0.04832, resSD=0.05061) ---
+
+ true stim:log(day) = +0.1165 (100% of observed)
+  N/group  | per-animal power | LME power
+  ------------------------------------------
+  3        |  0.28            |  0.46  <- observed
+  5        |  0.58            |  0.70
+  8        |  0.78            |  0.83
+  12       |  0.90            |  0.89
+  16       |  0.99            |  1.00
+  24       |  1.00            |  1.00
+
+ true stim:log(day) = +0.05823 (50% of observed)
+  N/group  | per-animal power | LME power
+  ------------------------------------------
+  3        |  0.08            |  0.17  <- observed
+  5        |  0.18            |  0.27
+  8        |  0.23            |  0.32
+  12       |  0.34            |  0.38
+  16       |  0.47            |  0.51
+  24       |  0.79            |  0.82
+
+Read per-animal as the honest power; LME matches the paper's power code (optimistic).