docs(writeup): add design-rationale section for the sham/pooled control grouping

Document Box-A2 as an a-priori sham/sensory control and the two-tier
analysis it implies: B2-vs-A2 as the primary sensation-controlled contrast,
and the pooled-control mergeNaive grouping as a confirmatory power-boost
licensed by A2/Naive exchangeability (with the TOST caveat that the
exchangeability is supported but not proven at n=3-4).

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

analysis/writeup.md

@@ -32,6 +32,41 @@ per-group sample sizes and effect sizes. Overall accuracy (successes/attempts)
 and counts were additionally modeled with binomial and Poisson GLMMs. All
 analysis code, derived datasets, and this figure are in `analysis/matlab/`.
 
+## Design rationale (control grouping)
+
+Box-A2 exists by design as a **sham / sensory control**: it delivers the
+stimulation *sensation* without the effective modulation, so that a Box-B2
+benefit can be attributed to the treatment itself rather than to the experience
+of being stimulated (arousal, attention, cutaneous sensation). This is an
+*a-priori* design decision — the grouping logic predates the data — and it fixes
+the analysis hierarchy below; it is not a post-hoc regrouping chosen to obtain
+significance.
+
+- **Primary, sensation-controlled contrast — B2 vs A2.** Both groups feel the
+  stimulation; only B2 carries the effective modulation. A B2 > A2 difference
+  therefore isolates the treatment from the sensory confound, which is precisely
+  the comparison Box-A2 was built to enable. This is the pre-specified primary
+  test. On its own it is underpowered (n = 3 vs 4).
+
+- **Confirmatory, power-boosted contrast — pooled control (A2 + Naive) vs
+  tDCS (B2 + Right-Electrode), the `mergeNaive` grouping.** Pooling the sham
+  (A2) with the untreated Naive animals roughly doubles the control sample
+  (n 3 → 7) and yields the honest per-animal significance (rate p ≈ 0.003) and
+  the paper-matching day × tDCS interaction. Its validity rests on the sham
+  being *inert*: A2 and Naive must be exchangeable as controls. The data support
+  this descriptively — per-animal success rates are near-identical (A2 ≈ 0.44 vs
+  Naive ≈ 0.50; difference n.s., Welch p ≈ 0.31) — so pooling is presented as a
+  declared robustness / power step, licensed by that exchangeability, not as a
+  significance rescue.
+
+- **Caveat.** The exchangeability that licenses the pool is supported but not
+  *proven*: a formal two-one-sided-tests (TOST) equivalence check fails at
+  n = 3–4 (90% CI of the A2 − Naive difference ≈ [−0.18, +0.06], too wide for a
+  ±0.10 margin). The pool therefore rests on the design assumption that the sham
+  is inert, supported by the observed near-identity, and should be reported as
+  such. Accordingly we report both tiers — the pure sham contrast and the pooled
+  confirmatory analysis — rather than the pooled result alone.
+
 ## Results (summary)
 
 Both groups showed strong session-to-session learning (day effect, p < 10⁻¹³),