experiments-database/analysis/writeup.md

tDCS reaching study — figure and methods

Figure 1. (A) Mean ± SEM successful reaches per session over the common 0–13 training-day window for the tDCS (Box-B2, blue) and control (Box-A2, green) groups; the dashed line marks the fast/slow phase boundary. (B) Per-animal learning slope (mean, 95% CI) in the fast (0–5) and slow (6–13) phases.

Methods

The number of successful reaches per session was modeled as a function of training day and stimulation condition. Sessions were indexed by training day (day 0 = the first analyzed day, i.e. the previous study's "Day 1"), and the two electrode conditions were compared as a binary tDCS factor (Box-B2 = tDCS, Box-A2 = control; n = 3–5 animals per group). We fit linear mixed-effects models (MATLAB R2025b, fitlme, Statistics and Machine Learning Toolbox) of the form successes ~ day * tDCS + (1 | subject) with a per-subject random intercept; the tDCS main effect (day centered at each window's first day) estimates the Day-1 group difference and the day × tDCS interaction estimates the difference in learning rate. Because the anchor groups' day coverage was unequal over the full range (Box-A2 data ended ~day 13 while Box-B2 continued), analyses were restricted to the common 0–13 window and, to separate acquisition from plateau, refit within a fast (days 0–5) and slow (days 6–13) phase. Given the small number of animals, the subject was treated as the unit of inference: per-animal learning slopes were compared between groups (Welch t, Mann–Whitney) and within groups across phases (paired t); the fitlme interaction tests, which use observation-level degrees of freedom, are anticonservative at this sample size and are reported only as a reference. Statistical power was estimated by Monte-Carlo simulation from the fitted early-phase model across a range of 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), following a fast-then-slow trajectory (Fig. 1A): steep gains over days 0–5 that flattened toward a plateau by day 13. The tDCS and control groups performed comparably on Day 1 (tDCS main effect n.s.), and the tDCS group acquired faster during the early phase (Fig. 1B; slope ≈ 15 vs 10 reaches/day; interaction +4.6, 95% CI [+1.0, +8.2]), converging by the late phase. At the subject level this early-phase difference was a consistent trend but did not reach significance (Welch p ≈ 0.11–0.25), and the study was underpowered at n = 3–5/group (≈30–70% power for the observed effect; ≈8/group would be needed for the observed effect, ≈20/group for half that, to reach 80% power). This is consistent with the previously reported days × tDCS interaction, here compressed into the early acquisition phase — plausibly because the improved protocol's higher performance ceiling leaves little late-phase headroom for a benefit to accumulate.