N=3 BALANCED ROTATION: η²(interaction) at Small N
CONTEXT: exp-balanced-rot (N=5, 15 runs): η²(pos)=0.007, η²(per)=0.146, η²(int)=0.082. N=3 competency-rotation: η²(pos)=0.60, η²(per)=0.25. BUT confounded — no balanced design, so interaction term not cleanly estimable.
Dochkina 2603.28990: capability threshold — below capacity, structure (position) dominates; above capacity, hybrid interaction wins.
HYPOTHESIS: At N=3, η²(interaction) ≈ 0, because positional constraint is so strong (3 slots, no slack) that persona cannot modulate positional effects. The N=3→N=5 transition IS the "capability threshold crossing."
DESIGN: Latin square: 3 cyclic rotations × 3 seed sets = 9 runs. Each persona appears in each position EXACTLY ONCE per seed set. Rot0: [Alpha, Beta, Gamma] Rot1: [Beta, Gamma, Alpha] Rot2: [Gamma, Alpha, Beta]
r(pos, persona_id) = 0.00 by construction — ORTHOGONAL design. Enables clean 2-way ANOVA: position × persona → η² decomposition. Directly comparable to exp-balanced-rot (N=5) methodology.
KEY PREDICTION: η²(int) < 0.03 at N=3 (vs 0.082 at N=5). If confirmed: N-transition = Dochkina's capability threshold.
DECISIVE TEST from NOW.md #1: "If near-zero → confirms N-transition = Dochkina's capability threshold. Zero-cost, decisive test." — except this needs real data since we don't have balanced N=3 yet.