BALANCED ROTATION DESIGN: Position vs Persona Decomposition at N=5
CONTEXT: N=3 competency-rotation: position DOMINATES (η²=0.60 >> persona η²=0.25). N=5 pooled analysis (14 runs): η²(pos)=0.14, η²(per)=0.11 — BOTH WEAK, 75% unexplained. BUT massive confound: r(pos, persona_id)=0.79 across dataset (12/14 runs have identical position-persona mapping). Cannot decompose effects with existing data.
DESIGN: Latin square: 5 cyclic rotations × 3 seed sets = 15 runs. Each persona appears in each position EXACTLY ONCE per seed set. Rot0: [Alpha,Beta,Gamma,Delta,Epsilon] (standard) Rot1: [Beta,Gamma,Delta,Epsilon,Alpha] Rot2: [Gamma,Delta,Epsilon,Alpha,Beta] Rot3: [Delta,Epsilon,Alpha,Beta,Gamma] Rot4: [Epsilon,Alpha,Beta,Gamma,Delta]
This gives r(pos, persona_id)=0.00 by construction — ORTHOGONAL design. Enables clean 2-way ANOVA: position × persona → η² decomposition.
KEY QUESTION: Is N=5 hierarchy position-driven, persona-driven, or stochastic?
Dochkina 2603.28990: position→hierarchy is universal LLM property. N=3 confirmed: last speaker = sink 100%, η²(pos)=0.60. N=5: does this weaken (dilution) or does persona emerge above noise?