Completion-First Analysis of Single-Leg Balance: Estimands, Participant-Level Inference and Simulation

Abstract

To estimate the probability advantage of one single-leg stance condition over another while retaining attempts that terminate before 30 s. A pairwise score assigned priority to stance completion, then compared duration between two terminated attempts or centre-of-pressure velocity between two completed attempts. Independent and matched effects, equal participant weighting, and bounds for technically missing velocity were derived. Eight six-state probability models were evaluated at 20, 60 and 120 independent participants per group, with 2,000 generated datasets per combination. Four additional settings contained three correlated attempts per participant. The 56,000 datasets were analysed using projection-based 95% Wald intervals; independent-attempt analyses also used a 499-resample percentile bootstrap. In an exact 16-record dataset, 37 wins, 25 losses and two ties gave a net advantage of 0.1875; pairing the same records by row gave zero. Across independent-attempt models, absolute simulated bias was at most 0.007351. Coverage was 0.9300–0.9530 for projection intervals and 0.9310–0.9570 for bootstrap intervals. A completion-probability difference of 0.20 was offset by a completed-sway contribution of −0.190125, leaving a net advantage of 0.009875. With correlated attempts, participant-level coverage was 0.9315–0.9420; treating attempts as independent reduced it to 0.7790–0.8080 and narrowed mean intervals by 33.97–34.50%. Completion, termination time and completed-stance sway define distinct contributions to the balance comparison. Participant-level inference preserves within-person dependence; the evaluated intervals retain finite-sample undercoverage. The evidence consists of mathematical derivations, constructed records and Monte Carlo data, without human force-platform measurements.