Single-leg stance duration: Interruption bounds and exact confidence coverage

Abstract

An observation-only stop during single-leg stance leaves a bounded amount of unobserved task time. At a fixed horizon, motor failure and withdrawal terminate the duration score, while verified horizon completion determines it exactly. This study derives sharp closed bounds for mean task duration and paired condition differences from termination codes and verified elapsed times. A bounded-mean confidence interval controls coverage of the entire population identified set for a fixed number of independent participants and prespecified endpoint ranges. Exact enumeration covers 90 binomial and 12 multinomial configurations. Twelve constructed pairs at a 30-second horizon give a mean difference of [−1.33, 2.00] seconds; deleting the two interrupted pairs gives 2.20 seconds for the remaining ten. With 20 independent pairs, a 5-second interruption time, and interruption probability 0.02, the normal-approximation interval has whole-set coverage of 33.24%. The bounded interval attains at least 99.59% coverage across all 102 configurations, above its 95% guarantee. Interruption associated with potential performance shifts the complete-case limit by ±3.43 seconds despite a zero underlying mean difference. These results quantify the effects of event classification, interruption timing, and endpoint range on duration uncertainty.