An Equivalence Testing Approach to the Calculation of Time to Stabilization Following Drop Landing on Force Plates in...

Current time to stabilization (TTS) calculation methods use a signal-to-threshold approach, whereby post-landing ground reaction forces (GRFs) are compared against fixed thresholds derived from a stable period. This approach does not formally test statistical equivalence and may be sensitive to arbitrary processing and threshold selection. This study proposes a new equivalence-based method, utilizing two one-sided tests of equivalence (TOST) to calculate TTS following a drop landing in athletic populations. Twenty-six elite freestyle ski athletes (males = 14, females = 12; age = 22.36 ± 2.14 years) performed five trials of a 50 cm drop landing on force plates. TOST was defined as the first time point at which a 50 ms rolling window, advanced one sample at a time, achieved and maintained statistical equivalence to a pre-defined equivalence region. The TOST method was tuned by systematically assessing the effect of the equivalence width (k) and persistence (dwell) on pre-defined criteria emphasizing differences in TTS due to parameter changes, reliability (intraclass correlation coefficient; ICC(2,5)), and measurement error (SEM). The final parameters were selected as the lowest k and highest dwell values resulting in 'good' reliability (ICC ≥ 0.75) within the behaviourally stable region, or the highest observed ICC where this threshold was not met. TOST was then compared to previous TTS calculation methods (no-processing (RAW), sequential average (SA) and third-order polynomial (TOP)) using Bland-Altman and by comparing the ICC and SEM. For the vertical GRF, equivalence scaling factors (k) ≥ 11 yielded behaviourally stable TTS estimates with consistently 'good' reliability (ICC(2,5) = 0.78 [95% CI: 0.61,0.89]) and low SEM (0.035-0.038 s), regardless of the dwell value. Anterior-posterior and medio-lateral GRFs showed low marginal changes in response to parameters at k ≥ 10 and 13, respectively, but the reliability was poor to moderate and, in the ML axis, fell below zero under some parameter settings, reflecting the limited horizontal demand of the task. Recommendations for TOST are therefore made for the vertical axis only. Comparisons between methods revealed high agreement between TOST and RAW in the vertical axis, while TOST demonstrated higher reliability. SA produced TTS values on a markedly different scale consistent with trial length dependence, while TOP systematically overestimated TTS with significant proportional bias, indicating that neither could be used interchangeably with TOST. This framework provides a statistically principled alternative to fixed threshold-based TTS definitions and, unlike trial length-dependent methods such as SA and TOP, requires only a trial long enough to capture a stable reference period, permitting shorter trials better suited to frequent testing with large groups of athletes.