An updated estimate of the lower speed boundary of preferred stride ratio constancy

Abstract The preferred stride ratio (PSR), defined as the ratio of step length to cadence, is approximately invariant across a wide range of walking speeds in healthy adults but breaks down at slow speeds. The lower speed boundary at which this constancy is broken was estimated by Murakami and Otaka (2017) to be approximately 62 m min−1 (≈ 1.03 m s−1) on the basis of unstandardised K-means cluster analysis applied to data from 21 healthy adults at five speed conditions. The present report re-examines this estimate using the digitised individual-level scatter of Fig. 1-A and the published group-level statistics of Table 1 of that study, applying three breakpoint estimators in parallel: (i) unstandardised K-means (replicating the original method), (ii) a Gaussian mean-and-variance changepoint estimator, and (iii) a piecewise-linear regression on PSR. Applied directly to the digitised scatter (n = 84 resolved markers from a total of 105; 44 of 44 slow-walk markers, 40 of 61 normal-walk markers), the unstandardised K-means estimator returned 62.0 m min−1, matching the originally reported value to the reported precision; the mean-and-variance changepoint estimator returned 55 m min−1; and the piecewise-linear estimator was numerically unstable on the raw heteroscedastic data. To quantify uncertainty, 5 000 Monte Carlo realisations of synthetic individual-level data were generated from a bivariate truncated-normal model conditioned on the published condition means and standard deviations and on the published within-cluster speed–PSR correlations. The Monte Carlo distributions gave median estimates of 61 m min−1 (95 % MC interval 55–67) for unstandardised K-means, 39 m min−1 (29–53) for the mean-and-variance changepoint estimator, and 35 m min−1 (19–49) for piecewise-linear regression. Under a log-normal sensitivity model the corresponding intervals were 60 [55, 66], 34 [20, 58], and 19 [5, 42] m min−1. The likelihood-based estimator placed the central tendency substantially below 62 m min−1, and its Monte Carlo intervals did not include the original boundary under either marginal-distribution model. An additional robust heteroscedastic segmented profile-likelihood analysis on log-PSR yielded lower Monte Carlo median breakpoints across all model specifications, although the full-variance intervals overlapped the original K-means boundary. The qualitative finding of Murakami and Otaka — that PSR constancy breaks down at slow walking speeds — is supported by the present reanalysis. The original 62 m min−1 boundary is reproduced under the unstandardised K-means estimator, where it reflects the location of the largest density gap in the published five-condition speed sampling rather than a formally estimated changepoint; estimators formally designed for changepoint detection localise the joint PSR mean-and-variance transition substantially below this value. Competing Interest Statement The authors have declared no competing interest. Footnotes This manuscript is a preprint and has not been peer-reviewed. Statistical computations re-implemented in MATLAB R2025b (Sections 2.3-2.8); image-processing routines for Fig. 1-A digitisation (Section 2.2) remain in Python. Monte Carlo interval endpoints shifted by <= 1 m/min relative to v1 owing to differences between Python and MATLAB random number generators; medians and direct-fit point estimates are unchanged. The Introduction has been restructured to motivate the reanalysis methodologically (K-means is not a formal changepoint estimator). The Abstract, Section 4.1, and Conclusion have been revised to characterise the original 62 m/min K-means boundary as the location of the largest density gap in the five-condition sampling, with the likelihood-based estimators positioned as the primary formal estimate. Figure 1 has been regenerated. The qualitative findings of v1 are unchanged.