Participants for the study were recruited from a pool of healthy young adults aged between 20 and 30 years. Those with walking impairments or comorbidities that could affect gait, as well as those suffering from cardiac, respiratory, metabolic, neurological, or musculoskeletal pathologies, were not included in the study. Additionally, volunteers with obesity (BMI >30 kg/m²) were also excluded. The study group consisted of 10 young adults (five males, average age 23 ± 1 years, age range 21–24 years, BMI 21.3 ± 2.2 kg/m²). Given a sample size of 10 subjects and analyzing the step length of the external leg between normal and slow subjects, the study was sufficiently powered (>80%) to detect an effect size that was Cohen's d = 0.22 or larger. All participants provided written informed consent prior to their participation in the study, which received approval from the local ethics committee. This study is based on the same experiment performed to validate the algorithm detecting spatiotemporal parameters during turning (Ulrich et al., 2019). Furthermore, this study is a follow-up study built on the experimental procedure described in Madrid et al. (2023). We asked the healthy young participants of the previous study to turn at a self-selected reduced speed and compared it to the young participants turning at normal speed. Hence, instead of comparing the spatiotemporal parameters during turning at different amplitudes between older participants and young participants, we compared the spatiotemporal parameters during turning at different amplitudes between young participants, volitionally reducing their walking speed, and young participants walking at normal speed. The data of young participants walking at normal speed, which represented the control group, was used in both studies.

Participants were fitted with reflective markers on their feet and pelvis, as described by Ulrich et al. (2019). Markers were positioned bilaterally on the posterior side of the calcaneus and the second metatarsal heads. On the pelvis, markers were placed on both the anterior superior and posterior superior iliac spines. Following this, participants were instructed to carry out practice trials and the recorded turning trials, without footwear, in a laboratory outfitted with a motion capture system that recorded at a sampling rate of 120 Hz (Vicon, Oxford, UK).

Participants were directed to walk in a straight line for 5 m, then make a 90°, 180°, or 360° turn around a 153 cm vertical rod, and subsequently continue walking straight for a minimum of 3 meters until they arrived at a predetermined point in the room, which was specific to the turn executed (Figure 1). There were no strict guidelines regarding the path the participant should take or whether the turn should be sharp or smooth. Therefore, we did not control for the turning radius, which could have influenced the turning strategy. For each turning amplitude, participants were requested to walk at their self-selected normal speed and at a speed slower than their self-selected normal speed. In contrast to slow walking, fast walking could potentially increase the difficulty of turning. Therefore, it would not have been possible to differentiate the effect of volitionally modulating the walking speed and the effect of increased difficulty on spatiotemporal parameters. For this reason, we did not test participants at speeds faster than their self-selected speed. The sequence of the turning amplitudes, walking speed conditions, and the direction of the turn (left or right) were randomized using a simple global randomization method. The direction of the turn was randomly chosen for each participant, who then performed all their trials maintaining the same turning direction. For each participant, nine trials were recorded for each walking speed condition and turning amplitude. Based on prior research, nine trials per condition seem to be a good tradeoff between sufficient data and unwanted effects such as fatigue (Madrid et al., 2023). The decision to include 10 participants per condition was informed by previous research on spatiotemporal parameters with similar descriptive and exploratory objectives (Bovonsunthonchai et al., 2014).

Events of heel-strike and toe-off were identified using foot marker trajectories, adhering to the recommendations proposed by Ulrich et al. (2019). Specifically, these gait events were calculated using versions of the algorithm suggested by O'Connor et al. (2007) for heel-strike and Zeni et al. (2008) for toe-off, both of which have been validated for turning. The turning period was defined as the segment of the trials where the angular walking speed of the pelvis surpassed 30°/s (Mellone et al., 2016). Based on this definition, spatiotemporal parameters were analyzed from the last toe-off prior to the onset of the turning period to the first heel strike following the end of the turning period. The computed spatiotemporal parameters included: (1) for the entire turn: walking speed, total duration, number of steps, and cadence, (2) for the external and internal legs during each cycle: stride length, step width, step length, gait cycle duration, stance duration, stance/cycle ratio, and initial double-support duration (Figure 2) (Perry and Slac Thorofare, 1992; Huxham et al., 2006). The external leg was defined as the one exterior to the turning cycle, while the internal leg was defined to be interior to the turning cycle.

Frequentist statistic methods, especially p-value-null-hypothesis-significance-testing (NHST), face a reproducibility crisis (Makowski et al., 2019; Keysers et al., 2020). The Bayesian framework solves many of these problems in an intuitive manner (Kruschke and Liddell, 2018). Notably, it enables the discrimination between the evidence of absence and the absence of evidence of an effect which is not possible in a frequentist framework (Keysers et al., 2020). We think this approach is particularly well suited to quantify knowledge and ignorance about clinical effects regarding the available data. Therefore, we decided to implement the Bayesian framework to perform inference (Dienes, 2014; Makowski et al., 2019; Keysers et al., 2020). Statistical analysis was performed using RStudio (v 1.2.1335, RStudio, Inc.).

For each participant, the measurements were aggregated across the nine trials of each turning amplitude. Subsequently, the mean and the within-subject standard deviation (SD), serving as an estimate of variability (Hausdorff et al., 2001; Galna et al., 2013), were computed for each aggregated dataset. This resulted in two data points (average value and variability) for each parameter, turning amplitude, and participant.

In order to ascertain whether walking speed and/or turning amplitude influenced the spatiotemporal parameters and their variability, statistical models were constructed separately for the mean and variability values of each parameter. These models incorporated a within-subject walking speed factor (normal walking speed or reduced walking speed) and a within-subject turning amplitude factor (90°, 180°, or 360°). This was achieved by performing 2 × 3 Bayesian repeated measures ANOVA and a Bayesian generalized linear model, with walking speed and turning amplitude as fixed effects and the subject's identification number as a random effect. Both walking speed and turning amplitude were treated as categorical variables.

We computed effect size estimates with 95% credible intervals and standardized effect sizes as Cohen's d (Cohen, 1988) or eta squared. In addition, we computed the Bayes factor (Dienes, 2014; Makowski et al., 2019), map-based p-values (Mills, 2018; Makowski et al., 2019) and the HDI+ ROPE method using the standardized effect size. The ROPE was calculated using a small effect size (0.2 standard deviations of all parameter data) as the region of practical equivalence (Kruschke, 2018). Hence, this study is not able to detect very small effect sizes. However we think they are not clinically significant (Cox, 2006).

We used residual plots and q-q plots to check the independence of observations, a non-explained trend in the residuals, linearity, normality, equality of variance and outliers. We investigated MCMC Convergence visually and using the Gelman diagnostic. We checked for Autocorrelation visually and used a minimum of 10,000 for the effective sample size of each parameter.

In the Bayesian framework, p-value corrections such as Bonferroni do not make much sense; therefore, we did not correct them (Berry and Hochberg, 1999; Gelman et al., 2012; Sjölander and Vansteelandt, 2019). Furthermore, even in a frequentist framework, p-value corrections are subject to debate (Rothman, 1990; Sjölander and Vansteelandt, 2019). We chose reasonably non-informative priors: we used a normal prior N(0;1.6) [it corresponds to a probability of 80% that the effect size lies between −2 and 2 (Gronau et al., 2020)]. We performed a Bayes factor robustness check visually to ensure that our prior had no significant influence on our posterior. To gain assurance about the accuracy of our complex model, we represented the actual data mean ± 95% CI statistics using bootstrapping and the model predictions graphically (Figures 2, 3 in Supplementary material 2, 4).

The significance level was set at a 95% credible Interval on the HDI ROPE of the standardized effect size for significance/equivalence testing.

Participants walked significantly slower when they were asked to decrease their walking speed (Cohen's d < −2.05). Furthermore, in both speed conditions, young adults decreased their speed with larger turning amplitudes (Cohen's d < −0.5). Turning duration between conditions were similar at 90° (Cohen's d −0.29, 0.50) and differed at 360° (Cohen's d 1.46, 2.31). The total number of steps was similar at 360° (Cohen's d −0.64, 0.15). Cadence was significantly decreased in the slow-speed condition compared to the normal condition for all turning amplitudes (Cohen's d < −2.42). At normal speed, cadence was similar between all turning amplitudes (Cohen's d −0.33, 0.51) while at slower speed, cadence was similar between all turning amplitudes (Cohen's d −0.39, 0.31) except between 90° and 180°.

When participants were asked to decrease their speed, stride length and step length of the internal and external leg were significantly shorter (Cohen's d < -0.33). At normal speed and for both legs, there was a decrease in stride length with higher amplitude between 90° vs. 180° and 180° vs. 360° (Cohen's d < -0.33), whereas for the slower condition and for both legs stride length decreased with higher amplitude at 180° and 360° compared to 90° (Cohen's d < -0.32). The step length of the internal leg decreased with higher amplitude between 90° vs. 180° and 180° vs. 360° for the slower and normal conditions (Cohen's d < -0.25). At normal speed, the step length of the external leg decreased for the 180° and 360° turns compared to the 90° (Cohen's d < -0.69). At a slower speed, the step length of the external leg was decreased only in 360° amplitude compared to the 90° amplitude (Cohen's d < -0.54). For the normal condition, the stride width of the external leg decreased with higher amplitude between 90° vs. 180° and 90° vs. 360° (Cohen's d < -0.53).

Gait cycle duration, stance duration, initial double support and stance/cycle ratio of the internal and external legs of all turning amplitudes were increased at a slower speed compared to normal speed (Cohen's d >0.43).

The gait cycle durations of the internal leg were similar for 90° vs. 360° and 180° vs. 360° at normal speed (Cohen's d −0.41, 0.52) and for 90° vs. 360° at slower speed (Cohen's d −0.24, 0.51). The gait cycle durations of the external leg were similar for 90° vs. 360° and 180° vs. 360° at normal speed (Cohen's d −0.48, 0.30). The stance durations of the internal leg were similar for 180° vs. 360° at normal speed (Cohen's d −0.24, 0.20) and for 90° vs. 360° at lower speed (Cohen's d −0.09, 0.43). The stance durations of the external leg were similar for 90° vs. 180° and 90° vs. 360° at normal speed (Cohen's d −0.35, 0.45), and for 90° vs. 360° at slower speed (Cohen's d −0.32, 0.20). The initial double support durations for the internal leg were similar at 180° vs. 360° at both normal and slower speeds, respectively (Cohen's d −0.38, 0.20). The double support of the external leg was similar for 90° vs. 360° and 180° vs. 360° at normal speed (Cohen's d −0.28, 0.37), and for 180° vs. 360° at slower speed (Cohen's d −0.28, 0.10). The stance/cycle ratio of the internal leg increased significantly at larger turning amplitudes in both speed conditions (Cohen's d >0.18). The stance/cycle ratios of the external leg were similar at 90° vs. 180° at normal speed (Cohen's d −0.31, 0.39).

These results are summarized in Table 1 and Supplementary material 1, 2.

Cadence's variability was significantly greater in the slower condition at 90° compared to the normal condition at 90° (Cohen's d >0.36) and significantly decreased between 90° and 360° for the slower condition (Cohen's d < −0.35).

The stride length and step width of the internal leg's variabilities were greater for the normal condition at 180° (Cohen's d < −0.37) compared to the slower condition. The stride length of the internal leg's variability increased for the normal condition between 90° vs. 180° and 90° vs. 360° (Cohen's d >1.04). The stride length of the external leg's variability increased for both conditions between 90° vs. 180° and 90° vs. 360° (Cohen's d >0.47). The step length of the internal leg's variability increased for the normal condition between 90° vs. 180° and 90° vs. 360° and for the slower condition between 90° vs. 180° (Cohen's d >0.42). The step length of the external leg's variability increased for the normal condition between 90° vs. 180° and 90° vs. 360° (Cohen's d >0.47). The step width of the internal leg's variability decreased for the normal condition between 180° and 360° (Cohen's d < −0.53).

The gait cycle duration of the internal leg and external leg variability was increased for the slower condition at 90° (Cohen's d >0.46) compared to the normal condition. The gait cycle duration of the internal leg's variability increased between 90° vs. 180° and 90° vs. 360° for the normal condition (Cohen's d >0.27). The stance duration of the internal leg's variability was significantly increased for the slower condition compared to the normal condition at 90° and 180° (Cohen's d >0.32) and the stance duration of the external leg's variability was significantly increased for the slower condition compared to the normal condition at 90° (Cohen's d >0.58). The initial double support duration of the internal leg's variability was significantly increased at 90° and 180° when participants were asked to decrease their speed (Cohen's d >0.31).

These results are summarized in Table 2 and Supplementary material 3, 4.