**3. Results**

The time trends of XUCOP, YUCOP and RD for one of the participants are displayed in Figure 6, together with the plots of the corresponding stabilograms (i.e., XUCOP-vs-YUCOP plot). Di fferent colors are used in the figures to highlight di fferences among the three phases (green for PHA, red for PHB, and black for PHC).

**Figure 6.** Time trends of the XUCOP (**a**), YUCOP (**b**) and RD (**c**), together with the corresponding stabilogram (**d**) for one of the participants.

In the displayed time series, the increase of the XUCOP and YUCOP range, together with the calculated RD, is remarkable throughout the test from the least engaging part (PHA) to the most demanding one (PHC). In addition, the stabilogram plot shows a significant increase in the swept area in PHC as compared to PHA and PHB. This increment of the seated sway excursion demonstrates that when volunteers are involved in a demanding cognitive task, there is a lower stability on the seat with respect to the phases of the test where the task to be performed is simpler. This can be due to the growing of a stressing condition that can cause a different position on the chair, as demonstrated in [21], and can also induce a different dynamic behavior.

The results of the statistical analysis are shown in Table 2, together with the mean values of the calculated parameters for all participants, and the corresponding standard deviations. For all parameters, except the sway area, the difference between coupled distributions resulted highly significant for PHA vs. PHC and PHB vs. PHC, thus validating the hypothesis that a different strategy for controlling the sway is assumed by subjects when cognitive engagemen<sup>t</sup> increases. Moreover, for the range parameters (i.e., RANGE, RANGEX and RANGEY), the difference between PHA and PHB resulted significant: the difference is higher for the y coordinate (i.e., anteroposterior) and this can be explained by the biomechanics of the hip. During a seated position, this joint has reduced swinging along the mediolateral direction (i.e., x direction) with respect to the anteroposterior one (i.e., y direction), so when posture is not well controlled, a greater instability along y is found.


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Finally, significant differences can be observed in the RMS distance values (RDIST and RDISTY) and in the 95% confidence circle area (mm2).

Figures 7–11 show the graphical representation of the calculated parameters' distributions. For MD values, it is noticeable that the increased engagemen<sup>t</sup> in PHC for the requested task significantly increases the distance from the UCOP center in both sway directions (Figure 7). The same results can be observed considering the RMS distances values (Figure 8). For both parameters, a greater excursion in the y direction (i.e., anteroposterior) is noticeable.

**Figure 7.** Mean distance distributions for each of the three phases PHA, PHB and PHC: (**a**) MD distributions, (**b**) MDX distributions and (**c**) MDY distributions.

**Figure 8.** RMS distance distributions for each of the three phases PHA, PHB and PHC: (**a**) RDIST distributions, (**b**) RDISTX distributions and (**c**) RDISTY distributions.

**Figure 9.** Range distributions for each of the three phases PHA, PHB and PHC: (**a**) RANGE distributions, (**b**) RANGEX distributions and (**c**) RANGEY distributions.

**Figure 10.** Mean velocity distributions for each of the three phases PHA, PHB and PHC: (**a**) MVELO distributions, (**b**) MVELOX distributions and (**c**) MVELOY distributions.

**Figure 11.** Area Parameters distributions for each of the three phases PHA, PHB and PHC: (**a**) AREA-CC distributions, (**b**) AREA-CE distributions and (**c**) SWAREA distributions.

These results are confirmed considering the range parameters distributions (Figure 9), where higher values of the maximum and minimum coordinates result in the UCOP excursion during PHC. It is also important to note that the range values in PHB are significantly lower than the ones in PHA: it can be speculated that after the first phase of the test, the volunteers reach a stable position where they feel comfortable both with the sitting posture and in performing the task. This condition is strongly modified in PHC and, since the total duration of the test is chosen not to induce muscular fatigue, the change of strategy in swaying can be explained by the increase in the difficulty of the task that induces a higher cognitive engagement.

Considering the velocity parameters distributions (Figure 10), a significant decrease in the velocity of the UCOP trajectory appeared in PHC, compared to both PHA and PHB. This evidence, together with the assessed high excursion, can confirm a decreased capability in controlling equilibrium in the most demanding condition: in fact, if the greater excursion would have been caused by an active rapid movement, the velocity would not have decreased as shown. The decrease of these values can therefore be explained by a reduced capability in controlling the UCOP trajectory and "corrective" actions performed to remain in a seated equilibrium.

Finally, area parameters distributions (Figure 11) reveal a larger area swept by the UCOP trajectory and a general instability achieved by subjects in PHC than in PHA and PHB, especially considering the 95% confidence circle and ellipse areas.
