## 2 Materials and Methods
### Data Reduction
#### 2.4.3 Determination of Approximate and Sample Entropy
Given the exploratory nature of this study and for the completeness of the graphics, [PERSON]'s intervals were included in the confidence interval graphics even though the F-test was not statistically significant. We graphed 95% confidence intervals (Figures 13 and 14) in a format similar to the raw data graphics but plotted only the confidence intervals, not the raw data. Significant intervals do not contain zero (horizontal black line). The two entropy methods, i.e., ApEn and SampEn, are shown in separate rows. For a direct comparison of ApEn and SampEn methods for each value of \(r\), we constructed histograms (Figure 15) of their difference at each value of \(r\). Values to the left of the vertical black line (zero) indicated that ApEn was larger, whereas values to the right of the vertical black line indicated that SampEn was larger. EOFT, EOTanDB, and ECTanDB. For the COP excursion in the anterior-posterior direction, (Figure 9) entropy values suggested the following:  
* Entropy values were larger in the most stable standing condition, i.e., eyes open feet together, for \(r\) = 0.05 \(\times\) SD and 0.1 \(\times\) SD;
* ApEn (red) and SampEn (blue) Loess curves were similar;
* Entropy values generally decreased as \(r\) increased, leveling off after; \(r\) = 0.2 \(\times\) SD;
* Entropy values were larger with tandem standing postures compared to eyes open feet together, but there did not appear to be differences in entropy values between eyes open and eyes closed for the tandem standing postures;
* Participant #4 demonstrated different entropy value patterns for the eyes open feet together and eyes open tandem dominant back conditions, compared to the other five participants. For the medial-lateral excursion of the COP (Figure 10), first note that the entropy scale (vertical axis) is different than in Figure 9, yet patterns of entropy values were similar in Figure 10. On the whole, we observed the following:  
* Entropy values were generally smaller in the eyes open feet together condition, but there do not appear to be differences in entropy values between eyes open and eyes closed for the tandem standing postures;
* ApEn (red) and SampEn (blue) Loess curves were similar;
* Entropy values generally decreased as \(r\) increased, but the decreasing slope of the Loess curves, as \(r\) increased, appeared to be reduced for medial-lateral excursions;
* Participants #4 and #5 exhibited different entropy patterns, with more variability. Because of the apparent greater variability, among participants #4 and #5 in Figures 9 and 10, we took a closer look at the variability across all participants and trials for both ApEn and SampEn for the COP excursion in the medial-lateral direction (Figures 11 and 12, respectively). Overall, it appeared that ApEn and SampEn values were quite similar. In particular, we noted that the lowest entropy values were generally less variable and associated with the eyes open feet together standing posture, whereas greater values were associated with the eyes closed tandem conditions. As noted previously but more apparent in Figures 11 and 12, participants #4 and #5 appeared different, i.e., larger entropy values than the other participants. Yet Figures 11 and 12 also revealed that participant #6 appeared to generally have lower entropy values than all other participants and also perhaps demonstrated less trial-to-trial variability. Finally, greater variability of the entropy values was demonstrated across all participants and trials for the more challenging tandem standing postures (both eyes-open and -closed conditions). Figure 8: Representative time series for ApEn and SampEn calculated every second for 30 s of participant 1 eyes closed, feet tandem, dominant foot back (ECTanDB), Trial 19 COP data; where \(N\) = 60 data points, \(m\) = 2, and \(r\) = 0.2 \(\times\) SD; in the anterior–posterior (AP) and medial–lateral (ML) directions, respectively.