## 2 Materials and Methods
### Data Reduction
#### 2.4.3 Determination of Approximate and Sample Entropy  
Approximate and sample entropy were estimated every second and averaged over a 30 s interval for all five trials under each condition using custom MATLAB(r) R2021b  
Figure 5: Representative time series for raw center-of-pressure (COP) data of participant 1 eyes closed, feet tandem, dominant foot forward (ECTanDF) Trial 29, where _f_s = 1200 Hz, in the anterior–posterior (AP) and medial–lateral (ML) directions, respectively. Figure 6: Representative time series for the downsampled center-of-pressure (COP) data of participant 1 eyes closed, feet tandem, dominant foot forward (ECTanDF) Trial 29, where _f_s = 60 Hz, in the anterior–posterior (AP) and medial–lateral (ML) directions, respectively. (The MathWorks, Natick, MA, USA) code. For each COP time series, \(N=60\) data points, pattern length, \(m=2\), and tolerance window, \(r=f\times SD\) for \(f=0.05\), \(0.1\), \(0.15\), \(0.2\), and \(0.3\), were used to estimate ApEn and SampEn. The choice of tolerance levels was motivated by exploring the responses of ApEn and SampEn for a range of \(r\) similar to previously reported research [16]. ApEn and SampEn were estimated as described in detail by [PERSON] and [PERSON] [1]. For approximate entropy, given a sequence of numbers \(u=\{u(1),\ u(2),\ldots,\ u(N)\}\) of length N, a non-negative integer \(m\), with \(m\ \leq N\) and a positive real number \(r\), define the blocks \(x(i)=\{u(i)\,,u(i+1),\ldots,u(I+m-1)\}\) and \(x(j)=\{u(j),u(j+1),\ldots,u(J+m-1)\}\), and calculate the distance between them as \(d[x(i),x(j)]=max_{k=1,2,\ldots,m}\big{|}u(i+k-1-u(j+k-1)\big{|}\). Then, calculate the value \(C_{i}^{m}(r)=(number\ of\ j\leq N-m+1\) such that \(d[x(i),x(j)]\leq r)/(N-m+1)\). This counts the number of _m-point_ patterns within tolerance \(r\), in the data. So, computing:  
\[\phi^{m}(r)=\frac{1}{N-m+1}\sum_{i=1}^{N-m+1}logC_{i}^{m}(r) \tag{2}\]  
we then define \(ApEn(m,r,N)(u)=\phi^{m}(r)-\phi^{m+1}(r)\), with \(m\geq 1\). Sample entropy eliminates the self-counting problem and defines the total number of possible _m-point_ pattern matches by calculating:  
\[B_{i}^{m}(r)=\frac{1}{N-m-1}\sum_{j=1,j\
eq i}^{N-m}[number\ of\ times\ that\ d[\ |x_{m}(j)-x_{m}(i)|]<r], \tag{3}\]  
and then averaging:  
\[B^{m}(r)=\frac{1}{N-m}\sum_{i=1}^{N-m}B_{i}  
Box plots are provided to illustrate inter-trial variability. Figures 11 and 12 illustrate the entropy variability at one \(r\)-value, i.e., \(r=0.25\times\) SD, for the medial-lateral COP excursion for ApEn and SampEn, respectively. There were 144 one-way ANOVAs with [PERSON]'s post hoc tests for the 6 participants, 6 values of \(r\), 2 axes, and 2 methods. Each analysis was performed within a single participant with entropy calculated from a single combination of \(r\), axis, and entropy method. The population for each statistical analysis was then entropy calculated with a particular combination of \(r\), axis, and method for all COP time series for an individual under the five standing postural conditions. Each sample is then 25 independent trials under the 5 standing postural conditions. Tables and graphics were generated for [PERSON] and [PERSON]'s test \(p\)-values below 0.05, indicating potential normality and heteroscedasticity issues. Note that the normality and heteroscedasticity were related to entropy values, not biomechanical measurements over time. Nonparametric tests were considered but few of the 144 tests indicated a possible need for them. It is known that ANOVA is robust to failures of normality, especially for symmetric errors. All [PERSON] test issues showed roughly symmetric errors in the Q-Q plots. ANOVA is also known to be robust to failures of equal variance in the case of equal group sizes. All group sizes were equal except for participant #5, for condition ECTDB, which did not fail either [PERSON] or [PERSON]'s tests. All of the ANOVA F-tests except six had \(p\)-values \(<0.05\).