## 4 Discussion
We agree with [38; 52] that looking for and using optimal, or widely used, values of \(m\) and \(r\) is not recommended, and researchers should look for how these values correlate to specific biological time series, i.e., what they mean biologically. Researchers should try different \(m\) values in combination with multiple \(r\) values that ensure relative consistency. Moreover, once the consistency of a particular combination of parameters (\(m\), \(r\), and \(N\)) is established for a particular type of biological time series it may effectively be used relative to longitudinal clinical testing, e.g., for pre- and post-treatment tests. Future research on the use of entropy as a relative value for testing intra-individual changes in clinical status is warranted. We calculated ApEn and SampEn related to the anterior-posterior and medial-lateral COP excursions during a variety of quiet standing postures and used \(r=0.05\), \(0.10\), \(0.15\), \(0.20\), \(0.25\), and \(0.30\times\) SD (Figures 8 and 9). For COP anterior-posterior excursion, we found that entropy magnitudes (ApEn and SampEn) in the EOFT condition were larger for \(r=0.05\times\) SD and \(0.10\times\) SD, and values decreased as \(r\) increased, leveling off after \(r=0.20\times\) SD. Entropy magnitudes for COP medial-lateral excursion were generally reduced in the EOFT condition compared to the AP excursion data, but decreasing entropy with increasing \(r\) mirrored the pattern seen for the AP data. Using long walking trials, [PERSON] et al. [16] reported a similar relationship between SampEn and changing \(r\), but a more variable relationship between ApEn and changing \(r\). Whereas, with quiet standing, [PERSON] et al. [52] showed that for chosen \(m\) values (two, three, four, and five) both ApEn and SampEn consistently decreased as \(r\) increased for COP time series in both the anterior-posterior and medial-lateral directions, which is similar to our findings for both feet together and tandem balance tasks. In other words, the COP time series exhibited more regularity (i.e., lower entropy values) for greater similarity tolerances and greater subseries lengths. According to [52], the increase in regularity for greater \(r\) values seems to be an expected result, as it is a reasonable assumption that a greater number of subseries will meet the similarity criterion for a more relaxed tolerance. [PERSON] results highlighted issues with relative consistency in COP time series for ApEn, as observed by the change in direction of differences between groups (known as \"flips\" or \"crossovers\") for some combinations of \(m\) and \(r\), which seemed to be accentuated for shorter time series (N = 600). In contrast, SampEn showed relative consistency. On the other hand, our data demonstrated relative consistency for both ApEn and SampEn with changes in the tolerance window, particularly for \(r\) = 0.20, \(r\) = 0.25, and \(r\) = 0.30 \(\times\) SD. Be reminded, however, that we examined quiet feet together and tandem quiet standing positions, whereas ref. [52] tested standard feet apart stances. Based on the relative consistency of both ApEn and SampEn using a range of \(r\)'s equal to 0.20, 0.25, and 0.30 \(\times\) SD, we suggest that future research investigating postural sway based on COP time series consider the method we used. Despite the consistency of the ApEn and SampEn values we report, we caution the reader that our choice for determining the tolerance window may be limited by factors, e.g., data length, non-stationarity of the data, spikes, and outliers, that affect data variance. Outliers and spikes were identified in some of our data, particularly for participants #4 and #5 (see Figures 8-11), in the ApEn and SampEn values for \(r\) = 0.05 and \(r\) = 0.1 \(\times\) SD, likely due to the overly stringent conditions. [PERSON] et al. [59] evaluated the impact of abnormal spikes on the interpretation of entropy results in the context of biosignal analysis and suggested removing these results, as they can misrepresent the signal regularity.