## 3 Results
### Comparative Analysis of Traditional and RQA-Based Methods in Assessing Aerobic Threshold
\begin{table}
\begin{tabular}{c c c c c} \hline
**Group** & **HR\_RQA (bpm)** & **HR\_Gex (bpm)** & **VO\_RQA (mL/Min)** & **VO\_Gex (mL/Min)** \\ \hline A (27) & 136.81 \(\pm\) 15.46 & 137.34 \(\pm\) 15.26 & 1776.56 \(\pm\) 445.95 & 1767.57 \(\pm\) 335.89 \\ O (19) & 110.22 \(\pm\) 14.06 & 112.37 \(\pm\) 14.09 & 1379.28 \(\pm\) 335.19 & 1359.12 \(\pm\) 316.4 \\ C (16) & 87.31 \(\pm\) 12.53 & 84.69 \(\pm\) 13.01 & 1051.09 \(\pm\) 462.49 & 902.79 \(\pm\) 242.67 \\ Y (49) & 126.36 \(\pm\) 14.13 & 121.16 \(\pm\) 14.18 & 1134.54 \(\pm\) 343.67 & 1056.57 \(\pm\) 260.37 \\ All (111) & 120.5 \(\pm\) 21.36 & 118.62 \(\pm\) 21.44 & 1320.57 \(\pm\) 472.98 & 1263.70 \(\pm\) 427.71 \\ \hline p method * & 0.50 & & 0.10 \\ p method X group & **0.04** & & 0.38 \\ p method X protocol & **0.03** & & 0.33 \\ p method X Wstatus * & 0.97 & & 0.62 \\ p method X Hstatus * & 0.87 & & 0.86 \\ p method X gender * & 0.98 & & 0.61 \\ \hline \end{tabular} Two factors (Gex vs. RQA) repeated measures for HR and VO\({}_{2}\) values across all participants, groups (A, C, O, Y), protocol (Cycle-ergometer or treadmill), Wstatus (obese and normal weight), Hstatus (healthy and disease) and gender (male, female). * Gex method vs. RQA-based method all \(p\) > 0.05; post-hoc power = 0.998, n = 111 subjects.  
\end{table} 
Table 2: Main Parameters at AerT by two methods (mean \(\pm\) SD) in athletes (A), cardiac patients (C), obese (O), and young athletes (Y). The mean percentage difference between the two assessment methods was below 2.5% for HR and under 8% for VO2, with these discrepancies not proving statistically significant (\(p>0.05\)) at the Aerobic Threshold. TE was considered acceptable, with values below 8% for HR and around 18% for VO2, indicating a high level of precision in the measurements [24; 25]. The Intraclass Correlation Coefficients (ICC) demonstrated excellent reliability, with scores of 0.90 for HR and 0.87 for VO2, indicating strong agreement between methods [22]. The effect size, calculated using Cohen's d, was found to be trivial for both HR and VO2, indicating minimal differences between the methods, as detailed in Table 4.  
The Ordinary Least Products (OLP) regression analysis plots for HR and VO2 at the AerT between both methods are visually depicted in Figure 5. Here, the OLP line of best fit is drawn as a solid line, while the line of unity is depicted as a dotted line, facilitating a clear comparison between the traditional and automated techniques. Furthermore, Bland-Altman plots, illustrated in Figure 6, showed no systematic bias for either HR or VO2. The plots indicated that the dispersion of differences was more contained for HR than VO2, highlighting VO2's greater variability. Only a few outliers were present, but they did not significantly affect the overall concordance between the methods, thereby reinforcing the robustness of the findings. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **r Pearson** & **ICC** & **Effect Size (d)** \\ \hline HR (bpm) & 0.82 ** ** & 0.90 (0.86 to 0.93) & 0.10 * \\ VO2 (mL/min) & 0.77 ** & 0.87 (0.81 to 0.91) & 0.14 * \\ \hline \hline \end{tabular} Pearson correlation coefficient (r Pearson), Intraclass Correlation Coefficient (ICC), and [PERSON]’s Effect Size (d); ** all large;* d \(<\) 0.2 trivial; (0.2 \(<\) d \(<\) 0.6 moderate); ICC \(>\) 0.9 excellent, 0.75 \(<\) ICC \(<\) 0.90 moderate.  
\end{table} 
Table 4: Agreement with Gex method for HR (bpm) and VO2 (mL/min) value. Figure 5: OLP regression line on (**a**) HR and (**b**) VO2 at AerT (VT1), all values correspond to the minima DETmin. The participants are divided into athletes (group A, blue cross), obese (group O, red circle), cardiac patients (group C, light-blue diamond), and young athletes (group Y, yellow circle).