## 3 'Speed-ID-Accuracy' Model: Numerical Cases  
In this section, starting from experimental data available in the scientific literature [19], the 'Speed-ID-Accuracy' model (Equation (5)) has been applied to both Tunnel Traveling Task (TTT) and Circular Traveling Task (CTT). Experiments relate samples of individuals with different age in accomplishing differently sized TTT and CTT. Field data observed revealed no significant difference between differently aged individuals. Some of the TTT row data available in the quoted paper are summarized in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**A (cm)** & **W (cm)** & **MT (s)** & **Success Prob. (\%)** \\ \hline
1.152 & 0.384 & 0.290 & 97.6 \\
1.536 & 0.384 & 0.379 & 96.9 \\
1.92 & 0.384 & 0.459 & 94.5 \\
1.728 & 0.576 & 0.353 & 98.7 \\
2.304 & 0.576 & 0.444 & 98.0 \\
2.880 & 0.576 & 0.549 & 97.3 \\
2.304 & 0.768 & 0.399 & 99.1 \\
3.072 & 0.768 & 0.515 & 98.0 \\
3.840 & 0.768 & 0.640 & 97.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental data on Tunnel Traveling Task (from [19]). Starting from the success probability values in Table 1, the corresponding error and z values are obtained for different A and W values. This allows determining the effective target width (We) by Equation (6) and the corresponding standard deviation values (SD\({}_{\text{TTT}}\)(x)) by Equation (7). Traveling length (A) and movement time (MT) values observed provide the average speed of tasks' execution. Finally, the corresponding ID values have been obtained by Equation (8). Results are in Table 2.  
By regressing SD\({}_{\text{TTT}}\)(x) values on speed and ID values, the parameters of the 'Speed-ID-Accuracy' model (Equation (5)) have been obtained; they are shown in Table 3.  
As one can see, the model (Equation (5)) fits well data available in [19] as witnessed by R\({}^{2}\) = 91.78% and \(p\)-value = 0.001. SD\({}_{\text{TTT}}\)(x) values are plotted in Figure 3a against task speed observed in experiments [19] for different ID values evaluated by Equation (8); similarly, dependency of SD\({}_{\text{TTT}}\)(x) on both task speed and ID values as calculated by the model (Equation (5)) is plotted in Figure 3b. It is worth nothing the significant dependency of SD\({}_{\text{TTT}}\)(x) on ID. Such a finding is due to the extension of the classical 'Speed-Accuracy' model by the model proposed. In fact, by neglecting the ID \begin{table}
\begin{tabular}{c c c c c c} \hline
**ID (bit)** & **Average Speed** & **Error (\%)** & **z-Score** & \
\begin{tabular}{c} **We/W** \\ **(Equation (6))** \\ \end{tabular} &
\begin{tabular}{c} **SD\({}_{\text{TTT}}\)(x) (cm)** \\ **(Equation (7))** \\ \end{tabular} \\ \hline
4.328 & 3.972 & 2.4 & 2.26 & 0.914 & 0.078 \\
5.771 & 4.053 & 3.1 & 2.17 & 0.952 & 0.084 \\
7.213 & 4.183 & 5.5 & 1.93 & 1.070 & 0.106 \\
4.328 & 4.895 & 1.3 & 2.51 & 0.823 & 0.094 \\
5.771 & 5.189 & 2.0 & 2.33 & 0.887 & 0.110 \\
7.213 & 5.246 & 2.7 & 2.23 & 0.926 & 0.120 \\
4.328 & 5.774 & 0.9 & 2.65 & 0.780 & 0.113 \\
5.771 & 5.965 & 2.0 & 2.33 & 0.887 & 0.146 \\
7.213 & 6.000 & 2.8 & 2.20 & 0.939 & 0.164 \\ \hline \end{tabular}
\end{table} 
Table 2: ID, Speed, We and SD(x) values for the Tunnel Traveling Task. Figure 3: Standard deviation of the endpoint position (SD) observed ([19], (a)) and predicted (model Equation (5), (b)) vs. ID (Equation (8)) and observed task speed. influence on SD\({}_{\text{TITT}}\)(x), the regression analysis on experimental data by Equation (4) (classical model) provides a less accurate goodness of fit, being R\({}^{2}\) = 73.46% and _p_-value = 0.003. Experimental data (Table 1) allowed regressing task speed (v = A/MT) on A and W values as:  
\[\text{v = a}^{\prime}+\text{b}^{\prime}\star\text{A}+\text{c}^{\prime}\star \text{W} \tag{17}\]  
The regression parameters of Equation (9) are in Table 4 as well as R\({}^{2}\) and _p_-values witnessing the goodness of fit of the regression. The 'Speed-ID-Accuracy' model (Equation (5)) has been tested for different ID and W values of the Tunnel Traveling Task.