# From When to When: Evaluating Naturalness of Reaction Time via Viewing Turn around Behaviors
## 3 Results and Discussion of Experiment I  
### Best Combinations between Before-and After-Reaction Time  
Figure 6 and Tables 1-5 show the results of each model. In the tables for each graph, the bold texts mean the highest value in each combination. The figure shows that the best combinations between before-and after-reaction times are different due to the models. As shown in the results, the peak is only one kind in each model. In this case, we do not need to consider complex equations for implementation, except for a visualization purpose of their trends; therefore, we just use the best combinations in each model for comparison. Even though the naturalness scores of other combinations are close to the best combination's value, using the best combinations is a reasonable approach in the context of implementing robots' behaviors. The participants felt more naturalness with relatively slow before-reaction time for the robot models and the female model (400-600 ms) compared to the male models (200 ms). On the other hand, the participants identified more naturalness with a relatively fast after-reaction time for Sota, Nao, and the female model (400-600 ms) compared to Pepper and the male models (800 ms).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Before**} \\ \cline{3-8}  & & **0** & **200** & **400** & **600** & **800** & **1000** \\ \hline \multirow{6}{*}{After} & 200 & 3.66 & 4.97 & 5.09 & 5.11 & 5.12 & 4.97 \\ \cline{2-8}  & 400 & 5.20 & 7.02 & 7.01 & **7.65** & 6.73 & 5.59 \\ \cline{2-8}  & 600 & 6.37 & 7.17 & 7.52 & 7.17 & 6.64 & 6.02 \\ \cline{2-8}  & 800 & 5.80 & 6.90 & 6.90 & 5.74 & 5.58 & 5.24 \\ \cline{2-8}  & 1000 & 5.27 & 5.87 & 5.69 & 4.66 & 4.40 & 4.69 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The perceived naturalness of [PERSON]. The bold text with a large font means the highest value.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Before**} \\ \cline{3-8}  & & **0** & **200** & **400** & **600** & **800** & **1000** \\ \hline \multirow{6}{*}{After} & 200 & 3.42 & 3.96 & 4.04 & 4.18 & 3.88 & 3.89 \\ \cline{2-8}  & 400 & 4.64 & 6.39 & 6.41 & 7.28 & 6.15 & 5.36 \\ \cline{2-8}  & 600 & 5.82 & 7.61 & **7.86** & 7.46 & 6.98 & 5.88 \\ \cline{2-8}  & 800 & 5.93 & 7.32 & 7.67 & 6.69 & 5.75 & 5.53 \\ \cline{2-8}  & 1000 & 5.47 & 6.47 & 5.96 & 5.04 & 4.68 & 4.79 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The perceived naturalness of Nao. The bold text with a large font means the highest value.  
Figure 6: Questionnaire results of perceived naturalness. In the table, the bold text with a large font means the highest value in each model. **(a)** [PERSON], **(b)** Nao, **(c)** [PERSON], **(d)** Male, **(e)** Female.  
For reference, we conducted a 3-factor ANOVA with perceived naturalness as a dependent variable with before-reaction, after-reaction times, and the model. The results showed that there is a significant effect on all factors. There were significant differences in the before-reaction time (\(F\) (5, 3870) = 231.735, \(p<0.001\), _partial \(\eta^{2}\)_ = 0.230), in the after-reaction time (\(F\) (4, 3096) = 1112.153, \(p<0.001\), _partial \(\eta^{2}\)_ = 0.590), in the model (\(F\) (4, 774) = 5.120, \(p<0.001\), _partial \(\eta^{2}\)_ = 0.026), in the simple interaction effects between before-reaction and after-reaction times (\(F\) (20, 15,480) = 53.198, \(p<0.001\), _partial \(\eta^{2}\)_ = 0.064), in the simple interaction effects between before-reaction and model (\(F\) (20, 15,480) = 5.129, \(p<0.001\), _partial \(\eta^{2}\)_ = 0.0026), in the simple interaction effects between after-reaction and model (\(F\) (16, 15,480) = 74.044, \(p<0.001\), _partial \(\eta^{2}\)_ = 0.277), and in the two-way interaction effect (\(F\) (80, 15,480) = 3.127, \(p<0.001\), _partial \(\eta^{2}\)_ = 0.016). Due to a large number of combinations, we did not describe the details of interaction effects.