## 3 Results
### Non-Parametric Analysis of Turn-Taking in the Touch Me and Dance-with-Me Games  
We performed a non-parametric test (Kruskal-Wallis) to analyze each competent rater across the _Touch-me_ and _Dance-with-me_ conditions. We found significant differences for all competent raters (six individuals), yielding a higher turn-taking ratio for the _Touch me_ condition than for the _Dance with me_ condition. The analysis resulted in the six significant differences that are presented in Table 1. Note that the values included in Table 1 are consistent with the expectations concerning \(tr_{\text{touch me}}\) and \(tr_{\text{dance with me}}\) discussed in Section 2.4. The results presented to this point (in particular Table 1) relate to the raters' consistency. The next results (Tables 2-4) directly address the research questions [Q1] and [Q2] from Section 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Rater No**} & \multicolumn{1}{c}{\begin{tabular}{c} _Me_ \\ _(Touch me)_ \\ \end{tabular} } & \multicolumn{1}{c}{\begin{tabular}{c} _Me_ \\ _(Dance with me)_ \\ \end{tabular} } & \multicolumn{1}{c}{\
\begin{tabular}{c} _H(2)_ \\ \end{tabular} } & \multicolumn{1}{c}{
\begin{tabular}{c} \(p\) \\ \end{tabular} } \\ \hline
1 & 1.056 & 0.005 & 13.377 & 0.0003 \\
2 & 1.000 & 0.066 & 14.925 & 0.0001 \\
3 & 0.955 & 0.041 & 14.004 & 0.0002 \\
4 & 0.955 & 0.036 & 14.560 & 0.0001 \\
5 & 1.100 & 0.020 & 13.418 & 0.0002 \\
6 & 0.838 & 0.071 & 13.866 & 0.0002 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Non-parametric (Kruskal–Wallis) test for turn-taking ratios by rater, regardless of diagnosis. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Child’s Diagnosis**} \\  & **Typical Development** & **Autism** \\ \hline commands executed & 29 & 7 \\ commands not executed & 1 & 23 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The amount of autistic and typically developing children who did, or did not, perform the _Touch me_ commands that were given by the robot. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Child’s Diagnosis**} \\  & **Typically Developing** & **Autism** \\ \hline commands executed & 23 & 7 \\ commands not executed & 7 & 23 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The amount of autistic and typically developing children who did, or did not, imitate the robot’s movements in the _Dance with me_ game. Next, we ran \(\chi^{2}\) test statistics in order to compare turn-taking behavior between both populations in the _Touch me_ condition. For this test, the results of \(tr_{\text{touch me}}\) were divided into two categories based on the median value (\(Me=1\)). This division indicated that among 30 observations of typically developing children (i.e., 6 raters observing 5 children), there were 29 observations of children who performed the robot's commands and 1 observation of a child who did not. Regarding autistic children, this division indicated that among 30 observations of these children (i.e., 6 raters observing 5 toddlers), there were 7 observations of them performing the robot's commands and 23 observations of children who did not. The results of this division are presented in Table 2. The \(\chi^{2}\) test revealed that the results of typically developing children were significantly higher than those of autistic children, \(\chi^{2}(\text{df}=1)=33.61\), \(p<0.001\). Subsequently, the \(\chi^{2}\) test was performed for the _Dance with me_ game. The results of \(tr_{\text{dance}}\) with me were divided into two categories based on the median value (\(Me=0.036\)). This division indicated that in 30 observations of typically developing children (i.e., observations of 5 children, carried out by 6 raters), there were 23 observations of children who imitated the robot's movements and 7 observations of children who did not.