## 2 Study Design
### Procedure and Materials
The rating procedure began with the instruction of the observational raters. They were given _The Observation Scale of Child's behavior in Interaction with a Robot_, and the experimenter verbally explained the scale content and the method of completing it. The experimenter introduced the scale to the raters and emphasized the most important points. The raters watched films of the interactions of the children and the robot. While watching the movie, the competent raters evaluated the children's behavior with _The Observation Scale of Child's behaviour in Interaction with a Robot_. For each film, the competent raters used a separate scale for each child to evaluate turn-taking behavior in the course of the interaction with the robot. With regard to both measurable indicators of turn-taking (see the point 1 of the Observation Scale in Table 11), while watching the films, the raters counted the presence of turn-taking behaviors presented by children in a given moment. In particular, in the _Touch Me_ game, it was assumed that turn-taking was manifested when the child properly followed the robot's instructions to touch its \"body\"; turn-taking when dancing with the robot was revealed by a child's behavioral imitation of the robot's movements. Thus, the numerical indicator, \(tr_{\text{touch me}}\), of turn-taking in the _Touch me_ game was the ratio parameter of touches of a robot's body performed by a child and counted by the raters, denoted by \(N_{\text{ch}}^{\text{touch me}}\), divided by the total number of _Touch Me_ commands given by the robot to the child, denoted by \(N_{\text{r}}^{\text{touch me}}\) for each child:  
\[tr_{\text{touch me}}=\frac{N_{\text{ch}}^{\text{touch me}}}{N_{\text{r}}^{ \text{touch me}}}. \tag{1}\]  
When the child's attempts to touch the robot were confirmed by the robot's voice, this was counted as a manifestation of turn-taking behavior. For some children, \(tr_{\text{touch me}}>1\), because the child could follow a single command from the robot more than once. It is a consequence of the _robot's voice command-child's reaction-robot's confirmation_ procedure discussed in Section 2.1. Due to imperfect sensors or inappropriate touch, the child sometimes has to make several attempts to receive confirmation from the robot. In other words, repeated touching was due to a lack of immediate response from the robot and was intended to elicit such a response (a turn-taking). This particular interaction is characterized by an effort to maintain contact with the robot for a longer period of time, which is cyclic in nature. The turn-taking lasts for an extended period of time, and therefore it cannot be associated with a single measurement. The child touched the robot until the robot's visible reaction confirmed the execution of the command. Thus, when a child sought contact with the robot, this demonstrated the phenomenon of turn-taking (i.e., the robot gives a command, the child executes it and the robot confirms the execution of the command). Given the advances in robotic technology, the problem of limited tactile sensors in NAOwill be eliminated in newer versions of NAO or its successors. We believe that behavioral outcomes of such technological constraint as it stands can be neglected because the child-robot interaction itself was not affected and distorted while the _Touch me_ scenario was in play. The indicator of turn-taking in the _Dance with me_ game, which is denoted by the ratio parameter \(tr_{\text{dance with me}}\), is equal to the ratio of the number of imitational behaviors of the robot's movements (performed by the child and counted by the rater), denoted by \(N_{ch}^{\text{dance with me}}\) (dance with me), and the total number of the robot's movements during the dance that could potentially be imitated by the child, denoted by \(N_{r}^{\text{dance with me}}\) (dance with me).