The cursor is not felt in the idle state, to avoid numbness.
The details about feedback and states machines are presented in the paper~\cite{gupta16}.
+\input{figures/tactiledm.tex}
+
We validated the concept with user evaluations of the proof of concept prototype.
First we validated that users are able to navigate and distinguish targets with a JND experiment on the maximum number of targets they were able to count.
In average, participants were able to count up to 19 targets.
We proposed a refined pointing model that takes into account this observation.
Finally we designed two tactile menus with 4 and 8 items and we showed that participants were fast and accurate.
-\input{figures/tactiledm.tex}
-
-\subsection{Haptic and embodiment in Virtual Reality}
+\subsection{The sense of embodiment in Virtual Reality}
\label{sec:embodiment}
We discussed in \refsec{sec:qualitative} that haptic feedback has qualitative benefits, in particular when it restores haptic sensations that are non existent or limited in gestural or multi-touch interaction.
They can also perform operations that the users cannot in the physical world like telekinesis or teleportation.
In fact, the appearance or behavior of the avatar has an influence on the way the users behave in the virtual environment.
For example, the \defword{Proteus effect} describes the way the visual representation of an avatar influences the behavior of the users that control it~\cite{yee07}.
-%rubber hand \cite{botvinick98}
-More generally, Kilteni \etal defined the \defword{sence of embodiment} of a virtual body~\cite{kilteni12}.
-It is based on de Vignemont's definition of artificial embodiment that also refers to protheses or tools for example~\cite{devignemont11}.
+At the opposite, visuo-tactile stimulation can lead people to consider a rubber hand as part of their body~\cite{botvinick98}, or that they have a sixth finger on their hand~\cite{hoyet16}.
+These effects are examples of extension of the \defword{sense of embodiment} of a virtual body~\cite{kilteni12}.
+%, or artificial artefacts such as protheses or tools for example~\cite{devignemont11}.
% Embodiment: E is embodied if and only if some properties of E are processed in the same way as the properties of one’s body.
-Kilteni \etal discuss three subcomponents of the sense of embodiment.
+Kilteni \etal discuss three subcomponents of the sense of embodiment that were extensively studied in the literature~\cite{kilteni12}.
\defword{Self location} refers to the “volume in space where one feels to be
located”.
\defword{Agency} refers to “the sense of having global motor control” over the virtual body.
And \defword{ownership} refers to “one’s self-attribution of a body”.
-We can measure the embodiment of an avatar in a virtual environment with questionnaires~\cite{roth20,gonzalezfranco18,peck21}.
-+ Tactile sensations, External appearance, response to external stimuli\cite{gonzalezfranco18}
+\subsubsection{Methodologies for measuring the sense of embodiment}
+
+There is a number of embodiment questionaires in the literature to measure the sense of embodiment.
+We discuss some of them in one of our studies~\cite{richard22}.
+%We can measure the embodiment of an avatar in a virtual environment with questionnaires~\cite{roth20,gonzalezfranco18,peck21}.
+There are recent attemps to standardize these questionnaires.
+For example Roth \etal propose a questionnaire with \defword{ownership}, \defword{agency}, and perceived change in the \defword{body schema}~\cite{roth20}.
+The latter notion is larger than \emph{self location} as it refers to any difference the users may perceive between their own body and the avatar.
+Gonzalez Franco and Peck proposed another questionnaire in which they added to Kilteni \etal's subcomponents : \emph{tactile sensations}, \emph{external appearance}, and \emph{response to external stimuli}~\cite{gonzalezfranco18}.
+They later improved and simplified their questionnaire, and evaluated it with many different tasks~\cite{peck21}.
+The subcomponents of this new questionnaire are: \emph{appearance}, \emph{response}, \emph{ownership}, and \emph{multi-sensory}~\cite{peck21}.
+Interestingly, \emph{agency} is not an identified subcomponent but rather distributed among the others, in particular to the \emph{response} subcomponent.
+%This does not mean that agency, touch or localization are not important for embodiment, (Kilteni et al., 2012), but rather that they are related to other senses and instead contribute to one of the four prominent embodiment categories. The questions on motor control and agency were mostly assigned to the Response category
+
+These questionnaires are typically used in controlled experiments after the participants performed a specific task in a virtual environment.
+We compare the overall embodiment and its subcomponents score in two or more conditions to identitfy the effects of these condition.
+The experimental protocol we can use depends on the task.
+For example some studies use a threat like a virtual fire or sharp blade as an objective measurement of embodiment~\cite{dewez19,argelaguet16}.
+Subjects are considered embodied if they attempt to avoid the threat despite its virtual nature.
+The issue is that this kind of metric requires participants to be surprized by the threat.
+However, this cannot be guaranteed with a \defword{within-subjects design} in which participants perform all the conditions one after the other.
+In such situations the experiment must follow a \defword{between-subjects design}, in which separate groups of participants perform a different condition.
+% There are however several other factors that influence the choice of experimental setup.
+% For example, between-subjects studies require more participants to reach the same statistical power.
+% Each participant of a within-subject study provides less data per condition if we would like to keep the same experiment duration.
+
+%When designing virtual embodiment studies, one of the key choices is the nature of the experimental factors, either between-subjects or within-subjects. However, it is well known that each design has ad- vantages and disadvantages in terms of statistical power, sample size requirements and confounding factors. This paper reports a within- subjects experiment with 92 participants comparing self-reported embodiment scores under a visuomotor task with two conditions: synchronous motions and asynchronous motions with a latency of 300 ms. With the gathered data, using a Monte-Carlo method, we created numerous simulations of within- and between-subjects exper- iments by selecting subsets of the data. In particular, we explored the impact of the number of participants on the replicability of the results from the 92 within-subjects experiment. For the between-subjects simulations, only the first condition for each user was considered to create the simulations. The results showed that while the replicabil- ity of the results increased as the number of participants increased for the within-subjects simulations, no matter the number of partici- pants, between-subjects simulations were not able to replicate the initial results. We discuss the potential reasons that could have led to this surprising result and potential methodological practices to mitigate them.
+%galvanic skin response \cite{kokkinara14}
+
+\paragraph{User study}
+
+In a between-subjects study, users are assigned to one of the conditions.
+There is therefore potentially a bias if the groups are not well balanced.
+We investigated this effect on embodiment studies~\cite{richard22}.
+We experimented a visuo-motor task with a synchronous condition and an asynchronous condition with a latency of \qty{300}{\ms} between the input and output response.
+This value is known to have a medium effect on embodiment in the literature~\cite{botvinick98,kilteni12,kokkinara14}.
+We chose a simple experimental task that requires no special equipment to facilitate replication.
+Participants were seated on a chair, with the legs on a table, and had to perform gestures with their feet (\reffig{fig:expewithin}), similarly to~\cite{kokkinara14}.
+92 participants performed this task in a balanced within-subjects design.
+To study the effect of the sample size and its effect on the statistical analysis we analyzed random data subsets of 10 to 92 participants.
+To study the effect of the experiment design we simulated between-subjects design by selecting the first condition of participants.
+We considered the analysis of all participants with the within-subjects design as the ground truth, which gave the same result as the literature~\cite{botvinick98,kilteni12,kokkinara14}.
+
+Our results show that all the random subsets with at least \num{40} participants with the within-subjects design gave the same result as the ground truth.
+However, regardless of the number of participants the between-subject analyses do not reveal the ground truth effect.
+Based on the debrieffing with participants, our main explanation of this phenomenon is that participants needed a reference to provide a value for each question.
+Therefore they calibrated their answers to the second condition relatively to the first one.
+Hence, we could not measure the effect with the first condition only.
+We discuss recommendation and possible mitigation strategies in the paper~\cite{richard22}.
+Interestingly, when we analyzed the second condition as a kind of calibrated between-subjects design we observed the ground truth effect.
+However, the effect size was about half the effect size of the within-subject analysis.
+Therefore, we wonder if both designs even measured the same phenomenon.
+We are still working on this subject, in particular to provide calibration methods and metrics to balance groups for between-subjects design in embodiment studies.
+
+\begin{figure}[htb]
+ \centering
+ \includegraphics[height=3.9cm]{figures/within-setup}\hfill
+ \includegraphics[height=3.9cm]{figures/within-environment}\hfill
+ \includegraphics[height=3.9cm]{figures/within-avatars}%
+ \caption[Setup of the embodiment methodology study.]{The user seated on a chair, performing leg movements, the virtual environment, and the two avatars.}
+ \label{fig:expewithin}
+\end{figure}
-Questionnaires \cite{roth20,peck21} Peck : sensorial aspect
+\subsubsection{Haptics and the sense of embodiment}
-interaction on embodiment \cite{argelaguet16}
+The study of the causes and effects of the sense of embodiment of an avatar in virtual reality is a hot topic in the Virtual Reality community.
+%Results show that the sense of agency is stronger for less realistic virtual hands which also provide less mismatch between the participant's actions and the animation of the virtual hand. In contrast, the sense of ownership is increased for the human virtual hand which provides a direct mapping between the degrees of freedom of the real and virtual hand.
+Interestingly, all the embodiment questionnaires such as those we discussed before have subcomponents related to the sensorimotor loop.
+It means that the sensorimotor loop is essential ot the sense of embodiment.
+For example, people have a stronger sense of ownership when they perform actions with a visually realistic hand, and a stronger sense of agency when they embody an abstract-looking virtual hand~\cite{argelaguet16}.
+Following this idea, we studied the effect on haptics on the sense of embodiment~\cite{richard20}.
-\cite{richard20,richard22}
+We performed a user study to compare embodiment for a drawing task with force feedback, tactile feedback, and a control condition with no haptic feedback~\cite{richard20}.
+The participants were seated on a chair, and they had to paint a mandala in an immersive virtual environment with a Phantom Desktop\footnote{Today called Touch X by 3D Systems \url{https://www.3dsystems.com/haptics-devices/touch-x}} device (\reffig{fig:expeembodiment}).
+In the force feedback condition they felt the surface resistance of hard objects, and the viscosity of paint.
+In the tactile condition, they felt a \qty{250}{\hertz} vibration whose amplitude was protortional to the interpenetration distance to the canvas surface.
+We attached an EAI C2 tactor to vibrate the Phantom stylus (\reffig{fig:expeembodiment}).
+In the control condition the Phantom was only used as an input device, with no force or vibration.
+We mesured embodiment with Gonzalez Franco and Peck's first standardized questionnaire\footnote{The second one was not published at the time.} with the \emph{agency}, \emph{self location}, \emph{ownership}, and \emph{tactile sensations} subcomponents~\cite{gonzalezfranco18}.
-\begin{figure}
+We observed a stronger embodiment in the force feedback condition compared to the control condition.
+In particular participants had a higher sense of ownership.
+However, we did not observe these differences between the tactile and control conditions.
+
+…
+task favored force feedback over tactile
+
+\begin{figure}[htb]
\centering
\includegraphics[height=3cm]{figures/embodimentdevice}\hfill
\includegraphics[height=3cm]{figures/embodimentenvironment}\hfill
\includegraphics[height=3cm]{figures/embodimenttask}%
- \caption[Setup of the virtual embodiment study.]{Haptic device setup, virtual environment and task of the virtual embodiment study.}
+ \caption[Setup of the haptics and embodiment study.]{Haptic device setup, virtual environment and task of the virtual embodiment study.}
\label{fig:expeembodiment}
\end{figure}
-task favored force feedback over tactile
+
+\subsection{Discussion}
\section{Conclusion}