Manipulating the Sense of Embodiment in Virtual Reality: a study of the interactions between the senses of agency, self-location and ownership

In Virtual Reality (VR), the Sense of Embodiment (SoE) corresponds to the feeling of controlling and owning a virtual body, usually referred to as an avatar. The SoE is generally divided into three components: the Sense of Agency (SoA) which characterises the level of control of the user over the avatar, the Sense of Self-Location (SoSL) which is the feeling to be located in the avatar and the Sense of Body-Ownership (SoBO) that represents the attribution of the virtual body to the user. While previous studies showed that the SoE can be manipulated by disturbing either the SoA, the SoBO or the SoSL


Introduction
Virtual Reality (VR) is a growing field, becoming more and more accessible to the public.Virtual bodies (usually referred to as avatars) are increasingly often used in Virtual Environments (VEs), due to the many applications of VR such as entertainment [ASK20], interactive training [BGB * 15], scientific visualisation [DMI * 18] or virtual therapy [Lin20].It is thus important to better understand the Sense of Embodiment (SoE): that is "the subjective experience of using and having a body" [BM09].In the context of VR, hardware and software can "substitute a person's body with a virtual one" [SNB * 14] and the SoE is typically characterised by three components (although being a topic of discussion [PGF21]): the Sense of Agency (SoA), the Sense of Self-Location (SoSL) and the Sense of Body-Ownership (SoBO) [KGS12].The SoA is the feeling of being the cause of our actions.The SoSL is the spatial experience of being inside a body.Finally, the SoBO is the feeling that the virtual body is the source of my sensations (like my real body).Deepening the comprehension of these three components would help better understand the SoE.However, the relationships and interactions between SoA, SOBO and SoSL still remain unclear, especially in a VR context, as many of the existing studies only focus on 1 or 2 components at the same time.In this paper, our aim is to better understand the SoE and the interactions between its components by 1) experimentally manipulating independently the SoA, SoSL and SoBO in VR, and 2) study to what extent each component can be selectively altered.To do so, we designed a within-subject experiment where 47 right-handed participants performed movements of their right-hand under different experimental conditions impacting the components of the SoE (see Figure 1): the SoA was modified by impacting the control of the avatar with a biased visual feedback, the SoSL was controlled via the user's point of view (first-person, third-person in peripersonal space or third-person in extra-personal space) and the SoBO was altered by modifying the realism of the virtual right hand (anthropomorphic cartoon hand or non-anthropomorphic "stick fingers").After each trial, participants rated their levels of agency, ownership and self-location on a 7-item Likert scale.To the best of our knowledge, this is the first time that SoA, SoSL and SoBO are manipulated in a same VR experiment to study their interactions.This paper is structured as follows.Section 2 gives an overview of related work on the SoE, SoA, SoBO and SoSL and details how they were previously manipulated.Section 3 presents the experimental protocol and design as well as our research hypotheses.Our results are analysed in Section 4 and discussed in Section 5. Finally, Section 6 concludes this work and presents some future works.

Related Work: The Sense of Embodiment in Virtual Reality
Although the Sense of Embodiment is studied in multiple communities [BM09,dV11,Gal00], we focus here on the SoE in the context of VR and present how it can be manipulated in VR experiments.
To do so, we study it through the prism of its three components, as defined by Kilteni et al. [KGS12].Many factors impact the SoE, e.g. the avatar's appearance, the Virtual Environment (VE), and also the user's personality and preferences [Fri20,Dew21].More precisely regarding the avatar, in addition to its appearance (which mostly relates to the SoBO), the amount of control of the avatar (re-lated to the SoA) and the point of view (linked to the SoSL) play an important role on the SoE.

The Sense of Agency
The Sense of Agency is defined by statements like "I am the one in control of my actions" or "this is me that opened the door".According to Gallagher, it is "the sense that I am the one who is causing or generating an action" [Gal00].Not only does this refer to generating an action, it also considers the outcome from this action, by making a change in the environment.Following the neuroscience community's definition of Blanke and Metzinger [BM09], the SoA refers to the sense of having "global motor control, including the subjective experience of action, control, intention, motor selection and the conscious experience of will".For a review of the SoA, see [BDS * 18, Hag17].
The way users interact with the VE and their avatar impacts their level of immersion: having controllers in hands or using handtracking will not result in the same experience of embodiment.For instance, having foot-tracking significantly improves the SoSL as well as the SoA [EMFM21].
It has been shown that the SoA can be modulated in VR by means of biased visual feedback, where the outcome of an action does not match the intended action [KIS * 15,PGFSV * 16,JAAL18].In [PGFSV * 16], the virtual hand of the avatar sometimes moved in the opposite of the intended direction.In [JAAL18], the SoA was manipulated in three different ways: (i) adding temporal lag in the user's movement; (ii) inverting two fingers; or (iii) having one finger moving by itself.All three manipulations altered the SoA.

The Sense of Self-Location
According to Kilteni et al. [KGS12], self-location "is a determinate volume in space where one feels to be located".In this way, the Sense of Self-Location refers to the spatial experience of being inside a body.The avatar can be embodied in a first-person perspective (1PP) [SSSVB10, PWL * 14, AHTL16, KBS13], imitating the way one observes the world in everyday life in healthy situations, or in third-person perspective (3PP), simulating an out-ofbody experience, and watching the body from an external point of view [LTMB07, SSSVB10, BBOS17, Ehr07].The SoSL is thus based on the visuospatial perspective (1PP or 3PP).However, it also considers vestibular signals, and tactile inputs.Vestibular signals consist of body information of rotation, translation, and orientation in relation to gravity [BM09].Patients who experienced outof-body experiences (feeling to be outside of their body with the visual perspective also coming from outside the body) had vestibular dysfunction [BLSS04].Finally, tactile inputs are related to the way the brain encodes its surrounding space relatively to the body (personal space -the skin; peripersonal space -everything at grasping range; and extrapersonal space -anything out of reach [KGS12]).
The SoSL can thus be manipulated in VR by (i) changing the point of view from 1PP to 3PP [LTMB07, SSSVB10, BBOS17, Ehr07], or (ii) with synchronous visuo-tactile stimulations.For instance, Normand et al. [NGSS11] embodied participants in avatars with different body volumes than their real body, which resulted in a differently perceived personal space.

The Sense of Body-Ownership
The Sense of Body-Ownership is defined by statements like "this is my hand" or "I am the one who is having this feeling" [BDS * 18].This feeling has first been addressed in the Rubber-Hand Illusion (RHI) experiment of Botvinick and Cohen [BC98].They showed that one can have a feeling of ownership toward a fake rubber hand, after stroking simultaneously with a brush one's real hand and the rubber hand.This experiment was extended to VR with a feeling of ownership toward a virtual hand [IdKH06,YS10], a virtual arm [LTMB07] and a full body [SPMESV09].For a review of the SoBO, see [BDS * 18].
The SoBO has been found to be impacted by the avatar's appearance [PE08, AHTL16], which can vary in shape, colour or height.It has been shown that increasing the avatar's realism improved the SoBO and therefore the SoE [AHTL16, LJ16] (although an uncanny valley effect can exist to a certain extent [Mor12,LLL15]).

Interaction between the components
As of now, we know that the three components of the SoE (SoA, SoSL and SoBO) are not independent but rather interact with each other.However, the interactions between them remain unclear.While a vast part of the literature investigates existing interrelations between them, there is still some variability in the results.In the previous sections, we reviewed how each component can be manipulated in VR experiments, but these manipulations may impact the other components as well.Indeed, as the visuospatial perspective is related to the SoSL, it was also found to play a role in the SoBO [PKE11].More precisely, SoBO and SoSL are strongly coupled, and breaking the SoSL reduces the SoBO.However, in their experiment, Maselli and Slater found that the SoBO and the SoSL can be selectively altered, depending on the distance between the user's perspective and the virtual body [MS14].
The link between the SoSL and the SoA is the least explored interaction.Nevertheless, David et al. [DBC * 06] claim that the two are independent.While using avatars, this experiment was however not in VR but on a screen-based desktop 3D environment.The SoSL was modified by changing the visuospatial perspective from 1PP to 3PP, and the SoA was either present in an active task (pressing a button to throw a ball) or absent in a passive task (indicating which avatar is throwing a ball).
Finally, there is some discrepancy in the results toward the interaction between the SoA and the SoBO.Some neuroscience studies (not in VR) showed that the two were related [TSBG07] while others (still not in VR) found them to be independent [KE12, TLH10].There are two models accounting for this interaction: an additive model in which they are both strongly related, and an independent model where the SoBO and the SoA are qualitatively different experiences, with distinct brain networks, as denoted by Tsakiris et al. [TLH10].In VR experiments, while the visual realism and appearance of the avatar were shown to impact the SoBO [AHTL16, LJ16,CHLL18], its relationship with the SoA is less clear.Indeed, it was sometimes found to also impact the SoA [AHTL16] and sometimes not [LJ16].The relationship between these two components of the SoE may vary depending on the experimental conditions, as stated by Chen et al. [CHLL18].
To the best of our knowledge, this is the first experiment studying the interaction between the three components at the same time.To summarise, existing results tend to show that the SoA and the SoBO are partly dependent, and that the SoSL may be independent from the SoA while closely related to the SoBO.

Material and Methods
In this section we present the participants, experimental protocol and measures used in our study and detail our research hypotheses.

Participants
Fifty (50) participants were originally recruited in the experiment.Three participants were removed due to issues during the recording of their data.So, a total of 47 participants (27 men, 20 women, 28.43±11.05year-old (mean±SD)) took part in the experiment.All participants had normal or corrected-to-normal vision.As the questionnaire was only in french, the population was restricted to french speaking people.Because we asked participants to perform right-hand movements, we also recruited only right-handed persons, as we cannot assess if handedness might impact our dependent variables in this study.The experimental protocol has been approved by the internal review board of Université de Nantes.

Experimental manipulation of the components of the SoE
Since there are multiple ways to study each component of the SoE (i.e SoA, SoSL and SoBO) as well as to study the impact of each manipulation to these components, we wanted to know to what extent each component could be selectively altered, based on the existing literature.In this section, we define and detail the manipulations implemented in the experiment.

Agency Manipulation
The SoA is manipulated by means of biased visual feedback (the outcome of an action does not match the intended action).In this experiment, there are two agency conditions: • Synchronous condition, where there is no manipulation on participant's hand tracking.There is a direct mapping from user's real hand movement to the avatar's hand; • Manipulated condition, where the visual feedback of the participant's hand movement is biased by one of three manipulations (see below).
The SoA is manipulated following Jeunet et al. experiment's [JAAL18] in three different ways: (i) adding 1s of temporal lag in the user's movement; (ii) having the thumb moving by itself; or (iii) inverting the 2 nd and 4 th fingers (see Figure 1).These three manipulations were kept in order to add variety to the experiment and be more representative of tracking issues that could alter the SoA.These manipulations of the SoA are nonetheless not distinguished in the experimental protocol nor in the analysis (as they were found to all have an effect in [JAAL18]).

Self-Location Manipulation
The SoSL is manipulated by changing the visuospatial perspective of the user (either 1PP or 3PP).In this experiment, there are three self-location conditions (see Figure 1): • 1PP condition, where the user's visuospatial perspective matches the avatar's position; • 3PP-PP condition, where the visuospatial perspective is shifted 20cm to the right of the user, remaining in the peripersonal space -everything at grasping range.• 3PP-EP condition, where the visuospatial perspective is shifted 50cm to the right of the user, being in the extrapersonal spaceanything being out of reach.
Indeed, as mentioned in Section 2.4, it was shown that the visuospatial perspective has an impact on the SoBO but only in certain conditions [MS14].In their experiment, Maselli and Slater changed the visual perspective of participants in a VR experiment: either (i) in 1PP with a total overlap of the participant's real body and the virtual body; (ii) in a 3PP shifted around 25cm to the right with the left leg of the participant being near the right leg of the avatar; or (iii) in a 3PP shifted 80cm to the right of the virtual body, so that there is no overlap at all between the participant's real body and the virtual body.The authors observed that the SoSL was altered in both 3PP conditions, but the SoBO was preserved in the 3PP at 25cm compared to the 3PP at 80cm.This is what we wanted to replicate in this experiment, in order to selectively alter each component.However, due to technological constraints, the virtual body could not be 80cm away from the participant since, at that distance, the hand tracking was lost when not looking at the hand.Indeed, when the visuospatial perspective is shifted laterally to the right, the users turn their head to the left to see the virtual body (see Figure 1) while their real hand stays in front of them.In that configuration, the VR headset was unable to perform stable hand-tracking, the real hand of the participant being outside of the range of the HMD's sensors.We experimentally found out that the avatar could be located at a maximum of ∼50 cm away from the participant for hand-tracking to work for an average participant.Fortunately, 50cm is at the border of peripersonal space (reported at 45 ± 7cm in [RFML20]).

Body-Ownership Manipulation
In VR, the SoBO can be manipulated with visuo-tactile asynchronous stimulations [BC98] or changing the appearance of the avatar's hand [AHTL16,LJ16,CHLL18].In this experiment, there are two body-ownership conditions: • Anthropomorphic-hand condition, where the avatar has an anthropomorphic cartoon hand (see Figure 1); • Stick-f ingers condition, where the avatar has a nonanthropomorphic hand with sticks as fingers (see Figure 1).
Because we are forced to have movements due to the study of the SoA, we could not use visuo-tactile asynchrony.In this way, we decided to change the appearance of the avatar's hand to alter the SoBO like previous studies [AHTL16, LJ16, CHLL18].In their experiment, Lin and Jörg showed that a SoBO can be created with different realistic representation of a hand, being a realistic hand, a toony or very toony hand, a zombie or robotic hand or even a wooden block [LJ16].Nevertheless, the effect is the weakest for the non-anthropomorphic block model.Moreover, it has been shown that in order to induce ownership toward an external object, a basic morphological similarity with the real body part (or whole body) is needed [AR03, TCJF10, TH05].
We expect the SoBO to be lower with a non-anthropomorphic hand, similar to the wooden block in [LJ16]'s experiment.Since we wanted participants to perform hand movements and more specifically fingers movements, this non-anthropomorphic hand needed to have "fingers" for the user to be able to reflect upon their movements.We thus decided to have 5 "sticks" as fingers, aligned (i.e., there was no "thumb-like" position for any of the sticks) and floating in front of the avatar's wrist (see Figure 1).Moreover, the sticks are not attached to the wrist to make it less anthropomorphic (as a SoBO was possible with a robotic hand in [LJ16]).
On the contrary, in the condition where a high ownership illusion was expected we choose to use an anthropomorphic cartoon hand (see Figure 1).This was preferred over a realistic hand for two reasons.The first one being that an uncanny valley effect can exist to a certain extent, and the second being that otherwise, the virtual hand would have to match the shape of the hand and skin colour of each participant to not be a potential impacting factor [Mor12,LLL15].It has also been found that a SoA is still possible for less realistic hands [AHTL16].In 3PP-PP and 3PP-EP conditions, the user could in addition see the avatar's head (only if they turned their head, which they were instructed not to do).Still, as a safety measure, the avatar had a hood covering all his head, such that the avatar's face could never be seen from a 3PP (see Figure 1).
With two conditions for the SoBO and SoA, and three for the SoSL, we explored a total of 2 × 2 × 3 = 12 distinct conditions.

Design and Hypotheses
The experiment followed a full factorial 2×2×3 design: SoAmanipulation (Synchronous vs Manipulated), SoSL-manipulation (1PP vs 3PP-PP vs 3PP-EP) and SoBO-manipulation (Anthropomorphic-hand vs Stick-f ingers).All variables were within-subjects.The goal was to study the interaction between the SoA, the SoSL and the SoBO manipulations on the SoA (resp.SoSL and SoBO) as evaluated by our custom questionnaire (1 question on a 7-item Likert scale for each component).The resulting SoA (resp.SoSL and SoBO) score is computed by averaging over repetitions.Our hypotheses regarding the SoA score were:

Apparatus
In this study, participants were immersed in a VE by means of an Oculus Quest 2 HMD (1832x1920px per eye and 89 • FoV), with head and hand tracking directly provided by the headset.Highfrequency tracking was activated to have 60Hz tracking.The VE was developed in Unity 2020.3.10f1.While the Oculus Quest 2 is an autonomous headset, it was wired to a laptop (Intel Core i7-8750H CPU and GTX 1070) to ensure optimal performance.

Experimental protocol
Participants had to fill and sign an informed consent form before the experimental protocol was explained to them.All participants were provided with the exact same written instructions, which indicated that they would have to perform three blocks of 5 minutes each, each block associated to a different movement type (either tapping, abducting/adducting the fingers or counting as in [JAAL18] -in order to introduce variability in the experiment, without considering the movement type as an impacting factor).The experimental VE was a virtual room where participants were embodied in an avatar seated in front of a table (205cm × 75cm × 67cm).In front of them, a TV hanged on the wall (1.60m from the virtual body, 158cm × 0.85cm), on which videos and signals were displayed (see Figure 1).The experimental protocol is depicted in Figure 2.
After the explanation of the experiment, the VR headset was installed.The experiment first started by displaying videos of the different right-hand movements participants would have to perform.Participants could repeat them while the video was playing, and were corrected if the movement was done improperly.Then, participants had to perform a small tutorial of 3 trials (see next paragraph) in order to introduce them to the experimental protocol and to get used to the VE.Finally, once all remaining questions from the participants were answered by the experimenter, the experiment consisting of 3 blocks of 12 trials each started (see Figure 2 and 3).
Participants could take a break between blocks if they wanted to.On average, it took 40 minutes for each participant to complete the whole experiment (including explanations).In total, participants performed 36 trials (3 blocks × 12 trials), resulting in 3 trials per condition.The movement associated with each block, as well as the order of the 12 conditions within a block were counterbalanced between the participants in order to avoid any order effect.The only fixed parameter was the first trial of each block being a "full embodiment" condition (Synchronous and Anthropomorphichand and 1PP) to get a reference for other trials.The tutorial's aim was to get the participants used to the SoSL manipulation, i.e changing the visuospatial perspective.Indeed, as trials are only 6s long, it could be unsettling for some people the first time in a third-person perspective.The tutorial consisted in 3 (non-recorded) predetermined trials using the tapping movement: the first trial was a "full embodiment" condition; the second trial was only altering the SoSL by putting participants in the 3PP-EP condition; then a third trial in "full embodiment" again.

Subjective Measures
Most VR experiments about virtual embodiment use a questionnaire after each condition to assess the level of embodiment of the participant.Usually, the questionnaire is inspired from Botvinick and Cohen's RHI experiment [BC98], but there are also questionnaires designed for the SoE [RL20,PGF21].These questionnaires usually contain multiple questions for each component of the SoE.Given the number of trials and conditions we wanted to test, it was impossible to have our participants fill-in this kind of questionnaire after each of the 12 conditions.As a consequence, we followed the procedure used in Jeunet et al. [JAAL18] to evaluate the SoE after each condition.After each trial, participants were asked to answer in VR 3 questions only, one to evaluate the SoA ("I was in full control of my actions in the virtual environment"), one to evaluate the SoSL ("I felt as if my body was located where I saw the virtual body"') and one to evaluate the SoBO ("I felt as if the virtual body was my body").These questions were inspired or taken from existing questionnaires [BC98, JAAL18, HBC * 20, PGF21].The questions were preceded by "When I moved my right hand" to make sure participants rated their SoE during the hand movement only.For each question, participants answered on a 7-point Likert scale from "Strongly disagree" to "Strongly agree" with no label in between.
Participants answered the questionnaire directly in VR in another virtual room, with their left hand, with only an Oculus hand appearing in the VE (and no avatar -see Figure 4 -and the Oculus left hand was never shifted regardless of the SoSL-manipulation level) as to not alter the feeling of the trial.Participants were asked to try to keep their right hand posture while answering the questionnaire to be ready to start for the next trial.

Results
Rstudio [RSt20] software was used to perform the statistical analyses and Python 3.8 was used to plot the figures with Seaborn/Matplotlib [Was21, Hun07].The significance level used is α = 0.05, corrected with Bonferroni methods.Three 3-way ANOVAs for repeated measures were performed considering as factors SoA-manipulation (Synchronous vs Manipulated), SoSL-manipulation (1PP vs 3PP-PP vs 3PP-EP) and SoBO-manipulation (Anthropomorphic-hand vs Stickf ingers).The goal of these analyses was to investigate relationships between one component of the SoE and the two others.For clarity, only significant and relevant results are reported.Full analyses data are available in supplementary material.
The 3 dependent variables were: the SoA score (s_soa), the SoSL score (s_sosl) and the SoBO score (s_sobo).For each of the 12 conditions, the score is defined as the mean of the 3 trials performed in this condition (1 per block).This ensures the assumption of independence of the ANOVA is met.Because the questionnaire and experimental design are similar to [JAAL18], we performed the same analysis.In the end, for each participant, there are 3 SoE components ×12 conditions = 36 scores.

Impact of the Manipulations on the SoA Score
In this analysis, the dependent variable was the average SoA score.The normality assumption was respected, based on the Shapiro-Wilk test performed on the residuals.However, according to Mauchly's test, the sphericity assumption was violated for the SoSL-manipulation variable (p = 0.010).So, the Huynh-Feldt correction was applied to the degrees of freedom.

Impact of the Manipulations on the SoSL Score
The dependent variable in this ANOVA was the average SoSL score.A Shapiro-Wilk test revealed a violation of the assumption of normality.Yet, these parametric methods are known for their robustness regarding non-normally distributed data when applied to Likert-scales [MA17,Nor10].The sphericity assumption was violated according to Mauchly's test for the SoSL-manipulation (p < 0.0001) variable, SoA-manipulation*SoSL-manipulation (p < 0.01) and SoBO-manipulation*SoSL-manipulation (p < 0.05) interactions.Thus, the degrees of freedom were corrected using the Huynh-Feldt correction.

Discussion
The aim of this study was to deepen the understanding of the SoE and the interactions between its components by 1) experimentally manipulating them in VR via a biased visual feedback, and 2) studying to what extend each component can be selectively altered.
Participants' scores of SoA, SoSL and SoBO showed that all manipulations worked on their main target (i.e the SoAmanipulation impacted negatively the SoA, supporting H1; the SoSL-manipulation impacted negatively the SoSL, supporting H6; and the SoBO-manipulation impacted negatively the SoBO, supporting H8).These results were expected from the literature, but we were able to confirm them in a different but similar experiment.
The experimental protocol failed to selectively alter each component.Nevertheless, this study also brings new insight to the interaction between SoE components.Indeed, to the best of our knowledge, this is the first time that the SoA, the SoSL and the SoBO are manipulated in a same VR experiment to study their interactions.Results showed that the SoE components are tightly coupled.

Interaction between SoA and SoSL
Results revealed that the SoA-manipulation interacts with the SoSL-manipulation (see Figure 5 and Figure 6).These results contradicts H3 and H4.Indeed, post-hoc tests showed that the SoSLmanipulation alters the user's SoA but only in the Synchronous condition (with a large effect size).In the current study, it could be argued that in the Manipulated condition, the SoA may be too low for the SoSL-manipulation to have an effect.There were also no significant difference in the Synchronous condition between 3PP-PP and 3PP-EP, so shifting the user's point of view by just 20 cm to the right might be already enough to alter the SoA.Likewise, results revealed that the SoA-manipulation has an effect on participants' SoSL only in 1PP condition.This again could be explained by the fact that in the 3PP-PP and 3PP-EP conditions, the SoSL may be too low to be impacted by the SoA-manipulation.

Interaction between SoA and SoBO
Interaction analysis and post-hoc tests showed that the SoAmanipulation interacts with the SoBO-manipulation (see Figure 5).This contradicts hypothesis H2 but supports hypothesis H7.Indeed, we did not expect the SoBO-manipulation to alter the user's SoA, but this occurred in the Synchronous condition (with a large effect size).This is coherent with [CHLL18]'s results stating that the relationship between the SoA and the SoBO may vary depending on the experimental conditions.This could be explained by the fact that in the Manipulated condition, the SoA score is already too low for the SoBO-manipulation to have an effect.Bottom-up factors might have a stronger effect than top-down factors: the SoBO-manipulation targets cognitive processes while the SoA-manipulation leads to incongruent stimuli at the perceptual level (the visual cues do not match the perceptual cues produced by the actual movement) [LW22].Likewise, results revealed the SoA-manipulation has an effect on participants' SoBO score with a large effect size, supporting H7.These results reinforce the idea that the SoBO and SoA are dependent.

Interaction between SoBO and SoSL
Interaction analysis and post-hoc tests showed that the SoBOmanipulation interacts with the SoSL-manipulation.We hypothesised that the SoSL-manipulation would impact the SoBO score only in 3PP-EP (H9).Indeed, we expected to find the same results as in Maselli and Slater's experiment [MS14] but it was not the case.While there is a difference between 1PP and 3PP-EP, we also observed a difference between 1PP and 3PP-PP in all conditions except in the Stick-f ingers+Manipulated condition, and thus we do not validate H9 nor replicate [MS14]'s results.Likewise, results showed that the SoBO-manipulation altered the user's SoSL, but only in the 1PP condition, which contradicts hypothesis H5.

Limitations
Despite being the first VR experiment where the SoA, SoSL and SoBO are manipulated at the same time to study their interactions (to the best of our knowledge), our study has some limitations.
In this experiment, we used a non-anthropomorphic hand (the Stick-f ingers condition) with five aligned stick fingers (i.e.without a thumb) instead of a robotic hand [LJ16] or a wooden block [LJ16] to alter the hand realism, because we needed hand and finger movements.Since this kind of hand has, to the best of our knowledge, not been used before, we do not know how it impacts the SoA.This hand could be perceived as inaccurate due to the incorrect position of the thumb, thus influencing the SoA.However, it is still unclear how the SoA is impacted by hand appearance, as sometimes it was shown to have an impact [AHTL16] and sometimes not [LJ16].We cannot conclude if the influence of hand realism on SoA in our experiment is due to the hand appearance or to the sticky fingers looking inaccurate.Nevertheless, the movements were not meant to be perfectly executed and we believe that this "sticky thumb" is not the cause of the impact of realism on the SoA.In most post-experiment verbal reports, participants indicated to be disturbed more by SoA manipulations even in the Stick-Fingers condition than by the hand realism.It remains an open question for future work.
Another limitation of this study is the short amount of exposure time.Indeed, each trial was only 6s long.It can thus be questioned if there were any sort of embodiment experienced by participants.With so many conditions, it was not feasible to have long exposition time for each condition with some repetitions, this is why we followed [JAAL18]'s experimental design.Participants however had to perform a tutorial first, in which they could get used to the virtual body and the hand tracking system.Moreover, in post experiment verbal reports, participants mostly reported to feel embodied during the experiment.Also, all manipulations relied on visual feedback, so participants could perceive the differences directly.
The use of the Oculus left hand to fill the questionnaire after each trial may have impacted the SoE.However, the questionnaire explicitly mentioned "When I moved my right hand" to make sure participants rated their SoE during the hand movement only, and this was insisted on during the explanation of the experiment.
Finally, as mentioned in subsection 3.6, we could not use standardised SoE questionnaires [RL20,PGF21] after each condition and relied on the method from [JAAL18]'s experiment.This hinders comparability with other experiments since SoE scores could not be calculated.However, our questions were taken from existing validated questionnaires, and more importantly, in this withinsubject experiment we were more interested in differences between the conditions to better understand the interactions between the components.Further experiments should explore other experimental designs in order to include these standardised questionnaires.

Conclusion
The presented experiment explored the relationships and interactions between the SoA, the SoSL and the SoBO.We were able to confirm previous results like the link between SoA/SoBO and SoBO/SoSL.Moreover, we observed that the SoSL and SoA seem to be not independent, and this is, we believe, the first experiment investigating the link between the SoSL and the SoA in VR scenarios.Finally, we confirmed that the three components are all interrelated regarding the SoBO score.Nevertheless, additional studies are required to explore the relationship between the components and better understanding the factors impacting them.

Figure 2 :
Figure 2: Experimental protocol.The "Full SoE" condition in the tutorial represents the Synchronous and Anthropomorphic-hand and 1PP condition together.Movement A, B and C are the three movements (tapping, adducting and counting) counter-balanced between the participants in order to avoid any order effect.
room (fade to black) Trial start

Figure 3 :
Figure 3: Workflow of a trial.Participants had to repeat the movement, while looking at their virtual right-hand until a signal STOP was displayed 6s after the GO signal.

Figure 4 :
Figure 4: Questionnaire being filled in VR with the left-hand using the standard Oculus hand representation and no avatar.