Grégoire Richard

Ferran Thomas Pietrzak

Argelaguet Sanz

Anatole Lécuyer

Géry Casiez

Ferran Argelaguet

Within or Between? Comparing Experimental Designs for Virtual Embodiment Studies

Keywords:

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INTRODUCTION

The design of a controlled experiment requires determining the number of independent variables to consider, and the number of levels taken by each of them. For any independent variable involved, the experimenter has to choose between a between-subjects design, where each participant is exposed to only one level, and a withinsubjects design where each participant tests each level. A betweensubjects design is required when investigating individual differences. For example, the effect of gender or age on a dependent variable, and a within-subjects design is required when studying learning or fatigue effects on an independent variable. However, most of the time the choice of an experimental design is not fixed and it is decided by the researcher.

Each design has its own advantages and disadvantages. Betweensubjects designs prevent confounding factors such as learning, fatigue, and frustration since each participant is exposed to a single level. The time taken to complete the experiment is also shorter than a within-subjects design. However, between-subjects designs are based on the comparisons between different groups of participants to study the effect of an independent variable. The results can be affected by individual differences making it harder to detect significant differences, reducing the power of the statistical analysis. It also increases the chances to detect differences that can be attributed * e-mail: gregoire.richard@inria.fr to differences between the groups instead of differences between the conditions, when the groups are too small and not homogeneous (e.g. typing speed when comparing different typing techniques [START_REF] Lee | A rapid screening and testing protocol for keyboard layout speed comparison[END_REF]). To reduce the impact of individual differences, between-subjects designs comparatively require larger groups compared to withinsubjects designs (m times larger if m is the number of levels of an independent variable). Mixed experiment designs can be used when considering two or more independent variables, where one or more independent variables are administered within-subjects and the others between-subjects, but it is beyond the scope of this work.

Controlled experiments in virtual reality (VR) to study user experience do not suffer an exception. Some contexts require to follow a within-subjects design, for example when studying the effect of VR therapy over different sessions on a phobia [START_REF] Rothbaum | The use of virtual reality exposure in the treatment of anxiety disorders[END_REF]. Other contexts, such as scenarios involving surprises/threats [START_REF] Dewez | Influence of personality traits and body awareness on the sense of embodiment in virtual reality[END_REF][START_REF] Fribourg | Influence of threat occurrence and repeatability on the sense of embodiment and threat response in vr[END_REF], typically follow a between-subjects design as being aware of the effect can alter participants' reactions. Other contexts, such as the study of embodiment, offer more freedom in the choice of an experimental design.

A key factor of user experience in VR is virtual embodiment, the "sense that emerges when [a body]'s properties are processed as if they were the properties of one's own biological body" [START_REF] Kilteni | The sense of embodiment in virtual reality[END_REF]. While a majority of virtual embodiment studies are designed following a within-subjects design, a fair amount follows a between-subjects design (see Table 1). For each design, it remains unclear how many participants should be involved in a study to detect an effect if it exists. Furthermore, to get the same statistical power between the two designs, the number of participants required in a between-subjects design may not be directly related to the number of levels. The behavior of participants when answering successive questionnaires may also influence the results, as they may answer the questions depending on their previous answers, for example.

To answer these questions, we evaluate in this paper the influence of the experimental design and the sample size in a virtual embodiment experiment with a single independent variable with two levels. We first report an experiment (n = 92), in which participants had to perform a visuomotor task adapted from previous studies [START_REF] Bourdin | A virtual out-of-body experience reduces fear of death[END_REF][START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF][START_REF] Maselli | The building blocks of the full body ownership illusion[END_REF]. The experimental design had one within-subjects variable with two levels, synchronous and asynchronous integration. The task and design were chosen to ensure that a significant difference could be observed between the two levels with lower embodiment scores for the asynchronous condition, as it has been previously shown [START_REF] Bourdin | A virtual out-of-body experience reduces fear of death[END_REF][START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF][START_REF] Maselli | The building blocks of the full body ownership illusion[END_REF]. We then evaluated the influence of the number of participants and the type of experimental design on the effect size and the ability to find the expected significant difference between the conditions. We used a Monte-Carlo method on different subsets of the collected data to simulate a number of participants ranging from 10 to 92 in the within-subjects design and 12 to 46 per group in the between-subjects design. Our results show that we could find the expected result with more than 95% chance from 33 participants with the within-subjects design, in agreement with the results from the literature. However, we were not able to replicate the expected result with the between-subjects design. We discuss the implications of these findings and provide guidelines on the design of virtual embodiment studies and embodiment questionnaires.

Virtual embodiment

The notion of embodiment usually refers to motor control and affective attachment over a body [START_REF] Vignemont | Embodiment, ownership and disownership[END_REF][START_REF] Kilteni | The sense of embodiment in virtual reality[END_REF]. It was historically laid out through the rubber-hand illusion (RHI) paradigm proposed by Botvinick & Cohen [START_REF] Botvinick | Rubber hands 'feel'touch that eyes see[END_REF], and further researched in many studies [START_REF] Ehrsson | 43 the concept of body ownership and its relation to multisensory integration[END_REF][START_REF] Kalckert | The moving rubber hand illusion revisited: Comparing movements and visuotactile stimulation to induce illusory ownership[END_REF][START_REF] Sanchez-Vives | Virtual hand illusion induced by visuomotor correlations[END_REF][START_REF] Tsakiris | Having a body versus moving your body: neural signatures of agency and body-ownership[END_REF]. Researchers use the concept of virtual embodiment because the sensations that enable embodiment are virtually simulated (i.e. visual and audio stimuli). Although in the original RHI experiment, Botvinick & Cohen showcased the illusion of ownership over a single limb, a number of studies have then explored the possibilities of full-body embodiment [START_REF] Dewez | Influence of personality traits and body awareness on the sense of embodiment in virtual reality[END_REF][START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF]. Embodiment can be studied in many contexts, through the visual appearance of users' virtual representations, also called avatars [START_REF] Argelaguet | The role of interaction in virtual embodiment: Effects of the virtual hand representation[END_REF][START_REF] Banakou | Illusory ownership of a virtual child body causes overestimation of object sizes and implicit attitude changes[END_REF], or visuomotor and visuotactile integration [START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF][START_REF] Richard | Studying the role of haptic feedback on virtual embodiment in a drawing task[END_REF][START_REF] Sanchez-Vives | Virtual hand illusion induced by visuomotor correlations[END_REF][START_REF] Waltemate | The impact of latency on perceptual judgments and motor performance in closed-loop interaction in virtual reality[END_REF]. The notion of embodiment has been shown to be correlated to the sense of presence [START_REF] Gorisse | De la présence à l'incarnation: proposition d'un méta-modèle pour la réalité virtuelle[END_REF], which has been defined by Lee et al. [START_REF] Lee | Presence, explicated[END_REF] as a psychological state where one cannot distinguish a virtual experience from reality.

Usually, the sense of embodiment is decomposed into multiple subdimensions [START_REF] Kilteni | The sense of embodiment in virtual reality[END_REF][START_REF] Roth | Construction of the Virtual Embodiment Questionnaire (VEQ)[END_REF]. The main subdimension is body ownership, referring to affective attachment and the feeling of owning the body. The second subdimension is agency, referring to motor control. These two subdimensions are recognized to be the main subdimensions of embodiment. The study by Kilteni et al. proposed a third subdimension they called the sense of self-location, which corresponds to the space where one feels located. These three subdimensions form the working model of virtual embodiment that is generally used by researchers. Using questionnaires is often the main measure of the sense of embodiment [START_REF] Gonzalez-Franco | The contribution of real-time mirror reflections of motor actions on virtual body ownership in an immersive virtual environment[END_REF][START_REF] Roth | Construction of the Virtual Embodiment Questionnaire (VEQ)[END_REF]. Recently, Peck & Gonzalez-Franco [START_REF] Peck | Avatar embodiment. a standardized questionnaire[END_REF] proposed a new questionnaire to measure virtual embodiment in an absolute way, basing their model of embodiment on previous work from Kilteni et al., and validating questionnaire items through controlled experiments. In the rest of this study, virtual embodiment and its subcomponents will be based on the work of Peck & Gonzalez-Franco [START_REF] Peck | Avatar embodiment. a standardized questionnaire[END_REF].

Impact of latency on embodiment

Introducing discrepancy between an action and its visual feedback can impair and even prevent the emergence of embodiment [START_REF] Botvinick | Rubber hands 'feel'touch that eyes see[END_REF][START_REF] Kilteni | The sense of embodiment in virtual reality[END_REF][START_REF] Tsakiris | Having a body versus moving your body: neural signatures of agency and body-ownership[END_REF]. In such a case, embodiment decreases mainly through the sense of agency and the sense of ownership [START_REF] Gallagher | Philosophical conceptions of the self: implications for cognitive science[END_REF][START_REF] Tsakiris | Having a body versus moving your body: neural signatures of agency and body-ownership[END_REF]. The discrepancy can be implemented experimentally by prerecording animations for the avatar movements [START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF][START_REF] Sanchez-Vives | Virtual hand illusion induced by visuomotor correlations[END_REF], or by adding artificial latency [START_REF] Imaizumi | Dissociation of agency and body ownership following visuomotor temporal recalibration[END_REF][START_REF] Waltemate | The impact of latency on perceptual judgments and motor performance in closed-loop interaction in virtual reality[END_REF]. In the case of artificial latency, perceived agency decreases around the threshold of 100-150 ms, and does not emerge for delays around 500 ms [START_REF] Franck | Defective recognition of one's own actions in patients with schizophrenia[END_REF][START_REF] Longo | Sense of agency primes manual motor responses[END_REF][START_REF] Waltemate | The impact of latency on perceptual judgments and motor performance in closed-loop interaction in virtual reality[END_REF]. Replications of the RHI [START_REF] Asai | Agency elicits body-ownership: proprioceptive drift toward a synchronously acting external proxy[END_REF][START_REF] Ratcliffe | The effect of visual, spatial and temporal manipulations on embodiment and action[END_REF][START_REF] Tsakiris | Having a body versus moving your body: neural signatures of agency and body-ownership[END_REF] found that embodiment still emerged at 500 ms, but with sharp drops. A recent study by Caserman et al. [START_REF] Caserman | Effects of end-to-end latency on user experience and performance in immersive virtual reality applications[END_REF] shows that 250 ms of latency did not impede agency but did reduce ownership. The study by Waltemate et al. [START_REF] Waltemate | The impact of latency on perceptual judgments and motor performance in closed-loop interaction in virtual reality[END_REF] provides great insights to understand the impact of latency on motor performance and embodiment. They measured embodiment through agency and body ownership but both were assessed through one questionnaire item. They found that embodiment diminished slowly between delays of 45 and 150 ms, while it dropped more sharply afterward, reaching approximately 65% of its optimal value at around 350 ms. It appears that artificial latency has little to no impact on embodiment under 100 ms and that it impedes embodiment up to 500 ms, where it drops sharply.

Experimental protocol designs for embodiment studies

We reviewed 40 studies from the literature regarding virtual embodiment, to better understand when and how each experimental design is used (see Table 1). It is important to stress out that this is not meant to be a systematic review of literature, and more aimed at providing an overview of experimental designs when it comes to embodiment in VR. Besides a few that did not have the choice for their design, it is interesting to note that the others did not provide the motivations for the choice of their experimental design. In regards to embodiment measures, some of these studies implemented both objective and subjective measures, while others used only subjective means. For studies implementing threats [START_REF] Argelaguet | The role of interaction in virtual embodiment: Effects of the virtual hand representation[END_REF][START_REF] Fribourg | Studying the sense of embodiment in vr shared experiences[END_REF][START_REF] Fribourg | Influence of threat occurrence and repeatability on the sense of embodiment and threat response in vr[END_REF], the objective measurement mainly consisted of participants' behavior and movement analyses.

Virtual replications of the RHI were prone to use proprioceptive drift [START_REF] Botvinick | Rubber hands 'feel'touch that eyes see[END_REF][START_REF] Imaizumi | Dissociation of agency and body ownership following visuomotor temporal recalibration[END_REF][START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF][START_REF] Sanchez-Vives | Virtual hand illusion induced by visuomotor correlations[END_REF], while others used other means, like the galvanic skin response (GSR) [START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF][START_REF] Krogmeier | Human-virtual character interaction: Toward understanding the influence of haptic feedback[END_REF]. Studies published before the recent propositions of standardized embodiment questionnaires [START_REF] Gonzalez-Franco | Avatar embodiment. towards a standardized questionnaire[END_REF][START_REF] Peck | Avatar embodiment. a standardized questionnaire[END_REF][START_REF] Roth | Construction of the Virtual Embodiment Questionnaire (VEQ)[END_REF] often proposed their own questionnaires, adapted from the presence questionnaire [START_REF] Witmer | Measuring presence in virtual environments: A presence questionnaire[END_REF] for the context of their experiment, sometimes being only a few items [START_REF] Waltemate | The impact of latency on perceptual judgments and motor performance in closed-loop interaction in virtual reality[END_REF]. More recent studies [START_REF] Andreasen | Agency enhances body ownership illusion of being a virtual bat[END_REF][START_REF] Aymerich-Franch | When your robot avatar misbehaves you are likely to apologize: an exploration of guilt during robot embodiment[END_REF][START_REF] Bovet | The critical role of self-contact for embodiment in virtual reality[END_REF][START_REF] Richard | Studying the role of haptic feedback on virtual embodiment in a drawing task[END_REF] only implement a subjective measure of embodiment. Embodiment questionnaires are either administered in the real world after conditions, after removing the VR gear [START_REF] Danieau | Enhancing audiovisual experience with haptic feedback: a survey on hav[END_REF][START_REF] Debarba | Characterizing first and third person viewpoints and their alternation for embodied interaction in virtual reality[END_REF][START_REF] Dewez | Influence of personality traits and body awareness on the sense of embodiment in virtual reality[END_REF][START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF][START_REF] Richard | Studying the role of haptic feedback on virtual embodiment in a drawing task[END_REF], or inside the IVE [START_REF] Fribourg | Influence of threat occurrence and repeatability on the sense of embodiment and threat response in vr[END_REF][START_REF] Kokkinara | The effects of visuomotor calibration to the perceived space and body, through embodiment in immersive virtual reality[END_REF][START_REF] Schwind | where's pinky?" the effects of a reduced number of fingers in virtual reality[END_REF][START_REF] Waltemate | The impact of latency on perceptual judgments and motor performance in closed-loop interaction in virtual reality[END_REF]. Some studies mention giving guidelines to participants to answer the questionnaires, mostly to answer based on what they felt and perceived [START_REF] Waltemate | The impact of latency on perceptual judgments and motor performance in closed-loop interaction in virtual reality[END_REF], while others gave a shortened questionnaire before the experiment for the participants to assess embodiment under a baseline condition [START_REF] Bourdin | A virtual out-of-body experience reduces fear of death[END_REF][START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF][START_REF] Kokkinara | The effects of visuomotor calibration to the perceived space and body, through embodiment in immersive virtual reality[END_REF][START_REF] Ratcliffe | The effect of visual, spatial and temporal manipulations on embodiment and action[END_REF]. Some other studies also implemented a familiarization phase [START_REF] Krogmeier | Human-virtual character interaction: Toward understanding the influence of haptic feedback[END_REF][START_REF] Peck | The impact of a self-avatar, hand collocation, and hand proximity on embodiment and stroop interference[END_REF][START_REF] Richard | Studying the role of haptic feedback on virtual embodiment in a drawing task[END_REF]. In particular, Bovet et al. [START_REF] Bovet | The critical role of self-contact for embodiment in virtual reality[END_REF] had participants get familiar with two extreme conditions before the experiment. We noticed that there is no systematic report of effect size for embodiment studies. Some studies report effect sizes for objective measurement [START_REF] Bovet | The critical role of self-contact for embodiment in virtual reality[END_REF][START_REF] Fribourg | Studying the sense of embodiment in vr shared experiences[END_REF][START_REF] Imaizumi | Dissociation of agency and body ownership following visuomotor temporal recalibration[END_REF][START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF], but only one study reported effect sizes for embodiment questionnaire answers [START_REF] Frohner | Can wearable haptic devices foster the embodiment of virtual limbs[END_REF].

From the 40 papers reviewed, 25 of these studies were conducted following a within-subjects design. Reported sample sizes range from 10 participants for Waltemate et al.'s study [START_REF] Waltemate | The impact of latency on perceptual judgments and motor performance in closed-loop interaction in virtual reality[END_REF], to 99 participants in Peck et al. [START_REF] Peck | Evidence of racial bias using immersive virtual reality: Analysis of head and hand motions during shooting decisions[END_REF]. There were on average 30 participants in the reviewed within-subjects studies. Within-subjects design can lead participants to certain behaviors, such as acting a particular way they think experimenters expect from them. This effect is known as the "demand effect" [START_REF]Experimenter effects in behavioral research[END_REF][START_REF] White | The influence of experimenter motivation, attitudes, and methods of handling subjects on psi test results[END_REF]. The demand effect is especially of concern for psychological experimental research and can induce a bias when administering questionnaires [START_REF] Charness | Experimental methods: Between-subject and within-subject design[END_REF].

Among these studies, 12 of them were designed following a between-subjects design [START_REF] Aymerich-Franch | When your robot avatar misbehaves you are likely to apologize: an exploration of guilt during robot embodiment[END_REF][START_REF] Banakou | Illusory ownership of a virtual child body causes overestimation of object sizes and implicit attitude changes[END_REF][START_REF] Banakou | Virtual embodiment of white people in a black virtual body leads to a sustained reduction in their implicit racial bias[END_REF][START_REF] Barberia | Virtual mortality and near-death experience after a prolonged exposure in a shared virtual reality may lead to positive life-attitude changes[END_REF][START_REF] Bourdin | A virtual out-of-body experience reduces fear of death[END_REF][START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF][START_REF] Krogmeier | Human-virtual character interaction: Toward understanding the influence of haptic feedback[END_REF][START_REF] Lugrin | Any "body" there? avatar visibility effects in a virtual reality game[END_REF][START_REF] Maselli | The building blocks of the full body ownership illusion[END_REF][START_REF] Won | Homuncular flexibility in virtual reality[END_REF]. For these studies, the number of participants ranged from 20 for the second experiment of Won et al. [START_REF] Won | Homuncular flexibility in virtual reality[END_REF], to 69 participants in the study of Lugrin et al. [START_REF] Lugrin | Any "body" there? avatar visibility effects in a virtual reality game[END_REF]. The size of the groups ranged from 10 participants to 23, for an average of 15 participants per group. The sample size for between-subjects is of importance, because of possible bias caused by possible individual differences. When conducting between studies, if the homogeneity of groups has not been accounted for, it may be possible that results could be explained by differences between groups of participants. This is particularly relevant for studies regarding body ownership and embodiment. For example, Kalckert et al. [START_REF] Kalckert | The moving rubber hand illusion revisited: Comparing movements and visuotactile stimulation to induce illusory ownership[END_REF] performed a systematic replication of the rubber-hand illusion (RHI) in order to compare visuomotor and visuotactile stimulations. In their review of literature, they noticed two studies [START_REF] Dummer | Movement and the rubber hand illusion[END_REF][START_REF] Tsakiris | Having a body versus moving your body: How agency structures body-ownership[END_REF] that followed different designs and bore different results. Tsakiris et al. [START_REF] Tsakiris | Having a body versus moving your body: How agency structures body-ownership[END_REF], in a within-subjects experiment, found no difference in ownership between visuomotor and visuotactile integration, while Dummer et al. [START_REF] Dummer | Movement and the rubber hand illusion[END_REF], in a between-subjects, found that ownership was higher under visuotactile stimuli than visuomotor. In summary, even though the majority of virtual embodiment studies are conducted as within-subjects, a non-trivial amount of them implement a between-subjects design. Besides specific contexts, there is no clear motivation to choose either one. Effect sizes for virtual embodiment studies are not massively reported. There is no standard effect size in the literature, and as such, the number of participants varies across studies. It remains unclear how the experimental design can influence virtual embodiment results. The next section presents an experiment and a protocol to compare within-subjects and between-subjects and study the influence of the number of participants.

EXPERIMENT

The main objective of our experiment is to compare experimental designs to study virtual embodiment in VR. We want to study the ability of within-subjects and between-subjects designs to detect effects when they exist. As there exists a direct relationship between the number of participants in an experiment and the ability to detect an effect, we also want to study how results are impacted by the number of participants.

Experimental Design

Our experiment requires the use of a ground truth established from results validated and replicated in the literature. There are a few experiments in VR that have been replicated besides visuotactile synchrony with the RHI [START_REF] Botvinick | Rubber hands 'feel'touch that eyes see[END_REF][START_REF] Kalckert | The moving rubber hand illusion revisited: Comparing movements and visuotactile stimulation to induce illusory ownership[END_REF][START_REF] Tsakiris | The rubber hand illusion revisited: visuotactile integration and self-attribution[END_REF] and visuotactile/visuomotor synchrony with the study of the latency on embodiment [START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF][START_REF] Sanchez-Vives | Virtual hand illusion induced by visuomotor correlations[END_REF]. Previous studies have shown that there is no significant difference in embodiment between visuotactile and visuomotor synchrony [START_REF] Kalckert | The moving rubber hand illusion revisited: Comparing movements and visuotactile stimulation to induce illusory ownership[END_REF]. We chose to replicate experiments based on visuomotor synchrony instead of visuotactile synchrony as their experimental setup and procedure are simpler to replicate, thus reducing potential bias. We also chose to test only two experimental conditions, one with minimal latency and the other with a level of latency known to significantly impact embodiment. It is the simplest experiment we can design and it simplifies the statistical analysis. Thus, it can be easily replicated in other studies to further strengthen results and methodological recommendations. Our experiment follows a within-subjects design where each participant experienced two different conditions: SYNCHRO and ASYNCHRO visuomotor (VM) integration. The two conditions are counterbalanced across participants to compensate for possible effects of presentation order and to be able to use the first condition tested by the participants as if we conducted a betweensubject design with the two conditions.

Conditions

The synchronous condition (SYNCHRO) integrates participants' movements with no additional delay between their actions in the physical and virtual environments.The asynchronous condition (ASYNCHRO) was designed to add a 300 ms delay compared to SYNCHRO.

Interactive systems have an inherent delay associated with the hardware, system, and processing. This end-to-end latency was the same in both conditions, we measured it with the LagMeter device [START_REF] Casiez | Characterizing latency in touch and button-equipped interactive systems[END_REF] in the experiment application coded with Unity. It corresponds to the delay between a physical input action and a resulting change on the screen. To do so, the LagMeter first detects and measures when a vibration resulting from a tap on the tactile pad occurs, using a piezoelectric vibration sensor attached to the index finger. Second, it measures when the associated screen response occurs using a photodiode fitted on the left screen of the VR headset. The application switches the screen headset from black to white upon receiving the event from the pad. We collected 50 measures of latency and found an average end-to-end latency of 63 ms (SD=12 ms), similar to what has been found in the literature [START_REF] Casiez | Characterizing latency in touch and button-equipped interactive systems[END_REF][START_REF] Chénéchal | Htc vive pro time performance benchmark for scientific research[END_REF][START_REF] Waltemate | The impact of latency on perceptual judgments and motor performance in closed-loop interaction in virtual reality[END_REF].

The latency for ASYNCHRO was artificially implemented by buffering all input events during a given time . This way ASYN-CHRO had a total latency resulting in about 360 ms. According to the literature, the synchronous condition has a latency that is unlikely to impact embodiment (under 100 ms) while the latency in the asynchronous condition is in the 100-500 ms upper range where latency is known to affect embodiment.

Methodology

Participants were first instructed with information regarding the procedure and the experiment: what they were expected to do in the visuomotor task, how to complete the task, and what to focus on during the immersion. Participants were asked to look at the virtual legs when completing the task. Then, they were then asked to sign an informed consent form and answer basic demographic questions. Among those questions, they could express their gender expression, which was used to choose the corresponding avatar.

Participants were instructed to seat on a real chair and place their legs on a physical table (120 cm × 120 cm × 50 cm) located in front of them and keep their arm still on each side of the chair (Fig. 1). The chair and table were co-located with a virtual table and a virtual chair of similar shape within the IVE, in order to get coherent passive haptic feedback in the IVE.

The task consisted in replicating patterns with both heels, through leg movements. Instructions for leg movements were displayed on a virtual screen within the IVE, located in front of the participants. Each instruction required participants to repeat the pattern 10 times, and there were 12 different patterns, for a total of 120 movements per condition. The task lasted for about 5 minutes.

Participants went through both conditions within one session. The order of the conditions was counterbalanced. Each experimental condition was followed by an embodiment questionnaire to assess subjective embodiment (see Section 3.6). Participants were asked to remove their HMD and controllers and to complete the questionnaire on a laptop. Participants could not see their answers to the first condition when filling the questionnaire for the second one.

Apparatus

The participants were immersed in the IVE by wearing a Valve Index headset, which provided visual feedback and a 6-DOF head tracking. The feet of the participants were tracked with a Vive Tracker attached to each of them, and inverse kinematics [69] was used to match the avatar's movements with the actual movements of the participants. The virtual environment was implemented using Unity3D (2019.2.12f1) and the Unity Steam VR plugin. The experiment ran on an Intel(R) Core(TM) i7-9750H 2.60GHz CPU with 32GB of RAM and a 8GB 2070 RTX GeForce Nvidia GPU. The virtual representations of the participants were two avatars of both gender expressions from the RocketBox library [START_REF] Gonzalez-Franco | The rocketbox library and the utility of freely available rigged avatars[END_REF].

Participants

92 participants volunteered to participate in the experiment, (64 male and 28 female), aged from 22 to 53 (M = 30.2; SD = 7.7). They were recruited by word of mouth. Participants had normal or corrected-to-normal vision. The experiment was approved by the local ethics board.

Embodiment Questionnaire

The sense of embodiment was self-reported by participants through an online questionnaire, using seven-point Likert scales. The questionnaire for embodiment was taken from the questionnaire proposed by Peck & Gonzalez-Franco [START_REF] Peck | Avatar embodiment. a standardized questionnaire[END_REF]. This questionnaire was validated through a large number of observations and is the most recent. From the 16 items proposed in that questionnaire, one original item was removed (R8 in the original paper), as it could not be adapted for our scenario (Table 2).

RESULTS

In this section, we first report the main scores for the within-subjects design (n = 92), then present an analysis as a between-subjects design, by only considering the first condition for each participant (two groups of n = 46). Then we present the simulations of withinand between-subjects designs when manipulating the number of participants 1 . Following the recommendations from [START_REF] Peck | Avatar embodiment. a standardized questionnaire[END_REF], questionnaire responses were aggregated to compute the Appearance, Response, Ownership and Multi-sensory sub-scores, and a general score for embodiment and then re-scaled between -3 and +3.

© 2022 IEEE. This is the author's version of the article that has been published in the proceedings of IEEE Visualization conference. The final version of this record is available at: 10.1109/VR51125.2022.00037

Results for the within-subjects design

As the normality assumptions were violated (Shapiro-Wilk normality test p < 0.0001, W = 0.99), in the following only non-parametric tests will be considered, with the exception of the following analysis to study interaction effects. Furthermore, to rule out order effects, we performed a repeated-measures ANOVA on Aligned Ranked Transformed data as the data did not follow a normal distribution [START_REF] Wobbrock | The aligned rank transform for nonparametric factorial analyses using only anova procedures[END_REF], in which the order of presentation was treated as a between-subjects independent variable and the VM condition as a within-subjects variable. The analysis did not show any significant effect of the presentation order (F(1,90) = 1.39, p = 0.24) or any interaction between presentation order and VM condition (F(1,90) = 0.51, p = 0.48).

Table 3 and Fig. 2 summarize the results, in which Response, Ownership, Multi-sensory and overall embodiment showed significant differences (Wilcoxon signed-rank analysis). The computed effect size was 0.53. The effect size for the Wilcoxon signed rank test was computed using the method proposed by Pallant [START_REF] Pallant | Survival manual. A step by step guide to data analysis using SPSS[END_REF]. More precisely, we used the wilcox_effsize function from the rstatix R-package [44]. The analysis on Appearance did not reveal a significant difference (p = 0.07). These results replicate the previous results in the literature as we observe significantly higher scores of embodiment for the synchronous condition.

Results for the between-subjects design

For the between-subjects analysis, we used a Wilcoxon rank-sum test on the first condition participants were exposed to (Table 4). No significant effect was found between the SYNCHRONOUS and ASYNCHRONOUS conditions on overall embodiment (p = 0.23) nor any of the sub-components. This analysis failed to replicate the results from the literature, as no significant differences were found.

Influence of the number of participants over the results for within-subjects studies

We analyzed the results from our 92-participants within-subjects study to evaluate the influence of the number of participants on the results regarding embodiment. Since the overall differences in embodiment scores were significant for the within-subject design, only the overall embodiment scores were considered in this analysis.

From the original 92-participants within-subjects study, we created virtual experiments by randomly selecting different subsets of participants according to a target sample size. As simulating all possible combinations is computationally too expensive, we used a Monte-Carlo method by creating several virtual experiments for each sample size, to get accurate estimations. To determine the right amount of simulations, we simulated between 10 and 1, 000, 000 virtual experiments for 12-participant within-subjects and betweensubjects. The 12-participants case is considered as a worst-case scenario as the variance is expected to be maximal. The results showed that 10, 000 simulations were enough to reach precise approximations for consistency and effect size. To keep a safety margin while remaining reasonable in terms of computational cost, we chose to run 100, 000 simulations for each sample size.

© 2022 IEEE. This is the author's version of the article that has been published in the proceedings of IEEE Visualization conference. The final version of this record is available at: 10.1109/VR51125.2022.00037

For each virtual experiment, a Wilcoxon signed-rank test was run between the SYNCHRO and ASYNCHRO conditions. As a significant effect was found in the original within-subjects study with the 92 participants, and according to the literature, we consider that any virtual experience with a significant difference (p < 0.05) between the two conditions, with the mean embodiment scores being higher in the SYNCHRO condition than the ASYNCHRO, is consistent with the original results. For each sample size, we computed the percentage of virtual experiments that were consistent with the original results and effect size (mean, 5 th percentile and 95 th percentile).

The blue line in Fig. 3 (bottom) shows the evolution of the consistency when varying the number of participants for the withinsubjects virtual experiments. As can be seen from the figure, and as expected, the consistency of the results increases together with the sample size. Consistency reaches 95% at 33 participants and is virtually 100% beyond 40 participants. Moreover, the blue line in Fig. 3 (top) shows the evolution of the effect size as the sample size increases. While the mean effect size is almost constant (0.53) no matter the effect size, the 5 th -95 th percentile range gets narrower as the sample size increases.

Influence of the number of participants over the results for between-subjects studies

To study the influence of the number of participants for the betweensubjects study, we used the same method as described in the section above. We selected only the condition of each participant to obtain a 92-participants between-subject study in which both groups had 46 participants. The results for the full between-subjects design were not significant (cf. Sect. 4.2). We define consistency as based on the results of the 92-participants within-subjects study and on the literature, i.e. that there is a significant difference in embodiment between the SYNCHRONOUS and ASYNCHRONOUS conditions. Thus, in this case, the original 92-participants between-subjects study is considered inconsistent. The green lines in Fig. 3 show the evolution of the effect size and consistency respectively. As it can be expected from the results of the 92-participants between-subjects study, consistency values remain close to zero percent for all simulations. Similarly, the mean effect size is lower (converges to 0.11) with a larger interquartile range for small sample sizes.

During the data analysis, we observed an interesting behavior for the results when only considering the second condition of the original 92-participants study. When considered alone, the second condition can be considered as a between-subjects design, although the results could be strongly biased by the first condition. Nevertheless, we report them as they provide interesting insights and match the initial hypothesis we had for the between-subject designs. The red lines in Fig. 3 show the evolution of the effect size and consistency respectively when considering the data from the second condition. Interestingly, the consistency of the results almost increases linearly according to the number of participants and reaches the 100% of consistency at around n = 84. The evolution of the effect size also followed a similar pattern as the previous simulations converging towards 0.30.

DISCUSSION

There were several objectives in this study, the main one being the comparison of within-subjects and between-subjects designs.

Within-subjects designs

Our first objective was to replicate results regarding the impact of latency on virtual embodiment, in a visuomotor task inspired by the literature [START_REF] Bourdin | A virtual out-of-body experience reduces fear of death[END_REF][START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF][START_REF] Maselli | The building blocks of the full body ownership illusion[END_REF]. We considered synchronous and asynchronous integration as several works have shown embodiment is impaired when participants perceive visuomotor and/or visuotactile discrepancy [START_REF] Botvinick | Rubber hands 'feel'touch that eyes see[END_REF][START_REF] Imaizumi | Dissociation of agency and body ownership following visuomotor temporal recalibration[END_REF][START_REF] Longo | Sense of agency primes manual motor responses[END_REF][START_REF] Waltemate | The impact of latency on perceptual judgments and motor performance in closed-loop interaction in virtual reality[END_REF]. Considering the results of the 92-participants within-subjects study, participants were significantly affected by visuomotor discrepancies during the asynchronous condition (latency around 360 ms), although the decrease of virtual embodiment scores compared to the synchronous condition was moderate compared to other works [START_REF] Imaizumi | Dissociation of agency and body ownership following visuomotor temporal recalibration[END_REF][START_REF] Waltemate | The impact of latency on perceptual judgments and motor performance in closed-loop interaction in virtual reality[END_REF]. This effect was also observed by three of the four sub-components proposed by Peck and Gonzalez-Franco [START_REF] Peck | Avatar embodiment. a standardized questionnaire[END_REF]. These results tend to validate both the protocol to elicit embodiment (the visuomotor task based on leg movements) and the value of delay to impede embodiment (360 ms).

The reported effect size for the 92-participants within-subjects study was 0.53. According to Cohen [START_REF] Cohen | Statistical power analysis for the behavioral sciences[END_REF], the effect size for Wilcoxon signed ranked test can be interpreted the same way as Cohen's d, so an effect size of 0.53 is considered medium. This appears coherent when considering that latency starts to affect embodiment around 100 ms and severely impacts it around 500 ms. As a result we could expect to measure a small effect size around 100 ms and a large effect size around 500 ms and a medium effect-size for 360 ms. However, effect sizes are rarely reported in the literature for virtual embodiment studies. The effect size measures the magnitude of an effect but it usually requires results from different studies on a given phenomenon to be able to establish what values can be considered as low, medium, or high. In its simplest form, the effect size can be considered as the difference of the mean or median values between two conditions. In our case, the difference of embodiment score between the two conditions is equal to 0.34 points on a 7-point Likert scale, which can be considered as small considering the differences obtained in other studies (Table 1). However such approximation does not take into account the variance of the data as methods to compute actual effect sizes do. In addition the results reported in the literature did not necessarily use the same questionnaires. Future embodiment studies also reporting effect size can help characterize the magnitude of ours.

In order to account for the impact of the sample size in the potential outcome and the replicability of the results, we simulated virtual experiments with sample sizes varying from n = 10 to n = 90. The results, as hypothesized, showed an increase of the replicability as the sample size increased, reaching the 100% of consistency when n = 40. 75% of replicability was reached for virtual experiments with 20 participants and up to 33 participants were required to reach 95%. These results show, considering the within-subjects experimental design, that 40 participants would have ensured an optimal number of participants to observe the effect of latency on embodiment.

Between-subjects designs

Contrary to our initial hypothesis, the results for the 92-participants between-subjects designs failed to replicate the results obtained for the within-subjects design. Assuming that the effect exists, as the within-subjects virtual experiments were able to detect, even reaching a 100% of consistency around 40 participants, and considering that the data set was the same, we hypothesize that the betweengroup design failed to detect an effect that does exist. A power analysis was run post-experiment, to determine the sample size that would have been required to detect an effect. This was done using the G*Power software [START_REF] Faul | G* power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences[END_REF], and sample size was computed using the © 2022 IEEE. This is the author's version of the article that has been published in the proceedings of IEEE Visualization conference. The final version of this record is available at: 10.1109/VR51125.2022.00037 effect size found in the initial 92-participants within-subjects study. The analysis revealed that a sample size of 170 was needed for the between-subjects, whereas the within-subjects yielded a required sample size of 44. This puts our results in perspective: the sample size for a between-subjects design, even with a factor with two levels, might need four times the number of participants in a within-subjects design to detect an effect. It is important to note that these results are heavily dependent on the effect size. Previous studies about embodiment, conducted using between-subjects designs, have also shown it was possible to find significant differences for effect sizes equivalent or smaller than ours, with less participants [START_REF] Lugrin | Any "body" there? avatar visibility effects in a virtual reality game[END_REF][START_REF] Won | Homuncular flexibility in virtual reality[END_REF]. While the task and context are different, there might be factors that are overlooked when conducting between-subjects studies regarding embodiment in VR, such as individual differences, like gender or age. Considering the results for the 92-participants between-subjects design, it was not surprising that the virtual experiments with a smaller number of participants also failed to consistently detect the effect. These results are in line with the work of Kalckert et al. [START_REF] Kalckert | The moving rubber hand illusion revisited: Comparing movements and visuotactile stimulation to induce illusory ownership[END_REF] which noted that results in the RHI could be different based on the experimental design.

Considering that no differences were found for the first condition between the group who started with the synchronous condition and the one who started with the asynchronous condition, the observed differences could only be explained by the second condition experienced by the participants and the way they answered the questionnaires. The analysis of the second condition between-group virtual experiments might reinforce this potential explanation, as consistency steadily increased as the number of participants increased. However, it is important to stress that the second condition cannot be considered as a pure between-subjects design as participants were exposed to both conditions. A possible explanation for the discrepancies between the first and the second condition is that participants first answered the questions in an approximate way. They would then have a better understanding how to answer it, and to which aspects of the task they need to pay attention when performing the second condition. Then, when filling the questionnaire a second time for the other condition, they would answer the questions in a relative way, based on what they remember of their answers to the previous questions. For instance, previous studies regarding the RHI [START_REF] Asai | Agency elicits body-ownership: proprioceptive drift toward a synchronously acting external proxy[END_REF] have made the argument that it is the comparison among conditions that are of interest. This tends to be further supported by informal feedback from a few participants regarding the way they interpreted the questionnaire, and the strategy they came up with. Six participants mentioned at the end of the experiment having focused more on what was going on during the second task after having answered the embodiment questionnaire once and getting an "idea of what [they are] expected to do", as one of them put it. One participant, after asking for help understanding a particular questionnaire item for the first questionnaire, told the experimenter that it was "easier the second time, because [they] have a reference now". Further studies, in the form of semi-structured interviews after filling the questionnaires, would be required to better understand the strategy participants follow when answering. If this type of strategy is confirmed, it would mean protocols need to be refined. For between-and within-subjects studies, a solution would be to help participants answer questionnaires in an absolute manner, by presenting for instance examples of situations for the two extremes of the scale for each question. Another one would be to set up a training phase where the participants would discover a baseline condition, and the questionnaire before going through the experimental condition. The direct downside of such a solution is that participants would be aware of the questionnaire, just like in a within-subjects design. For within-subjects studies other solutions could be envisioned. For example, the answers to the questionnaire in the previous condition can be presented to the participants to help them answer to the current condition in a relative way. Another solution would be to provide questionnaires with scales that are relative to the previous condition.

The fact that a number of embodiment studies have found significant differences in between-group designs could be explained by a smaller effect size found in our study. Overall our results suggest that a within-subjects design should be preferred over a between-subjects design in embodiment studies when this is an option.

LIMITATIONS

The main limitation of this study concerns the generalization of our results. They are indeed related to the effect size that depends on the value of latency used in the asynchronous condition. Higher values of latency would increase the effect size and increase the chance of detecting the effect using a between-subjects design. There is also the possibility that the sample size for the between-subjects was too small, as post-experiment power analysis showed a 170-participants required sample size. Nevertheless, the differences found among within-and between-subjects designs might be related to the actual measure of embodiment.

Indeed, embodiment can be measured using subjective measures with questionnaires but also objective measures. We only used subjective measures to keep the experiment simple, and in particular, one embodiment questionnaires measuring absolute values of embodiment. Other embodiment questionnaires could have been used [START_REF] Roth | Construction of the Virtual Embodiment Questionnaire (VEQ)[END_REF], which could have provided different results. Future work could combine subjective measures with objective ones to better characterize the ability to detect effects when they exist.

Furthermore, due to the highly heterogeneous experiments assessing embodiment, embodiment questionnaires need to be adapted to each experiment. We adapted an embodiment questionnaire to the best of our knowledge but the phrasing of the questions could introduce some noise in the answers to the questions. Further work comparing different adaptations of a questionnaire to a given experiment could help measure the impact of the adaptation of the questionnaires.

CONCLUSION

This paper presented a methodology to compare within-subjects and between-subjects designs. From a ground truth established by the literature, our study managed to show that depending on the experimental design and the effect size, it was possible to fail to detect an effect that exists. While we observed the expected effect of latency on embodiment with a within-subjects design, we did not detect it with a between-subjects design. Overall, within-subjects design is much more able to detect small to medium effect sizes, with a smaller required number of participants. We proposed explanations of this phenomenon. Participants most likely answered the second questionnaire relatively to the first one, and the measured difference in embodiment is due to this difference, not to the absolute values. Therefore our recommendation for embodiment studies is to use a within-subjects design. However, we acknowledge that some experimental tasks require a between-subjects design. Hence, we plan to conduct semi-structured interviews to better characterize the way participants answer embodiment questionnaires. Then we will study calibration methods that could enable participants to give better assessments of embodiment in between-subjects design studies. It could take the form of a baseline condition with an embodiment questionnaire, which could give participants the necessary perspective to answer less arbitrarily. Another possibility is to provide participants an idea of what extreme levels of virtual embodiment could feel like, similarly to Kokkinara et al. [START_REF] Kokkinara | Measuring the effects through time of the influence of visuomotor and visuotactile synchronous stimulation on a virtual body ownership illusion[END_REF].

Figure 1 :

 1 Figure 1: Experimental setup, with headset, controllers and trackers fitted on a participant (left), the virtual environment with the male avatar (middle), and the two avatars (right).

Figure 2 :Figure 3 :

 23 Figure 2: Overall and sub-components embodiment score in the within-subjects design for SYNCHRO and ASYNCHRO conditions.

Table 1 :

 1 Summary of the reviewed virtual embodiment studies. *Effect is expressed as the difference in mean questionnaire answers between conditions. It is expressed in points, on a 7-point Likert scale. **Studies that reported effect sizes for embodiment questionnaire answers. The reported value here corresponds to Cohen's d.

	Reference Year Design Nb levels Nb participants Objective measurements	Subjective Measurements	Effect (pt)*
						Number of questions Reference questionnaire
	[74]	2010 Within	2	14	Proprioceptive drift	11	[11]	1.29
	[80]	2010 Between	2x2x2	24	Heart rate	8	-	1.1
	[60]	2011 Within	2	22	Behavior	11	[11]	1.25
	[66]	2011 Within	2	20	GSR	9	-	0.75
	[7]	2013 Between	2	30	Performance	4	-	1.25
	[59]	2013 Between	2x2	18	Heart rate	7	[53, 80]	1
	[46]	2014 Between	2x2	60	GSR	8	[87]	1.25
	[61]	2014 Within	2x2	15	Proprioceptive drift	12	[11, 74]	0.38
	[89]	2015 Between	3	53	Performance	10	-	0.21
	[58]	2015 Within	2x2x2	43	Proprioceptive drift/GSR	13	[11, 43, 79]	2
	[41]	2015 Within	6	13	Proprioceptive drift	2	-	1.4
	[2]	2016 Within	3	33	Behavior and movement	8	-	0.5
	[8]	2016 Between	2x3	60	Behavior	5	-	0.75
	[40]	2016 Between	2	24	Performance	12	[52, 80]	0.3
	[85]	2016 Within	5	10	Performance	2	[41]	-
	[23]	2017 Mixed	2x2	48	GSR	10	-	0.75
	[12]	2017 Between	2	32	Performance/Behavior	7	[52, 80]	1
	[67]	2017 Within	2x2x2	39	Behavior	14	[55]	0.9
	[21]	2017 Within 3x3x2x1	23	-	6	[2, 57, 80]	1.4
	[37]	2017 Within	2	28	Performance	10	[2, 24]	0.75
	[75]	2017 Within	2x4	24	-	32	[87]	-
	[5]	2017 Within	2x2	22	Behavior	12	[55]	2.5
	[30]	2018 Within	3	20	Performance	9	[43]	1.5
	[1]	2018 Within	4	25	-	18	[2]	3.75
	[32]	2018 Within	3	32	Proprioceptive drift	10	[55]	0.8**
	[42]	2018 Within	2	10	Behavior	16	[6]	1
	[56]	2018 Between	3	75	Performance	13	[72]	0.35
	[77]	2018 Within	5x2	41	Performance	14	[11, 58]	1.15
	[13]	2018 Within	3x2	21	-	2	-	-
	[48]	2019 Between	5	60	GSR	4	[79]	2
	[38]	2019 Within	3x2	34	Performance	12	[2, 24, 37]	0.25
	[76]	2019 Within	3x3	37	Performance	5	[77]	0.55
	[81]	2019 Within	2	16	-	16	[43]	0.45
	[14]	2019 Within	2	30	Performance	12	-	1.3
	[4]	2019 Between	2x2	64	Behavioral	4	[9]	1.1
	[31]	2020 Mixed	2x3	30	Behavior	14	[35]	1.5
	[65]	2020 Between	2x2	60	Performance	11	[35]	1.5
	[64]	2021 Within	2x2x2	99	Performance	24	[35]	-
	[68]	2021 Within	3	24	Performance	14	[35]	0.35
	[78]	2021 Mixed	2x2	74	Performance	4	[17]	0.6

Table 2 :

 2 Embodiment questionnaire adapted from Peck & Gonzalez-Franco.

	ID	Questions
	R1	I felt out of my body.
	R2	I felt as if my (real) body was drifting toward the virtual body or as if the virtual body was drifting toward my (real) body.
	R3	I felt as if the movements of the virtual body were influencing my own movements.
	R4	It felt as if my (real) body was turning into an "avatar" body.
	R5	At some point it felt as if my real body was starting to take on the posture or shape of the virtual body that I saw.
	R6	I felt like I was wearing different clothes from when I came to the laboratory.
	R7	I felt as if my body had changed.
	R9	I felt that my own body could be affected by the virtual body.
	R10	I felt as if the virtual body was my body.
	R11	At some point, it felt that the virtual body resembled my own (real) body, in terms of shape, skin tone or other visual features.
	R12	I felt as if my body was located where I saw the virtual body.
	R13	I felt I could control the virtual body as if it was my own body.
	R14	It seemed as if I felt the touch of the table in the location where I saw the virtual legs touched.
	R15	It seemed as if the touch I felt was caused by the table touching the virtual body.
	R16	It seemed as if my body was touching the table.

Table 3 :

 3 Summary of the results of the 92-participants within-subjects study.

	Metric	p-value	V		Sync.	Async.
				Mdn	IQ	Mdn	IQ
	Response	< 0.001* 743	0.0	[-0.8, 0.7] -0.2	[-1.4, 0.6]
	Ownership < 0.001* 623.5 0.83 [0.25, 1.42] 0.16 [-0.5, 0.92]
	Appearance	= 0.07 1528.5 -0.38 [-1.13, 0.5] -0.69 [-1.25, 0.38]
	Multi-sensory < 0.001* 922	1.33	[1.0, 1.75]	1.17	[0.34, 1.5]
	Embodiment < 0.001* 959.5 0.42 [0.01, 1.00] 0.08 [-0.56, 0.74]

Table 4 :

 4 Summary of the results of the 92-participants between-subjects study.

	Metric	p-value	W		Sync.		Async.
				Mdn	IQ	Mdn	IQ
	Response	> 0.9 1048.5 0.0	[-0.95, 0.4]	0.0	[-1.34, 0.8]
	Ownership	> 0.2	920	0.58	[0.04, 1.46]	0.5 [-0.17, 1.17]
	Appearance	> 0.2	909 -0.38 [-1.09, 0.34] -0.63 [-1.25, 0.22]
	Multi-sensory > 0.1	886.5	1.5	[0.83, 1.96]	1.17	[0.67, 1.5]
	Embodiment	> 0.2	905	0.38 [-0.02, 0.93] 0.21 [-0.43, 0.84]

More can be found at ns.inria.fr/loki/WithinBetween

ACKNOWLEDGMENTS

This work was funded by the Inria Avatar project.


Emmanuelle Bouilly

Virginie Dutoya

Marie Saiget

Introduction: Gender Knowledge: Epistemological and Empirical Contributions from the Global South

Keywords:

Women's and gender studies are now accepted academic subjects in many Global South countries, whether the field is well established-even institutionalized-or still emerging. However, this phenomenon is under-studied, even though the history, ideas, and key concepts of women's, feminist, and gender studies are becoming well documented in Europe and America (Lagrave; Brown; Bard; Clair and Heinen). This special edition therefore aims to shed light on knowledge production about women and gender in and by Southern countries, and not about these countries, as is often the case. On the one hand, this edition brings out the local, regional and global dynamics of gender knowledge production and circulation and, on the other hand, it focuses on the content of this knowledge and highlights its specificities (or lack thereof) at the theoretical and epistemological levels. Bringing together Northern and Southern feminist researchers, both junior and senior, offers an empirical and decentered analysis of gender knowledge production "from the margins" (hooks).

Questioning the International Division of Gender Knowledge Production: A Collective North-South Reflection

Our reflection is based on a paradox: while research on gender has increased exponentially since the 1990s in Global South countries, the latter are rarely considered to be sites of knowledge production or theoretical debates (Connell, "Rethinking Gender from the South"). The first criticisms of women's and gender studies' ethnocentrism were formalized in the 1980s (Amadiume; Mohanty; Oyěwùmí). More recent works have shown that while the postcolonial and decolonial critique has influenced the field of women's and gender studies, it remains structured by North-South relations. Indeed, the so-called Global South countries are most often seen as fields for study and as repositories for concepts developed in Northern academia (Spivak, "'Can the Subaltern Speak?'"; Wöhrer). However, it is striking to note that most of the early criticism of women's and gender studies' ethnocentrism came from researchers who were institutionally based in the Global North, even though they might come "from" the Global South. This is symptomatic of a division of intellectual labor whereby fieldwork and data are located in the Global South while theory remains the preserve of the Global North (Hountondji; Connell, "Rethinking Gender from the South"; Verschuur). This phenomenon is part of a double logic of marginalization and reification of the Global South within the social sciences that can be traced to the colonial period (Said, Orientalism; Keim et al.). In the meantime, gender has become a tool for public action (Ampofo et al.; Cîrstocea et al.; Imam et al.). These dynamics impact the way gender knowledge is produced, and how the concept of gender circulates. Both the unequal division of intellectual labor that structures social sciences in the widest sense and the institutionalization of gender studies will be at the very heart of this special issue.

Here we use the term "Global South" to refer to Latin America, Asia, Africa, and Oceania, in other words, to the regions outside Europe and North America, which are "mostly (though not all) low-income and often politically or culturally marginalised" (Dados and Connell 12). Those areas are often described as sharing an "entire history of colonialism, neo-

imperialism, and differential economic and social change through which large inequalities in living standards, life expectancy, and access to resources are maintained" (Dados and Connell 13). There are however debates on the geographical boundaries of the Global South, as well as on the heterogeneity of economic, social, and political situations that it contains. Taking those debates into account, we understand this category less geographically than relationally, i.e. in relation to the Global North, and within economic, political, and intellectual power relations, as well as "a distinctive positionality and an ethical subjectivity", like "Third World" or "Periphery" (Tickner and Smith).

The initial impetus for this collective endeavor came from our own difficulties, as French researchers, working from France on gender issues in Global South countriesrespectively, Burundi, Senegal, and India and Pakistan. How could we produce gender knowledge relating to these countries without reproducing different forms of domination, without falling back, as Gayatri C. Spivak would put it, "on a colonialist theory of most efficient information retrieval" (Spivak,"'Draupadi' by Mahasveta Devi" 382)? In 2018, we had the opportunity to develop this collective reflection, as we received a grant from the French Gender Institute4 to develop a network and organize scientific events. In 2019, we organized two events. First, a two-day bilingual (English & French) international conference, entitled "Production and circulation of gender knowledge in the Global South"5 , was set up in Paris in the spring of 2019. Second, a panel was organized at the international Conference "Globalisations et circulations des idées, des savoirs et des normes" [Globalization and circulation of ideas, knowledge, and norms] in September 2019 in Paris6 . We then organized a seminar-which is still ongoing-at the École des Hautes Études en Sciences Sociales (EHESS) in Paris. These events enabled us to open a discussion among researchers working on gender in the Global South but based (institutionally and physically) in different countries and continents. This also showed us the difficulties of establishing a lasting dialogue due to material difficulties (getting visas and funding), linguistic barriers, time differences, as well as the COVID-19 pandemic which has tended to accentuate those constraints. For instance, the initial ambition was to open a dialogue between French and English-speaking countries, and while we managed to do this in the conference, it became increasingly difficult to implement in terms of publication. We also found ourselves reproducing some academic legitimacy criteria while selecting papers and inviting scholars from around the world. Indeed, we also had to cope with the expectations of those providing funds and the fact that the organization of such an event was part of the evaluation process we have to go through to obtain tenure or career advancement (Belinga et al. 9), which is also true for Southern colleagues who are also forced to internationalize, i.e., to connect with the Global North. In this respect, the coordination of these events, and later this publication, illustrate how both local and global systems of domination are intermingled. This does not mean that we doubt the overall privileges that we have as researchers from the Global North, but it highlights the importance of examining precisely how these privileges deploy themselves and affect knowledge production processes at all levels. All the contributors to this special edition have participated in one of these events and committed themselves to continue this reflection collectively. Thus, despite the variety of locations, languages (English, French and Spanish), and disciplines (sociology, anthropology, political science, and history), the papers, and their authors, speak to one another. Grounded in empirical data, they all decenter the history of gender and women's studies from various contexts in Latin America, Africa, and Asia. They thus show how gender knowledge production combines with a set of economic, social, and epistemological power relations, while opening up possibilities of creating autonomous and subversive knowledge.

In the following sections, we first discuss the interaction of social sciences and imperialism and the way women's and gender studies have been a focus for both contestation and reproduction of North-South inequalities. Second, we come back to the dual patterns of institutionalization and globalization of women's and gender studies. Third, we discuss the specificity of gender knowledge as it is produced in the Global South and whether it is "different" or "similar" (Bilgin) and the limits and difficulty of reconstructing the canon from this perspective. Fourth and finally, we present the eight articles that comprise this special edition.

Social Sciences and the (De)construction of Power

Colonialism relied heavily on the collection of information and the production of knowledge (Said, Orientalism). Thus, the formal decolonization of the Global South did not result in the decolonization of knowledge (Keim). As shown by the notion of "academic dependency" (Alatas), the development of the social sciences in Global South countries is characterized by a division of intellectual labor, in which the Global South supplies fieldwork and data, while theory, methodology, and teaching paradigms remain the prerogative of the Global North (Connell, "Rethinking Gender from the South" 520). Despite their subversive stance, gender studies are not immune to this criticism. Various authors have shown the effects of the interweaving of women's and gender studies in North-South relations, both in terms of the domination of theoretical frameworks forged in the Global North (or in the West, in the often-preferred terminology) and the appropriateness of the conceptual frameworks employed (Bhaskaran; Dutoya, "Defining the 'queers' in India: The politics of academic representation"; Oyěwùmí). The invisibility of subaltern women and their experiences (Spivak, "'Draupadi' by Mahasveta Devi") or, on the contrary, their exoticization and reduction to the status of victims (Abu-Lughod; Win) have also been singled out.

These criticisms take several directions. Going further than denouncing the invisibility of "Third World women", authors such as Chandra T. Mohanty have deconstructed the "methodological universalism" that informs many feminist publications from the 1970s and 1980s (Mohanty 346). However, at the same time, she retained "women" and "gender" as useful analytical categories inasmuch as she called for contextualized and nuanced research into the realities of life experience for women from so-called Third World countries.

On the contrary, in her book The Invention of Women, Oyèrónké Oyěwùmí discusses the relevance of the Western concept of gender within the African context. She disqualified gender as being rooted in a Western-specific form of social organization: the heterosexual and nuclear family system, irrelevant, in her view, to understanding African realities. She defends the idea that the precolonial Yoruba family, as well as Yoruba language, are "non-gendered". Instead, she highlights the importance of "seniority" (age) in ranking and differentiating people. This argument has received a lot of attention and criticism-including from African researchers-"as both an inaccurate account of precolonial society, and as replacing an essentialism of bodies with an essentialism of culture that helps to legitimize postcolonial patriarchy" (Connell, "The sociology of gender in Southern perspective" 555; Bakare-Yusuf; Pereira; Panata in this edition). Although some pre-colonial African societies are structured differently from European societies, gender is nonetheless a central category of differentiation and hierarchization. As Pallavi Banerjee and Raewyn Connell sum up:

The factual grounding of the claim that gender was introduced by colonialism is flimsy. The assertion of a unique African way of being is marked by cultural essentialism and conservatism. Pre-colonial African societies-and the same can be said for pre-Columbian American societies 7 -did have gender hierarchies, did interact with each other, and constantly changed over time. We do not need to romanticize pre-colonial societies to recognize the strongly gendered character of colonization and its violent impact. (Banerjee and Connell, 2018: 64) Paradoxically, even though Oyěwùmí asserts that "gender" is a product of colonialism, hence strongly reacting against Northern feminism, her contribution has been recognized by and included in Global North gender studies.

Overall, authors from the Global South (but more often from the Global South and having made a career in the Global North) are now recognized as major contributors to gender studies and are part of the "canon". This growing recognition of the postcolonial and decolonial currents 8 within gender studies led Raewyn Connell to posit that gender studies are an example of a plural and "multi-centred" academic field (Connell, "Sociology for the Whole World"). Yet, such a vision is partial. An analysis of gender studies textbooks and reference publications has shown the pre-eminence of North America and Western Europe and researchers who are institutionally attached to them (Wöhrer). This raises an important question of who can access the global academic field as well as how and why. Furthermore, this growing recognition does not compensate for the general lack of awareness of women's and gender studies' dynamics within the Global South. Southern societies are often considered as receptacles for concepts developed by Northern academia (Keck and Sikkink; Naples and Desai; Desai). Without denying the primary emergence of gender as a concept in North America, the paradigm of dissemination and of a passive reception of women's (and then gender, studies) is not always the most relevant (John, "Feminist Vocabularies in Time and Space"). Despite the extensive and rich reflexive literature produced on this subject (Rege; Bhagwat and Rege; Chaudhuri; John, Women's Studies in India: A Reader), the history of women's studies in India, its methodological, pedagogical, and epistemic debates are little known beyond the subcontinent. Similarly, the theoretical contribution of work on gender in Africa and South America is still too often neglected (Ampofo et al.; Amadiume; Imam et al.; Sow; Valdés; Lugones; Vigoya; Sadiqi; Oyěwùmí, The Invention of Women: Making an African Sense of Western Gender Discourses; Oyěwùmí, "Conceptualising Gender: Eurocentric Foundations of Feminist Concepts and the Challenge of African Epistemologies"). Knowledge is still validated by the Global North: top academic journals are based there, as well as most international conferences, the English language dominates academic publications, and the translations of academic works circulate mainly from the centers to the peripheries, while relations between the peripheries are often mediated by the centers (Heilbron). Thus, while being grounded in a strong critique of power, women's and gender studies sometimes reproduce the structural inequalities at play in global knowledge production.

Exploring these issues requires a sociological study of the "structure, institutions and workforce of the global knowledge economy, its diversity of situations, and especially the relationships through which it operates and the dynamics of change in these relationships" (Connell et al. 740). To that end, our special edition pays close attention to the mechanisms 7 Oyěwùmí's critique has been espoused by Maria Lugones in Latin America (Lugones, "Heterosexualism and the Colonial / Modern Gender System"; Lugones, "The Coloniality of Gender"). 8 Postcolonial and decolonial feminism are two different currents. While postcolonial feminism emerged from/against the subalternist movement and within debates on South Asian historiography, decolonial feminism has its roots in Latin America, the two regions having very different colonial histories. This led to differentiated positions vis à vis Marxism, and global feminism, however, both currents question the hegemony of the Global North. For more details about the differences between these two currents, see Mendoza's work on the coloniality of gender (Mendoza). and actors in the institutionalization and globalization of gender knowledge, analyzing how these processes are differently experienced in the Global South.

The Political Economy of Gender Studies: Policy and Academia at the Crossroads

Since the United Nations Decade for Women (1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985), in development and aid policies, gender has become a "buzzword" (Cornwall and Brock), even a "globalized category of public action and knowledge production" through gender mainstreaming (Cîrstocea et al.). In India for instance, the professionals, often women, in charge of these gender policies within public bodies, international organizations, NGOs, and private companies (Menon; Dutoya, "La Professionnalisation de La Cause Des Femmes En Inde" [The Professionalization of the Women's Cause in India]) become experts and gender knowledge producers (Bustelo et al.; Prügl; Thompson and Prügl; Direnberger). In this respect, gender knowledge has expanded from the academic field, even though academics themselves can participate in the dissemination of gender outside universities, acting as consultants and moving between different professional worlds. Secondly, the globalization of social sciences, which accelerated in the 1990s (Heilbron, Boncourt, et al.), is characterized by the increasing amount of travel undertaken by Southern researchers, many of whom have been trained or worked in the Global North, as illustrated for example by the careers of Oyèrónké Oyěwùmí, Chandra Talpade Mohanty, Gayatri C. Spivak, Fatou Sow, and Amina Mama.

The effects of this double globalization are widely debated. Some see it as a recuperation, a de-politicization, or a de-radicalization of feminist concepts and struggles, a standardization and a uniformity of thinking, a perpetuation of imperialism and inequality, etc. Various authors have highlighted the dilution of the critical scope of gender due to its use beyond academic and feminist fields (Menon; Cîrstocea). Others prefer to emphasize the access of women's movements to resources, the democratization of girls and women's education, the appropriation, and the circumvention of unequal power relations by local female actors, the development of new conceptual tools, etc. Here lies the key issue: can gender be both a universal and institutionalized concept and remain a useful category of (critical) analysis (J. W. Scott; Menon; Cîrstocea). This is also true of other concepts related to gender and studied in this edition, such as "queer" (Dutoya) or "intersectionality" (Govinda; Panata; Sarkar). As Connell attests, "one of the most important [consequences for gender studies] is the framing of much gender research by economic development agendas" (Connell, "The sociology of gender in Southern perspective" 559). But it is worth asking whether dependence on international aid necessarily equates with the imposition of donor-driven agendas on gender research. Indeed, specialists in area studies have long demonstrated the agency and the resistance of subaltern actors and Southern societies, even in structurally unequal power relations (Bayart et al.; J. C. Scott).

Going beyond this debate about globalization effects requires empirical, locally rooted data to question concrete methods of legitimization and circulation processes, and concrete methods of appropriation of gender as a concept in various Global Southern contexts. Borrowing from a sociological approach to the circulation of ideas (Bourdieu), this edition aims to map the channels and the actors (publishers, universities, transnational institutions, activists, and teacher-researchers) who shape the fabric of gender knowledge (Heilbron,Guilhot,et al. 129). What textbooks, or concepts circulate? What are the social characteristics and trajectories of the actors involved? What are their resources and capital? What are their academic and professional backgrounds? Moreover, what are the institutional conditions, both local and global, of knowledge production? What tensions does the interaction between different worlds (governmental public action, international organizations, activists, scientists, non-governmental organizations, etc.) produce with respect to gender knowledge? By moving away from the postulate of a univocal domination by the North, we want to highlight the (possibly asymmetrical) mechanisms of knowledge co-production. This implies analyzing the role of feminist scientific networks linking Global South countries, the national contexts and historicity of the processes under study, and the material conditions of knowledge production, especially funding, be it local or international, public, or private. Apart from a few well-resourced universities in the Global South, notably in Brazil, India, and South Africa, the scale of resources available for gender studies and research in the Global South remains low compared to the North. Although they are increasing, there are still few universities offering programs in women's or gender studies in Africa (about 30 throughout Africa in the early 2000s) and they face many obstacles, including a lack of qualified staff and institutional support as shown by Amina Mama (see also Adedeji Adebayo in this edition). To counter these problems, academics willing to develop such programs must turn to other sources of funding, such as international organizations or private foundations. In Brazil for example, the Ford Foundation assisted the emergence and institutionalization of gender studies as an academic field, by awarding grants to researchers, universities, and journals from 1978 to 1999 (Grossi, 2004). Addressing this phenomenon therefore involves thinking beyond academic actors and feminist organizations and including governments and local authorities, political parties, nongovernmental organizations, international institutions, private foundations, and think tanks, gender-focused or otherwise.

Considering that gender studies "is involved in a global economy of knowledge" that leaves no culture untouched or separate (Connell, "The Sociology of Gender in Southern Perspective" 554), we should question how this process affects the concepts and methods used in gender research and teaching. Thus, our third and final research focus sheds light on the major and singular contribution of the Global South to the production of gender knowledge.

Decolonizing Knowledge: Re-building the Canon and Bridging Epistemic Communities

The epistemological scope of Southern approaches to gender is often minimized, which contributes to maintaining a division of scientific work between theory (in the Global North) and data (in the Global South). Hence, this special edition thoroughly examines the power and originality of this knowledge as well as its ambiguity. As we have already stated, Northern wealth and power do not necessarily produce intellectual domination. On the other hand, knowledge about gender as produced in the Global South is not always radically "different" nor "resistant" to Northern knowledge. Instead, it can highlight a certain "similarity", which cannot be explained through "'teleological Westernization' ('they all seek to become like us anyhow') but as the 'effects of the historical relationship between the "West" [or Global North] and the non-West' [or Global South] in the emergence of ways of thinking and doing that are 'almost the same but not quite'" (Bilgin 6).

Scholars and activists from both the Global North and Global South are facing aggressive anti-gender campaigns (Corrêa et al.), which make dialogue and cooperation more essential and reinforce epistemic communities. This convergence can be seen in the identification of a common set of concepts and analytical categories between the Global North and the Global South, such as gender, intersectionality, queer, and so on, through which sexual, racial and class power relations and division of labor can be understood. And despite the debates and criticisms these authors generate, Connell noticed that "the conceptual world of Marx, Foucault, de Beauvoir and Butler" continues to shape most gender analysis "even when it is talking about sexuality in India, identity in Australia, migration in the Mediterranean or factories in Mexico" (Connell, "The Sociology of Gender in Southern Perspective" 553). This "similarity" is also manifest in the sharing of data collection methods and modes of knowledgebuilding with critical feminist approaches, such as participatory action research (Tickner 9) or the belief that "emotion and intellect are mutually constitutive and sustaining oppositional forces in the construction of knowledge" (Code 47 quoted in Tickner 10).

Although "similar", knowledge about gender as forged in the Global South is not exactly the same as in the Global North. Researchers from the Global South tend to confront this "conceptual world" with their local context, re-shaping it in the process. This is particularly evident in Gayatri C. Spivak's work, as she can mobilize in the same text Derrida, Freud, Guha, Marx, Mahasweta Devi, and extracts from the Vedas (see for instance (Spivak, "'Draupadi' by Mahasveta Devi"; Spivak, "'Can the Subaltern Speak?'"; Spivak, En d'autres Mondes, En d'autres Mots : Essais de Politique Culturelle [In other Worlds, in other Words: Essays in Cultural Politics]). Hence, gender translation strategies (Kaplan et al.), i.e., the operations of screening, reinterpretation, contestation, and adjustment of this concept, need to be considered more systematically. Furthermore, the building of new concepts and methods in and from the Global South, as well as their contribution to the new impetus in global gender research (Bose and Kim), should also be examined. How can we qualify the epistemology resulting from the knowledge production process? Are we witnessing the emergence of "borderlands epistemologies" (Harding 163)? Should we rather talk about "in-betweenness" or "rooted cosmopolitan knowledge"? Furthermore, is a new canon emerging in and from the Global South? Finally, under what conditions is a global dialogue possible between gender conceptions and feminist cooperation across national borders?

This special edition highlights the Southern actors' agency and unique agenda in adopting-by adapting and reformulating-or rejecting Northern ways of thinking, researching, and teaching, but also in formulating new concepts and methodologies. There is such a diversity of fields that this edition does not postulate a unified use of the gender concept in the Global South, but suggests that there are common practices and questions, particularly regarding the very appropriateness of the concept of gender, the choice of vocabulary studied, and the need-or absence thereof-to produce "indigenous" knowledge and concepts (Oyěwùmí; Vanita).

The Articles

This special edition brings together eight original contributions addressing gender knowledge production issues in different Global South countries: Costa Rica (Fournier Pereira), India (Dutoya, Govinda and Sarkar), Nigeria (Abebayo, Panata), South Africa (Gouws), and Tanzania (Wenzek). Spanning three continents, and with different methodologies, they share important hypotheses and premises. First, they go beyond the paradigms of dissemination, domination, and theoretical dependency. Second, they move away from top-down perspectives and propose empirical approaches sensitive to the on-going sociological processes of knowledge formation in and from Global South countries, looking at actors, places, and actual channels of knowledge circulation, such as scientific journals (Gouws), research projects (Sarkar), or researcher mobility (Wenzek, Govinda). Brought together, the articles shed light on the many actors and institutions (universities, international and non-governmental organizations, associations, activist movements, foundations, etc.) involved in the processes of gender knowledge production and dissemination. For example, Amanda Gouws investigates the role of academic journals and editors (such as Agenda) in South Africa, while Virginie Dutoya, Florence Wenzek, and Adedeji Adebayo focus on the institutionalization of women's and gender studies at universities, respectively in India, Tanzania, and Nigeria. More specifically, Virginie Dutoya (India), and Florence Wenzek (Tanzania) analyze interactions between academics/universities and women's and feminist movements. Some articles explore the knowledge formation process within specific research projects: a doctoral thesis in the case of Mar Fournier Pereira on transwomen in Costa Rica, and a Ford Foundation-funded research project on LGBT groups in India by Debarun Sarkar.

Finally, Radhika Govinda's article uses the classroom as the site for analyzing gender knowledge production. By examining her own teaching experience, she interrogates the ambition of intersectionality as a critical pedagogy. Third, the papers all pay attention to the historicity of the processes under study, and the local meanings and situated contents of knowledge. The plurality of "indigenous" meanings and epistemic proposals, beyond the wellknown debate about the (ir)relevance of gender as a notion and its eurocentrism, are particularly well documented. In the articles by Sara Panata, Debarun Sarkar, and Radhika Govinda, the concept of intersectionality appears as a striking example of this on-going gender-related discussion and knowledge production between the Global South and Global North. Not only is the concept "essentially contested" (Gallie), but, as shown by Radhika Govinda and Sara Panata, to a large extent because of the realities of their local situation in the field, researchers in India and Nigeria had an intersectional understanding of gender even before the concept was coined.

The articles bring new answers to the debate around the disciplinary status of gender studies. In a nutshell, it has been traditional to oppose the disciplinary strategy, whereby women's (and later gender) studies are defined as a separate academic discipline, and the mainstreaming strategy, which advocates bringing a gender component into all disciplines. Our edition shows, unsurprisingly, that the situation on the ground is generally somewhere between these two poles. India and Nigeria offer a mixed picture in this respect. In the case of Nigeria, Adedeji Adebayo highlights the difficulties in developing gender studies as a multidisciplinary field, especially with a view to accumulating knowledge. In India, Virginie Dutoya explains that while in the 1980s the dominant view was that mainstreaming gender would be the best option, in the 1990s women's studies have de facto become a discipline, with the development of specific degrees, research centers and reviews. Today there are more than a hundred centers for women's and gender studies and teaching programs ranging from undergraduate electives to PhDs (University Grants Commission). However, in both cases, the issue of obtaining human and financial resources remains central and often unresolved. The development of gender studies as a specific discipline in India does not preclude the possibility of crossfertilization with other fields of study such as postcolonial and subaltern studies. Beyond the Indian case, the intimate, yet conflicted relationship between gender studies and post-or decolonial studies has been underlined by different authors in this edition (see Virginie Dutoya, Mar Fournier Pereira, Radhika Govinda and Debarun Sarkar in particular). And it emphasizes the importance of paying attention to the Global South to understand current developments in gender studies worldwide. It also becomes evident that while gender studies are becoming increasingly established in the academic field and teaching, gender studies' interdisciplinarity and openness need to be preserved. The papers also remind us how women's and gender studies have been developed by individual as well as collective activism, and the interweaving of personal as well as academic trajectories, as shown by Radhika Govinda and Mar Fournier Pereira.

In this respect, the articles insist on the agency of those involved in gender knowledge production, while acknowledging and documenting domination logics. In most articles, the material domination of the Global North is striking. Without the Ford Foundation (mentioned in three articles in this edition: Dutoya, Sarkar, and Wenzek) or the United Nations, women's and gender studies would have undergone very limited development in the South. Florence Wenzek's and Debarun Sarkar's articles show clearly how donor dependency has implications for the nature of the knowledge produced, in terms of subjects and areas studied, methodologies, and paradigms or concepts advocated. For example, funders might privilege quantitative research that is more easily translatable in terms of outputs. However, by and large, the authors detail the ability of local actors to retain their intellectual independence. Another important finding in this edition is that North-South domination interplays with other forms of power dynamics, such as those resolving around class, sexuality, caste, or race. The fact that those who produce knowledge are often part of the local elite complicates unilateral perceptions of academic dependency. In any event, agency occurs through conceptual and theoretical innovations. These are sometimes little documented because researchers from the Global South might not have access to global circuits of knowledge circulation or might not present them as such. For instance, Radhika Govinda, Amanda Gouws, and Sara Panata show that, in their chosen countries, gender was conceived as intersectional long before the concept of intersectionality was created in the United States. This concept is now central to this on-going gender-related discussion and knowledge production between the Global South and Global North. The innovations are also methodological and epistemological. In her article, Mar Fournier Pereira defends the role of affectivity in research, presented as "sentipensar". Radhika Govinda and Debarun Sarkar place themselves at the center of research, which they conduct with autoethnography and reflexivity. These approaches are not limited to gender or Global South studies, but they are particularly well-developed in both fields. Indeed, in a context where sources are often difficult to locate, archives not always accessible and data scarce, researchers must develop innovative research methods and combine multiple methodologies.

As Mary E. John, professor of women's studies in Delhi argues, one must not fall into the trap of "false particularism" to avoid "false universalism" (John,"Intersectionality" 75). In this respect, we must walk that fine line in order to produce a heuristic dialogue between researchers working on gender and women's studies, eager to produce knowledge together, in spite of, and on the basis of our different positions within academic and social spaces. This edition is one more step towards a collective and normative reflection on how to be more reflexive and inclusive in the way we participate in gender knowledge production and circulation. We hope to be able to continue this dialogue.

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