Tracking and simulating dynamics of implicit stereotypes: A situated social cognition perspective

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1 Tracking and simulating dynamics of implicit stereotypes: A situated social cognition perspective Annique Smeding* Savoie Mont Blanc University - LIPPC2S Jean-Charles Quinton* Clermont University / CNRS UMR Pascal Institute Grenoble Alpes University / CNRS UMR Laboratoire Jean Kuntzmann Kelly Lauer Savoie Mont Blanc University Laura Barca Istituto di Scienze e Tecnologie della Cognizione - CNR Giovanni Pezzulo Istituto di Scienze e Tecnologie della Cognizione CNR Authors note * These authors contributed equally. We extend our gratitude to Fei Wang for providing the material from Yu, Wang, Wang, & Bastin This research was supported by the French National Center for Scientific Research (CNRS) through the PEPS «Humanités Mathématiques Sciences de l information» scheme and Université Savoie Mont Blanc through the International Relations Grant (RI). Requests for reprints should be addressed to Annique Smeding, LIPPC2S, Université Savoie Mont Blanc, BP 1104, Chambéry cedex, France. Phone: ; Annique.Smeding@univ-savoie.fr, or Jean- Charles Quinton, LJK, Grenoble Alpes University, F-38041, Grenoble, France. Phone: ; e- mail: Jean-Charles.Quinton@imag.fr Disclaimer Prepublication version 2.13, 8/17/16. This paper was accepted in Journal of Personality and Social Psychology under APA copyright, and the published version can be found on the journal and APA websites, following This article may not exactly replicate the final version published in the APA journal. It is not the copy of record.

2 Abstract Adopting a situated social cognition perspective, we relied on different methodologies one computational and three empirical studies - to investigate social group-related specificities pertaining to implicit gender-domain stereotypes, as measured by a mouse-tracking adapted Implicit Association Test (IAT) and IAT(-like) tasks. We tested whether the emergence of implicit stereotypes was partially determined by associations congruent with the self, by visuospatial features of the task and subsequent competition at both sensorimotor and abstract levels. We tracked human and simulated artificial participants hand movements among gender stereotypical (e.g, male engineers) and counter-stereotypical (e.g., female engineers) social groups. In the computational study, data were simulated by a novel generative connectionist model integrating strengths from recent developments in embodied models of decision-making. Results support the self-congruency hypothesis and suggest the presence of competition at both levels. Discussion focuses on the generalizability of the self-congruency hypothesis and on the relevance of a situated perspective for implicit social cognition. difference Keywords: implicit gender stereotype, mouse-tracking, dynamical system, connectionist model, social group 2

3 Introduction Explicit, expressible stereotypes are, by definition, social cognitions referring to shared social knowledge in a given cultural context. This shared knowledge may, in turn, have an impact at a more implicit and subtle level. Therefore, when studying stereotypes, researchers often focus on the average stereotypical representation in the general population. However, knowing that, on average, math is implicitly more strongly associated to male than to female (Nosek, Banaji, & Greenwald, 2002) does not tell us whether some social groups, which are counterstereotypical or do not fit the stereotype, may display specificities at the implicit association level, and if so, which processes may account for it. In the present research, using different methodologies (empirical studies and computational modeling), we investigate social group-related specificities pertaining to implicit gender-domain stereotypes, as measured by a mouse-tracking adapted Implicit Association Test (IAT, Greenwald, McGhee, & Schwartz, 1998) or IAT-like implicit measures. Particularly, complementing existing theorization on the central role of the self in implicit social cognition (e.g., Greenwald, Banaji, Rudman, Farnham, Nosek, & Mellott, 2002), we claim that rather than social group differences per se, a determining factor underlying the emergence of implicit genderdomain stereotypes is whether associations are congruent with the self or not. In other words, our primary objective is to test for the specific social groups under investigation - whether binding between the self and group/domain concepts is a factor continuously influencing decision making processes in IAT(-like) tasks. A second and related objective is to test the relevance of taking into account the task-dependent bindings as another factor influencing decision making processes. This implies testing whether part of the variance on the types of implicit social cognition measures used in the present research can be accounted for by visuospatial features of the task and subsequent competition at the motor level, variance that cannot be accounted for by competition at the abstract level alone. This would complement existing models of implicit social cognition (e.g., Freeman & Ambady, 2011a; Greenwald et al., 2002) that place competition at the abstract level only. In this sense, the present research aims at providing evidence in favor of a (strong) situated social cognition perspective on implicitly measured, implicit stereotypical associations: Here and now encompasses not only what I am in the situation and what I have learned, but also the very features of the sensorimotor apparatus and experimental design. 3

4 The Implicit Association Test and Unified Theory In their Unified Theory, Greenwald et al. (2002) define stereotypes as the association of a social group concept with one or more (nonvalence) attribute concepts (p.5). In this theory, stereotypes are embedded in a social knowledge structure, with concepts being interlinked through various associations of various weights. This framework is particularly relevant when studying implicit gender stereotypical associations, like those linking math more strongly to males than to females (Nosek et al., 2002). One valuable input from research on these implicit gender-math stereotypes is converging evidence that domain counter-stereotypical women - those majoring in science, technology, engineering, and mathematics (STEM) - display weaker implicit male-math associations than more domain-stereotypical groups (STEM men or humanities women; Nosek & Smyth, 2011; Smeding, 2012; Stout, Dasgupta, Hunsinger, & McManus, 2011). In other words, evidence suggests that some social groups display specificities at the implicit association level and that, according to Unified Theory, the self plays a central role in the emergence of stereotype-related specificities, a point to which we will return later. One measure widely used to study implicit stereotypical associations is the IAT (Greenwald et al., 1998). In its original form, the IAT is a reaction-time measure, in which participants categorize words in four categories such as male, female, math, and language in the case of a gender-math IAT (Nosek et al., 2002). For stereotype-congruent trials, participants are asked to respond with one key press to words representing male and math, and with another key press to words representing female and language. For stereotype-incongruent trials, male and language share a response key and, likewise, female and math. Outcomes of interest are mainly mean latencies, which are longer for incongruent than for congruent trials for most individuals (albeit not necessarily for counter-stereotypical ones). This IAT effect emerges because associations between categories are, on average, stronger for congruent than for incongruent trials. Although extremely valuable for various endeavors (e.g., overcoming motivational biases and introspective limitations, improving predictive validity as compared to self-reports; Greenwald & Banaji, 1995; Nosek, 2005; Nosek et al., 2009), keypress-based reaction time measures are not without limitations. Specifically, they tell us little about the ongoing decision making processes underlying categorization, as only final outputs (latencies, error rates) are available. They can also be sensitive to faking and response strategies (e.g., slowing down on stereotype congruent 4

5 trials; Fiedler, Messner, & Bluemke, 2006). Because IAT effects typically involve a comparison of latencies between congruent and incongruent trials, strategic responding and limited understanding of the underlying processes are a concern, especially when investigating specificities among different social groups (e.g., one group implementing them, but not the other). Recent developments using continuous measures of performance may represent a promising alternative to overcome limitations. Most notably, mouse-tracking, that is, tracking (hand-initiated) computer mouse movements has proven to be very effective in revealing the online decision-making dynamics underlying (social) categorization (e.g., Freeman, Ambady, Rule, & Johnson, 2008; Freeman, Dale, & Farmer, 2011a; Spivey & Dale, 2006). The continuous nature and fine-grained spatiotemporal sensitivity of mouse-tracking data reflect motor traces of the mind (Freeman et al., 2011a, p.2), as temporal constraints of the task force hand movements to be initiated as soon as the trial starts. Thus, strategic corrections will be traceable in the data, as initial attraction toward the opposite side of the screen at the onset of stimulus presentation ought to be observable in response curves or speed profiles. Recent research on person perception and social categorization has relied on mouse-tracking techniques (Freeman & Ambady, 2009, 2010; Freeman et al., 2011a), putting a strong focus on the intertwined bottom-up (stemming from visual face stimuli) and top-down (stemming from stereotypes) processes guiding social categorization (Freeman, Penner, Saperstein, Scheutz, & Ambady, 2011b; Hehman, Ingbretsen, & Freeman, 2014; Johnson, Freeman, & Pauker, 2012). This mouse-tracking methodology allows to take a dynamical systems perspective, according to which choice is a competitive process among response alternatives, with convergence toward an attractor (e.g., Conrey & Smith, 2007; Spivey & Dale, 2006; Spivey, Grosjean, & Knoblich, 2005). In this perspective, the very notion and characteristics of competition must be conceived of as situated, hence including (but not limited to) the sensorimotor apparatus and experimental design, which both put constraints on the decision making dynamics. Competition, in this perspective, may therefore occur at both the abstract and sensorimotor levels and, following this rationale, both types of dynamic competition are required to thoroughly account for decision processes in IAT and IAT-like tasks. 5

6 Despite the advantages of the dynamical systems approach and of mouse tracking techniques, the IAT literature has remained silent with respect to these theoretical and methodological advances, for the exception of Yu, Wang, Wang, & Bastin (2012). However, the Yu et al. (2012) research investigated valenced associations only, not stereotypes, and did not focus on different social groups. This aspect is of primary importance given that differences in associations for different groups should directly influence decision-making dynamics. Even more crucially, Yu et al. (2012) did not develop a computational model to simulate these dynamics and related group differences. Using a combined empirical and computational approach allows a thorough understanding of competing dynamics between internal processes and between motor actions, as the computational model permits simulating nonlinearities, deviations, and online changes in decisions observed among human participants. Minimalist generative models can also produce unintended subtle differences in the dynamics. Such differences, which would not draw our attention and would thus be hardly predictable from high level theoretical models alone, can subsequently be tested in human data. Previous connectionist models on social categorization (Freeman & Ambady, 2011a; Greenwald et al., 2002) do not allow generating the required dynamical outputs because they do not integrate motor actions into decision making. Here we have the unique opportunity to generate such data, by combining advances in models from both social categorization and embodied decision-making literatures (Pezzulo, Barsalou, Cangelosi, Fischer, McRae, & Spivey, 2013). This strong situated social cognition approach is absent in the existent literature on social categorization or IAT(-like) social cognition tasks. In the present research, we use mouse-tracking adapted IATs or IAT-like procedures to investigate the dynamical processes underlying implicit gender-domain associations among gender stereotypical (i.e., male STEM and female non-stem students, expected to display stronger male-math associations) and counter-stereotypical (i.e., female STEM and male non-stem students, expected to display weaker male-math associations) social group members. Here we are interested in the implicit gender-domain stereotypical associations at the abstract level, with a focus on social categorization based on linguistic stimuli only, not on person perception as in previous research (Freeman & Ambady, 2011a; Greenwald et al., 2002). Although variations across words were not of primary interest, we consider they are part of the experimental design and as such ought to contribute to variations on mouse-tracking indicators. 6

7 Reframing the IAT rationale within a dynamical systems perspective, we assume that a conflict arises when category bindings are incongruent with the self, as compared to when category bindings are congruent with the self. To illustrate, for STEM women, binding of the female and math categories is self-congruent in the case of a classical gender-domain IAT, whereas for female non-stem students, this same binding is self-incongruent in the task. Selecting one of these categories when they are associated/binded should be facilitated for the former, while the competition between the two-alternative forced choices should be stronger for the latter, dynamics that should be traceable in the data. Of importance, this competition is not merely expected at the abstract level, as usually assumed in social psychological research, but also at the motor level, and thus introduced at both levels in the computational model (see also Quinton & Smeding, 2015). Assuming and implementing competition not solely at the abstract but also at the motor level represents a major change in how we may conceive of implicitly measured, implicit stereotypical associations. It indeed implies that the situation (the here and now ) encompasses not only what defines me as an individual or a social being (e.g., culture, knowledge), but also what defines me as a physical agent (e.g., sensorimotor capabilities and skills) as well as the experimental design. Overview The present research aims at providing evidence in favor of a situated social cognition perspective on implicitly measured, implicit stereotypical associations. The general rationale is that here and now not only encompasses what individuals are in the situation and what they have learned, but also the very features of the sensorimotor apparatus and experimental design. Our first assumption is that rather than social group differences per se, a determining factor underlying the emergence of implicit gender-domain stereotypes is whether associations are congruent with the self or not. Our second assumption is that part of the variance on the types of implicit social cognition measures used in the present research can be accounted for by visuospatial features of the task and subsequent competition at the motor level, variance that cannot be accounted for by competition at the abstract level alone. In a series of studies, using different methodologies (empirical studies and computational modeling), we investigate social group-related specificities pertaining to implicit gender-domain stereotypes, as measured by a mouse-tracking adapted IAT or IAT-like implicit measures. In studies 1 and 2, the focus is on establishing fine-grained group differences via in-depth mouse-tracking data analyses, coupled with computational modeling. In study 1, 7

8 mouse-tracking data is recorded for different real-life social groups (STEM vs. non-stem students). In the computational study, mouse-tracking data are simulated by a generative dynamical connectionist model parameterized to reflect intergroup differences. Because decision dynamics can be quite complex, simulating them with generative models allows a deeper understanding of these phenomena and the production of new hypotheses (see Quinton, Catenacci Volpi, Barca, & Pezzulo, 2014). Vice versa, it is only with real participant data that researchers can refine such a model, yet keep it simple enough to maintain explanatory power. Based on past IAT and mouse-tracking research, we expected diverging implicit associations for stereotypical and counter-stereotypical social groups to be observable in the decision-making dynamics for stereotype-congruent and stereotype-incongruent trials. Specifically, for stereotypical group members, mouse trajectories should be straighter for congruent than for incongruent trials, whereas the reverse pattern should be found for counter-stereotypical ones, reflecting the impact of self-congruency from a participants perspective. See Tab.1 for the hypothesized congruency of IAT associations for the different social groups. In addition, exploiting the full potential of mousetracking data by computing statistics on the trajectory dynamics, we can observe the early automatic activation of implicit associations, something not achievable with mere reaction times. We would thus expect trajectories to display early attraction toward the stereotype congruent association for stereotypical group members, and toward the stereotype incongruent association for counter-stereotypical group members. Indeed, according to Unified Theory, different response patterns can emerge because initially unlinked concepts (e.g., female and math) are reinforced if these concepts share a first-order link with a third concept (e.g., self). For example, female STEM students have associations linking self and female, but also self and math, resulting in a strongly expressed (counterstereotypical yet self-congruent) association between female and math. These counter-stereotypical associations are precisely required to facilitate the decision-making process on incongruent trials. Study 1 investigated decision-making processes for congruent and incongruent trials, with data collected for female and male STEM students, and female and male non-stem students. In study 2, the model simulated the experimental data permitting to test mechanistic hypotheses on the decision-making processes. In particular, we compare the decision-making dynamics of (simulated) participants from different social groups with stronger or weaker counter-stereotypical associations constructed via the self, while leaving all other parameters unchanged. 8

9 This is of great theoretical importance as it allows examining, with data from a single IAT, the central role of the self in the construction of counter-stereotypical associations, an assumption that has remained untested so far. The computational study relied on a dynamical connectionist model, where nodes represent concepts that can be activated, and links represent associations between these concepts (for a similar approach, see Spivey, 2007). Depending on the symmetry of the associative links, as well as on the rules used to update the activity in the simulated system, this type of system can be reframed into a recurrent neural network (Freeman & Ambady, 2011a) or a probabilistic graphical model (Yedidia, Freeman, & Weiss, 2003), where links may correspond to conditional probabilities between concepts (e.g. probability of female category to be relevant when observing the word woman). These links are not limited to individual knowledge about abstract concepts, but cover a whole range of associations from (i) social knowledge (e.g. math-male stereotype), (ii) identity (e.g. self-math or self-female), (iii) general task constraints (e.g. binding of father and brother into the male category), to (iv) block and trial dependent constraints (e.g. male-left defining the mapping from the conceptual space to visuomotor space, see Quinton & Smeding, 2015). As such, this approach very much relates to the distributed and situated social cognition approach (Smith & Semin, 2004, 2007). During the simulation, activity is propagated from nodes directly activated by observations (e.g. words), generating indirect activations from first-order links (e.g. probability of math category to be relevant when observing the word father, even if there is no direct math-father link). In the present mouse-tracking paradigm, trajectories thus emerge from the dynamic interplay between various stimuli and links (individual knowledge, conceptual constraints imposed by forced-choice tasks, grounding of decisions in sensations and actions). Each link introduces a constraint on how, and to what decision the system will converge. The statistically significant differences for responses on congruent and incongruent trials result from differences in the graph structure and connectivity, for instance whether stereotypically associated categories are mapped to the same target (e.g. math-left, male-left for stereotypical blocks), and whether individual associations are congruent with this mapping (e.g. me-male, me-math for male STEM students). In study 3 our rationale was, in a complementary vein of the analyses performed in studies 1 and 2 as a function of social group membership per se, to test the relevance of the self-congruency factor at the trial level. Particularly, 9

10 we aimed at distinguishing between two orthogonal factors: the stereotype-congruency factor and the selfcongruency factor. As we assume that binding between the self and group/domain concepts drives implicit associations, we expect the self-congruency factor to better account for the data than the stereotype-congruency factor. In study 4, we will also test for the consistency of this self-congruency factor, but under conditions where the category bindings evolve constantly. In study 4, a final step is then to test whether self-congruency related findings are maintained even when task requirements are severely modified for instance by introducing random switches in category binding between trials. If the self-congruency factor still emerges as a relevant factor, this would provide strong evidence in favor of the concomitant competition at the abstract and sensorimotor levels. Study 1 Method Participants Forty six (21 female) engineering and 44 (22 female) humanities undergraduates volunteered to take part in the study. Data were collected separately for engineering and humanities students, as they attended different universities. Additionally, as engineering students have a very busy schedule, it was particularly difficult to have them taking time away from their studies to participate in the research. This, combined with the scarcity of female engineering students, resulted in two sessions of data collection for engineering students to have similar sample sizes for engineering and humanities students. Procedure and materials The gender-math IAT was adapted from Nosek et al. (2002) with male, female, math, and language being the target categories. The full list of stimuli words is provided in the Supplemental Material. The IAT procedure closely paralleled that of a reaction time IAT, except that response choices were made by mouse movements. Participants were instructed to click a START button at the bottom center of the screen to start each trial. They categorized each stimulus word (appearing at the center of screen) by hovering over the chosen category (top-left and top-right corners of the screen) with the computer mouse. Blocks 3, 4, 6, and 7 (double categorization blocks, order counterbalanced across participants) were the critical blocks (see Greenwald, Nosek, & Banaji, 2003). During the entire task (blocks 1 to 7), x, y coordinates along the mouse trajectory were recorded. The full setup is displayed in 10

11 Fig.1. Although we took care of having similar parameters for engineering and humanities students, as the two groups did not perform the task on the same computers (different universities), small differences in absolute values on our main indicators (see below) could be expected. Words were displayed on the screen at the onset of each trial. Throughout the task, participants were asked to initiate mouse movements very quickly (the word Faster was displayed on the screen after 500 ms if no movement was initiated). Upon task completion, participants provided demographic information and were fully debriefed. Measures Geometric mouse-tracking measures. We tested our central predictions on the Area Under the Curve (AUC) indicator, that is, the geometric area between the observed mouse-trajectory and an idealized straight-line trajectory drawn from the start and end points (Hehman, Stolier, & Freeman, 2015, p. 388). We also performed analyses on the Maximum Deviation (MD, which is the length of a perpendicular line between the idealized straightline trajectory and farthest point from that straight line in the observed trajectory, Hehman et al., 2015, p. 388). Although the MD results closely paralleled AUC in most cases, we chose to focus on AUC for reliability and consistency across studies. In the literature, studies most often used either AUC or MD indicators, indistinctly. However, in our view, AUC represents a more reliable indicator because, as compared to MD, it is less influenced by sudden, very local or extreme deviations. Regarding Reaction Times (RT), findings in mouse tracking paradigms have been inconsistent, with some studies reporting effects on both mouse-tracking and reaction time indicators (e.g., Yu et al., 2012), and others on the former only (e.g., Wojnowicz, Ferguson, Dale, & Spivey 2009). In our view, however, RT on mouse-tracking adapted IATs may not be conceived of as RTs on typical keypress IATs, nor should these measures directly be compared: Many sensorimotor processes occur in between the initiation time and the final decision in mouse-tracking, processes which are likely to influence other decision-making processes in time (see Pärnamets, Johansson, Hall, Balkenius, Spivey, & Richardson, 2015) and final RTs only reflect the final outcome of these dynamics. This does not occur when only keypresses are used. Sensorimotor components thus occupy a larger share of the overall decision and action time, and may compensate delays due to implicit associations with increased velocity (for a thorough description of these dynamics, see Freeman, Pauker, & Sanchez, in press). 11

12 Dynamic mouse-tracking measures. In contrast to geometric measures, which allow testing statistically significant differences between entire trajectories, we turn here to fine grained measures of the decision-making dynamics. Specifically, we computed the x-coordinate velocity profile (shortened as x-speed hereafter), which corresponds to the mouse speed along the left-right dimension of the screen at each point of time (see Hehman et al., 2015). Since all trajectories were remapped rightward and error trials were removed, smaller or negative values for the x-speed indicate an attraction toward the incorrect target. We therefore focused on the x-speed minimum value noted Vmin, observed at time Tmin. Analyzing the differences in shape or bifurcation patterns between conditions and social groups also allows to go beyond basic mouse-tracking statistics, and to determine how and when top-down influences may impact on the decision. This might reveal which cognitive processes may be common to all participants, and which ones may be specific to some groups. Results Geometric mouse-tracking measures Information regarding data preparation is reported in the Supplemental Material. Analyses were performed using mixed-effects regression models, with AUC values regressed on trial congruency, gender, academic domain, and all interactions between these variables (effect size coefficient Ω 2 0 = 0.14). As we expected straighter trajectories for congruent than for incongruent trials for stereotypical group members and the reverse pattern for counterstereotypical ones, our focus was on the 2(Congruency: congruent, incongruent) 2(Gender: male, female) 2(Academic domain: engineering, humanities) interaction effect. This effect was significant, B = 0.24, t(9437) = 5.36, p <.001, 95% CI [0.15,0.33]. As expected, AUC for female humanities students was higher for incongruent trials (M = 0.47, SD = 0.60) than for congruent trials (M = 0.41, SD = 0.55), t(2372) = 3.0, p <.01. For male engineering students, AUC for incongruent trials was higher (M = 0.64, SD = 0.63) than for congruent trials (M = 0.58, SD = 0.58), t(2579) = 2.75, p <.01. Thus, the two gender stereotypical group members mouse movements reflected more direct trajectories for stereotype congruent than for stereotype incongruent trials. Of importance, this pattern was not observed for female engineering or male humanities students. Female engineering students AUC reflected more direct trajectories for incongruent (M = 0.59, SD = 0.58) than for congruent trials (M = 0.66, SD = 0.57), t(2186) = , p <.01, that is, counter-stereotypical associations at the implicit level. Male humanities students displayed the 12

13 same pattern, with higher values for congruent (M = 0.48, SD = 0.59) than for incongruent trials (M = 0.44, SD = 0.53), t(2300) = -2.01, p <.05. Results are displayed in Fig.2. Fig.3 illustrates the average trajectories for congruent and incongruent trials for each social group separately (panels a, b, c and d). Fig.4 illustrates the set of trajectories produced for all congruent vs. incongruent trials by 2 human participants from the study (differing on trajectory variability). Dynamic mouse-tracking measures X-speed profiles for stereotype congruent and incongruent trials (averaged over all participants) are reported on Fig.5a. As classically found in non-iat mouse-tracking tasks (Hehman et al., 2015), velocity is initially smaller for stereotype incongruent trials. This is true, even though we ran the experiment on stereotypical and counterstereotypical social groups of equal sample size, groups which may display opposite patterns (as expected from the geometrical results). Using mixed-effects models at each timestep, x-speed values for all trials were regressed on trial congruency. A significant effect appears from 470ms, t(9696) = 2.03, B = 0.39, p < 0.05 (also see Fig.6 for the bifurcation pattern). This early differentiation is to contrast with the average response time of 831ms in this study, or to the average RT of 700ms (across all types of trials) in classical IAT studies (e.g., Greenwald et al., 1998; Blair, Ma, & Lenton, 2001). The focus of our study being on social group differences in stereotype related decision-making dynamics, we must further look at the velocity profiles for each social group separately. For instance, Fig.5b and Fig.5c display the qualitative differences between engineering male and female students. We thus performed a similar timestep by timestep mixed-effects analysis on x-speed, this time including trial congruency, gender, academic domain, and all interactions between these variables. The 2(Congruency: congruent, incongruent) 2(Gender: male, female) 2(Academic domain: engineering, humanities) interaction effect was significant even earlier, from 305ms, B = 0.32, t(9787) = 1.99, p <.05. In addition to partially reversed dynamics between stereotype congruent and incongruent trials, counterstereotypical participants show a stronger initial attraction toward the counter-stereotypical answer for stereotype congruent trials (the one supposedly congruent with their self ). We therefore need to turn to statistics extracted from each x-speed profile separately, if we want to account for the contrasted response patterns and temporal 13

14 dynamics of the different groups and individuals. Performing mixed-effects analysis on Vmin, the minimum x-speed value, we better explain the differences (effect size coefficient Ω 2 0 = 0.96), in contrast with the previous timestep based approach (from Ω 2 0 = 0.07 at t = 470ms up to Ω 2 0 = 0.23 at t = 595ms). We again focused on the 2(Congruency: congruent, incongruent) 2(Gender: male, female) 2(Academic domain: engineering, humanities) interaction effect, which was significant, B = 0.15, t(86) = 2.20, p <.05, 95% CI [ 0.29, 0.01]. For example and as expected, Vmin for female engineering students was higher for incongruent trials (M = 0.09, SD = 0.12) than for congruent trials (M = 0.17, SD = 0.23), t(168) = 2.37, p <.05. The average time at which Vmin appears for stereotype-congruent trials (labeled Vmin on Fig.5c) for engineering female students is 315ms (i.e. when the attraction toward the opposite response is the strongest). This may reflect an automatic counter-stereotypical association to be compensated or inhibited to perform well on stereotype congruent blocks (see Supplemental Material for ruling out alternative explanations). Additional analyses. In addition to the fixed effects previously reported, random effects of the mixed effects model on AUC are also of interest. The estimates for the Participant random effect logically demonstrate a large inter-individual variability (sd = 0.18), previously analyzed in terms of intergroup fixed effects. The random effect corresponding to the stimulus (word to be categorized by the participant) is smaller (sd = 0.062) but displays a non-normal and non-homogeneous distribution across stimuli categories: Math (M = 0.003), Language (M = 0.067), Male (M = ), Female (M = ). This difference is confirmed when introducing a factor to test the difference between the Male-Female against Math-Language stimuli in the previous analysis (B = , t(21.7) = -3.82, p <.001), with Math-Language generating larger deviations, all previously reported results not being altered. This finding suggests, at a methodological level, that there is an asymmetry between categories of stimuli in the present IAT (see Supplemental Material for the associated figure). We will return to this point in studies 3 and 4. Discussion In accordance with expectations, results from study 1 showed specificities at a very fine-grained implicit level between stereotypical and counter-stereotypical groups. Counter-stereotypical groups displayed straighter trajectories for incongruent trials, whereas the reverse pattern was observed for stereotypical group members, with 14

15 deviations being smaller for congruent trials. Also, counter-stereotypical female engineering students x-speed profiles showed an early attraction toward counter-stereotypical answers for stereotype congruent trials, a pattern not observed among their male counterparts. X-speed profiles also revealed partially reversed dynamics between congruent and incongruent trials for stereotypical versus counter-stereotypical groups. In study 2, our aim was to replicate those group specificities with data simulated by a generative connectionist model parameterized to reflect intergroup differences differences which only rely on variations in strengths of associations between self and gender, and self and domain - and to integrate sensorimotor control at the trial level. These two features allow combining recent developments in embodied models of decision-making with those of social categorization, along with testing the requirement to model competition at both abstract and motor levels to reproduce human participantlike data. Study 2 Method Forty six (21 female) engineering and 44 (22 female) humanities students were simulated in the study. Simulated participants shared the same connectionist network, composed of a set of nodes ci {math,language,male, female,left,right...}, with certain pairs of nodes (ci,cj) interacting through a link of strength wij. In particular, all artificial participants had identical stereotype knowledge (reflected by link strengths math male = 0.1, female humanities = 0.1). The only differences between simulated social groups were the strength of associations between self and gender, as well as between self and domains (e.g. me math = 0.5 for engineering students). Each artificial participant went through the exact same procedure as the human participants, controlling the mouse dynamically to select the response on the same blocks and trials. Fig.7 illustrates the set of trajectories obtained from 2 arbitrary artificial participants from the study (to be contrasted with human trajectories from Fig.4). The current model is thus a generative model, going down to sensorimotor control at the trial level, while bridging the gap with social group belonging and implicit associations at the conceptual level. As such, the model combines strengths from recent developments in embodied models of decision-making (e.g. Embodied Choice model from Lepora & Pezzulo, 2015) with those of social categorization (e.g. Dynamic Interactive Model of Person Construal from Freeman & Ambady, 2011a). 15

16 Link configuration In this type of complex system with close to chaotic dynamics, weak links and small changes in activity are sufficient to generate non-linear bifurcations in the phase space, and therefore lead to different decisions. However, in our task context, perturbations from the social knowledge (stereotype) must not override explicitly relevant features (block configuration) and task instructions (limited number of words in fixed categories). Stereotypes must indeed be inhibited for the participant to perform efficiently in the counter-stereotypical blocks. The task and block related links must therefore be stronger than stereotypical links. Thus links between words and categories are boosted, since only a few different possibilities are left to the participant, in contrast with the richness of daily experience. Referring again to conditional probabilities, this context dependent modulation of weights would be reflected by a priori probability distributions over concepts being defined by the experimental instructions. As a consequence, the model is robust to intra and inter-individual variability in parameters, as long as this order on link strengths is respected. To respect these constraints while introducing inter-participant variability, link strengths were fixed for each participant, but sampled from probability distributions. To generate link strengths, the distribution means reported in Fig.8 were scaled by a random number sampled from a normal distribution centered on 1.0, with standard deviation of 0.1. This process allows large variations in link strength, while maintaining their sign. All links between observed gender-related words and their associated categories (e.g. father male) were arbitrarily centered on 0.8, since we did not study or hypothesize any difference between specific words. Similarly, the mean strength for links between domain related words and categories (e.g. equation math) was set to a slightly smaller value (0.7) to reflect a plausible weaker activation for less salient or fuzzier categories, as well as to test the independence of the model results to this inter-target factor. Stereotype related links (math male and language female) have a mean set to 0.1 for all participants (common knowledge), reflecting a much weaker influence due to their non-relevance for the participant s task, but sufficient to generate a decision bias (and thus deviation of the mouse trajectory). For all participants, the me-gender mean was arbitrarily set to 0.8 (e.g. me male = 0.8 and me female = 0 for male participants). 16

17 Finally, the identity and domain specific links were designed as follows: math me = 0.5 and language me = 0.6 for engineering students, and math me = 0.5 and language me = 0.4 for humanities students. Since the engineering students followed a highly selective curriculum in STEM, their association to math was set to a slightly higher value than the me-language link of humanities students. Although the negative link is not mandatory in the current model, it facilitates the stability of the network activity. As reported in the Supplemental Material, the dynamics of interest still holds when this inhibition is diminished. In other words, had we changed the weights for the self-related domain to parallel those used for the self-gender associations, results would have been unchanged if the relaxation term is adjusted (i.e. to compensate the reduced inhibition in the network). It is mainly the difference between the strength of the two associations (e.g., self-math versus self-language) that matters. In the end, the congruency effect depends on both the type of block and the social group of participants simulated. As illustrated in Fig.8 (colored nodes), a smaller deviation should be observed when most links consistently orient the activity flow towards a single target, i.e. for stereotypical participants on stereotypical blocks and for counterstereotypical participants on counter-stereotypical blocks. The slight asymmetry between the two models comes from the stereotype related links, which are impeding the convergence on counter-stereotypical blocks for counterstereotypical participants only, because they indirectly activate the opposite target. While the partial order (i.e. inequalities between the strength of certain pairs of links) and asymmetries between links must be preserved to guarantee consistent behaviors and qualitative differences in behavior between simulated social groups, the exact value of the link strengths may drastically vary. Such variability is introduced in the computational model in order to reproduce the variability expected from a random human sample. A sensitivity analysis was run to demonstrate the robustness of the model to parameter tuning and replicability of the results for a given set of parameters, using a multidimensional sampling lattice. Additionally, and to further test the robustness to statistical sampling, we also run Monte-Carlo simulations with 40 runs of the 90 simulated participants, using random sampling over the parameters space for each run, and 60 trials in each block of interest (stereotype congruent vs. incongruent) for each participant (see Supplemental Material for details and figures). 17

18 Competition between hypotheses and actions Humans can only take a single action at any time when using a single effector (hand) to control a single pointer on the computer display, while the coexistence or co-activation of hypotheses and concepts at the neural level is plausible. Computational models on previous mouse-tracking experiments have rather focused on the competition dynamics at the conceptual level (Freeman & Ambady, 2011a), which would in our case lead to a direct opposition of male and female categories, as well as math and language. Similarly, this type of competition is found in the Unified Theory, with the use of bipolar-opposed identities such as male and female (Greenwald et al., 2002, p.18). However, it is not explicitly emphasized in Unified Theory, since the focus is on explaining the differences in reaction times and activation patterns between congruent and incongruent trials. Competition at an abstract level appears to lack flexibility to account for the fact that, depending on task demand and context, concepts may be grouped together or segregated according to different criteria (e.g. categorization of IAT stimuli such as grandfather, grandmother, son or daughter will differ depending on whether the target categories are young/old or male/female). This dynamic binding of concepts into categories is, in our model, naturally realized by the visual binding of the targets, which is a direct consequence of the spatial organization of targets in the various experimental blocks (stereotypical or counter-stereotypical). Although the timescale of the links in our model may span from the whole life of an individual (culture) to the instant (task constraints), the behavior is not fully determined by them. Even if we were to consider a single network with a fixed topology and fixed weights, the way the simulated participants perceive and categorize is also dependent on their immediate context, here determined by the visual stimulation provided (leftward or rightward location of the target words, and stimulus word). It is only through the interplay of structure (network) and activity (with bottom-up and lateral propagation) that the mouse trajectory emerges and satisfies all constraints. Models of the IAT using one or several types of competition have been explored in Quinton and Smeding (2015), but will not be further discussed here. We here chose to make competition occur both at the conceptual and motor levels, in order to remain compatible with previous models of both the sensorimotor aspects of mouse-tracking tasks (Lepora & Pezzulo, 2015; Quinton et al., 2014) and more abstract models from social psychology (Freeman & 18

19 Ambady, 2011a; Greenwald et al., 2002). This dynamical competition is reflected on Fig.8 by the (dashed) inhibitory links between nodes (only left and right, since all inhibitory links could not be represented). Node activity and network dynamics As originally introduced in Quinton and Smeding (2015), a dynamic activity ai is associated to each node ci in the connectionist network. This activity is ruled by Eq.1, using a continuous time version of existing stereotype models based on recurrent neural networks (Freeman & Ambady, 2011a). This equation enables non-linear bifurcations in the dynamical system towards one response or the other, while guarantying inertia and continuity in movement. τ a i t = a i + w ij σ(a j ) + ε i (1) j where τ is the time constant (0.5s), ai is a relaxation term allowing the activity to return to zero in absence of external or lateral stimulation, wij σ(aj) corresponds to the influence of connected nodes (with wij the link strengths and σ being a non-linear activation function), and i is a noise term. To make the dynamics highly stochastic, introduce variability in trajectories and demonstrate the robustness of the model to perturbations, i is sampled from a centered normal distribution of standard deviation 0.5. To be simulated on a computer, temporal discretization with an Euler scheme is applied to the equation ( t = 0.01s). At any time during each trial, nodes directly related to observed stimuli see their activity set to 1.0. For instance, if the word father is presented, afather = 1. Also, instead of setting the activity of all nodes to zero at the beginning of each trial, only the sensorimotor nodes are reset (since the participant has to stop over the START button), while the activity of conceptual nodes (all but left and right) decay by 80% (coefficient α in Algo.1). This is done in order to reproduce the dependence between subsequent trials observed in humans. Indeed, the presence or absence of change in location of the correct target respectively impedes or facilitates the correct response selection, while increasing or decreasing the deviation of the mouse trajectory. The entire model thus guarantees within trials variability (noise), between trials variability (stimuli sequence, congruent/incongruent blocks), between participants variability (random sampling of parameters), and between social groups variability (different means in weight distributions). 19

20 Action selection and mouse movements To control mouse movements on the computer screen, Cartesian coordinates are used in the screen frame of reference. The position (xm) and speed vector (vm) for the mouse pointer are computed at all times as the output of the connectionist model, by combining the activity of the competing sensorimotor nodes (left and right). The system therefore generates smooth trajectories on the screen with semi-realistic dynamics. It is indeed not taking into account the complexity of the motor apparatus, yet demonstrating human-like trajectories. The heavy time constraints of the forced-choice task are introduced for the artificial participants by introducing a speed-up factor between the network outputs and the actual movement (g), while bounding their maximal movement speed to something humanly plausible (15 units/second, with units as defined in the Data preparation section of the Supplemental Material). This process models the gain modulation widespread in the nervous system, especially for controlling limb movement (Salinias & Sejnowski, 2001). In practice, the speed vector vm is a linear combination of vleft and vright, which correspond to normalized speed vectors respectively pointing to the left and right targets on the display, weighted by the evidence accumulated for the left and right nodes (aleft vs. aright), following Eq.1. This computational step collapses the competing hypotheses into a single decision (and thus movement) at all times. v m = g a k v k k (2) with k {left,right} in this task, since we deal with a two forced choice task. The mouse position xm is then simply updated by integrating vm over time, using an Euler scheme with timestep t. This is quite similar to what is found in the Embodied Choice model (Lepora & Pezzulo, 2015) or earlier models of hand control in mouse-tracking task (Quinton et al., 2014), but with a varying speed able to qualitatively reproduce the speed profiles produced by human participants. As the accumulation of evidence is also performed in a stochastic way, this reproduces and extends the random walk behavior observed with the Drift Diffusion Model (DDM) classically used to model human decisions for two-alternative forced choice (Ratcliff & McKoon, 2008). Since the sensorimotor nodes activity is reset for each trial, the absolute speed is initially minimal, increasing when evidence is accumulated for each of the hypotheses. Yet it only reaches its maximal value when a single node (left or right) remains in activity (i.e. when reciprocal inhibition progressively disappears and the winning node activity can be maximized). For a comparison with human 20

21 participants, the set of trajectories produced by 2 artificial participants are reproduced on Fig.7 (with low and high variability as for human subjects). A sequential version of the algorithm for the entire artificial system interacting with the mouse-tracking experimental setup is provided in Algo.1, while the Supplemental Material provide details on how to access and run the original source code. Results Geometric mouse-tracking measures The same analyses as in the experimental study were run on the simulated participants data. Results for the 2(Congruency: congruent, incongruent) 2(Gender: male, female) 2(Academic domain: engineering, humanities) interaction effect was significant for AUC, B = 0.62, t(10453) = 34.06, p <.001, 95% CI [0.59,0.66] (effect size coefficient for the entire model, Ω 2 0 = 0.17). Replicating the human data, the difference in AUC for female humanities students between incongruent (M = 0.24) and congruent trials (M = 0.04) was highly significant, t(10535) = 22.08, p <.001, reflecting strong stereotypical associations. The same pattern was found for male engineering students, (Mincongruent = 0.28, Mcongruent = 0.03, t(10535) = 28.50, p <.001). However, the pattern was reversed for female engineering (Mincongruent = 0.08, Mcongruent = 0.19, t(10535) = 11.78, p <.001) and male humanities students (Mincongruent = 0.09, Mcongruent = 0.15, t(10535) = 6.57, p <.001). These results were not the outcome of a sampling bias, as they were confirmed by both a sensitivity analysis and a Monte-Carlo simulation over the participant s parameter space (see Supplemental Material for details). In the Supplemental Material, AUC results for simulated stereotypical and counter-stereotypical groups are illustrated. Average trajectories for the congruent vs. incongruent trials obtained for all simulated social groups are reproduced on Fig.9. As our goal was to qualitatively replicate the differences at the social group level, but not specifically the results for each individual, we chose to have a high level of noise in the network, and no fine tuning of the network parameters was done. Yet, the parameters in Eq.1 were chosen to allow quick bifurcations and therefore amplify differences between congruent and incongruent trials, for a better interpretability of the results and readability of the figures. Again, a sensitivity analysis was run to assess the influence of social group differences on trajectories and categorization, which is the focus of the current paper, demonstrating the robustness of the effect relatively to the parameter values. 21

22 Dynamic mouse-tracking measures As for humans, x-speed is on average higher for congruent trials when all participants are considered together (see Fig.10a). The effects of opposite gender and domain identification for different and balanced social groups cancel out when considering the entire sample, but the remaining difference reflects that the stereotype still has an effect on all participants. Using mixed-effects models at each timestep, x-speed values were regressed on trial congruency. Due to the non-biased sources of variability of the model, a significant effect appears as soon as t = 10ms, t(10456) = 2.40, B = 0.001, p < 0.05, the maximal difference between the congruent and incongruent trials occurring at t = 480ms, t(10438) = 4.10, B = 0.71, p < Fig.10b and Fig.10c display the qualitative differences between simulated engineering male and female students, with partially reversed dynamics between stereotype congruent and incongruent trials. The fact that the congruent and incongruent profiles are not simply swapped between social groups is essentially due to the effect of the stereotypical associations, which always have a facilitating effect for stereotype-congruent blocks, and thus break the symmetry. As for the empirical study and to study social group differences, we ran a timestep by timestep mixedeffects analysis on x-speed including trial congruency, gender, academic domain, and all interactions between these variables. The 2(Congruency: congruent, incongruent) 2(Gender: male, female) 2(Academic domain: engineering, humanities) interaction effect was significant from 30ms, B = 0.004, t(10453) = 2.00, p <.05. Discussion In addition to the empirical evidence provided by study 1, study 2 gives a computational proof of concept of how the specific patterns for stereotypical and counter-stereotypical groups can emerge, demonstrating how the influence of stereotype congruency can start very early and spread to the whole decision-making process. Consistent with a situated (social) cognition view of implicit stereotypes, the model and results of study 2 speak in favor of a reconceptualization of IAT effects as not solely stemming from dynamical competition at the abstract level (e.g., between female and male, or math and language in the case of gender-math IAT) as is typically assumed in previous models of social categorization but also from competition at the motor level. In other words, IAT effects cannot merely be understood as resulting from competition between abstract categories, but also from competition emerging from the sensorimotor constraints of the task. Indeed, the generation of (simulated) mouse trajectories 22

23 for different social groups on the basis of a computational model integrating motor level into the decision-making process was required. In other words, without both types of competition, no human participants-like trajectories could be generated, suggesting implicit social cognition must be situated. Central in this situated social cognition perspective is the self, and more specifically whether implicit associations both at the abstract and sensorimotor levels are self-congruent or not. In other words, one way to reconceptualize the stereotypical versus counter-stereotypical group distinction a labeling that ultimately reflects the dominant and shared general population viewpoint is in terms of self-congruence. For instance, for STEM women, binding of the female and math categories is self-congruent in the case of this particular IAT task, whereas for female humanities students, binding of female and language categories is more self-congruent in the task. Thus, in a complementary vein of the in-depth MT analyses and computational model developed in studies 1 and 2 as a function of social group membership per se, our rationale in study 3 was to test the relevance of the self-congruency factor at the trial level. Particularly, we aimed at distinguishing between two orthogonal factors: the stereotypecongruency factor and the self-congruency factor. As we assume that the binding between the self and group/domain concepts drives implicit associations, we expect the self-congruency factor to better account for the data than the stereotype-congruency factor. Study 3 In study 3, conducted on human participants, we wanted to test whether the self-congruency factor better accounted for AUC variations than the stereotype-congruency factor. To do so, we adapted the gender-domain IAT to contrast self (in-)congruent bindings with stereotype (in-)congruent bindings. As our previous findings demonstrate that decision making in the case of a classical IAT paradigm involves competition at both the abstract and sensorimotor levels, we adapted the IAT so as to contrast the self-congruency factor with the stereotypecongruency factor on the same screen. Method Participants, materials, and procedure Twenty six engineering (13 female) and 44 humanities (22 female) undergraduates from study 1 accepted to voluntarily take part in the study. They completed a mouse-tracking adapted IAT-like task consisting of 4 blocks. 23

24 Blocks 1 and 3 only comprised single categorizations contrasting the self with the relevant gender group (female category when female participants, and male category when male participants), with each category displayed at the top-left and top-right corners of the screen (order counterbalanced within participants). Blocks 2 and 4 were the critical blocks, corresponding to the double-categorization task, with the self plus domain binding being contrasted with the gender group plus alternative domain binding. These double categories were displayed at the top-left and top-right corners of the screen (order counterbalanced within participants). Category labels and stimulus words for the math-language categories, and the gender group categories were the same as in the previous studies. The self category was labeled Me and stimulus words were adapted from Nosek et al. (2002). Mouse-tracking setup was the same as in study 1, with participants being instructed to click a START button at the bottom center of the screen to start each trial and to categorize each stimulus word by hovering over the chosen category with the computer mouse. During the entire task, x, y coordinates along the mouse trajectory were recorded. The full setup is displayed in Fig.11a. Here one may observe that the me/math binding when contrasted with the female/language binding corresponds to a self-congruent and stereotype-congruent trial for female STEM students, but to a self-incongruent and stereotype-congruent trial for female non-stem students. Results and Discussion Data preparation relied on the same criteria as in study 1. Given the asymmetry between categories of stimuli (Math-Language/domain versus Female-Male/Gender) reported in the Additional analyses section of study 1, and to be consistent with our situated social cognition perspective, we included category of stimuli as a fixed effect in the analytic models. Analyses were performed using two mixed-effects regression models, with AUC values regressed on stereotype-congruence (stereotype-congruence factor, with -0.5 for stereotype-congruent trials and +0.5 for stereotype-incongruent trials), category of stimuli (-0.5 for Math-Language and for Male-Female) and their interaction. The second model included self-congruence (self-congruence factor, with -0.5 for self-congruent trials and +0.5 for self-incongruent trials), category of stimuli, and their interaction. For the first model, only a main effect of category of stimuli was found, which was qualified by the significant interaction effect, B = 0.06, t(7290.6) = 2.53, p <.02, 95% CI [0.01,0.11]. This interaction effect signals that the effect of stereotype-congruence is actually driven by the Female-Male category of stimuli. Regarding the model including the self-congruency factor, results 24

25 showed a main effect of category of stimuli, B = -0.07, t(27.5) = -3.26, p <.03, 95% CI [-0.11,-0.03], signaling larger deviations when Math-Language related stimuli were categorized. A main effect of self-congruence was also found, B = 0.02, t(7276.2) = 1.99, p <.05, 95% CI [0.003, 0.04], signaling smaller deviation when self-congruent stimuli were categorized (as compared to self-incongruent stimuli, see Fig.12). In a complementary vein, as our primary aim was to contrast the effect of the self-congruency factor with that of the stereotype-congruency factor, we performed a comparison of models. This model comparison provided positive evidence against the stereotype-congruence model ( BIC = 4), with a 87% probability that the selfcongruence model minimizes information loss ( AIC = 4). The AIC and BIC criteria were selected due to the common random effect structure and the non-nested nature of the models (Burnham & Anderson, 2004). Putting both congruence factors in a single mixed-effects model analysis did not change the regression coefficients, demonstrating that the factors had no shared variance on AUC, the two factors being uncorrelated (r = -0.02). For consistency reasons, we report in the Supplemental Material this mixed-effects model comparison for study 1, contrasting the same (although adapted to the classical IAT task of study 1) self-congruency and stereotypecongruency factors. Consistent with study 3, this model comparison for study 1 provides very strong evidence against the stereotype-congruence model. It should be noted that reconceptualizing (and reanalyzing) the stereotypical versus counter-stereotypical group distinction in terms of self-congruence does not change parameters of the computational model, as it merely consists in a simplification at the trial level. In addition to the evidence in favor of the self-congruency factor against the stereotype-congruency factor, the present findings show that category of stimuli played an important role in accounting for the variation on AUC. This effect of category of stimuli was already highlighted in the additional analyses of study 1, with Math-Language generating larger deviations. This effect was independent of the effect of the self-congruency factor on AUC. Although not initially the focus of the present research, we nevertheless consider the category of stimuli finding to be relevant for our general situated social cognition approach. We observed this effect in both study 1 and study 3, and will test for its consistency in study 4 as well. To summarize, findings of study 3 support the relevance of the self-congruency factor when contrasted with the stereotype-congruency factor in accounting for participants decision making dynamics in this IAT-like task. 25

26 Specifically, participants deviated less when categorization was congruent with the self than when it was congruent with cultural gender stereotypes. This effect was obtained in a categorization task that actually included the self category, a category that was not directly present in studies 1 or 2. Taken together, studies 1, 2, and 3 suggest that a determining factor underlying the emergence of implicit gender-domain stereotypes is whether associations are (in-)congruent with the self rather than (in-)congruent with cultural stereotypes per se. In study 4, we will again test for the consistency of this self-congruency factor, but under conditions where the category bindings evolve constantly. Indeed, one limitation of the block structure of the classical IAT is that participants may use a recoding process to perform congruent blocks (but not incongruent blocks), a process that reduces the need of in depth processing of each stimulus (Rothermund, Teige-Mocigemba, Gast, & Wentura, 2009). This possible confounding process cannot be ruled out with the classical block structure of the IAT. In the present research, it is important to rule out this possibility to ensure that the effect of self-congruency cannot be accounted for by strategic recoding on the self-congruent blocks, but not on the other blocks. To rule out this alternative, we designed study 4 to test whether self-congruency related findings would be maintained even if task requirements are severely modified for instance by introducing random switches in category binding between trials. This can be done efficiently with the recoding-free IAT (Rothermund et al., 2009), on which congruent and incongruent category bindings are randomly switched between trials, eliminating the classical block structure and the possibility of recoding. Coupling mouse-tracking with a recoding-free IAT may be thought of as a worst-case scenario as it may seriously increase task-completion constraints. The advantage, however, is that if the self-congruency factor still emerges as a relevant factor in explaining AUC variation, this would provide strong evidence in favor of the concomitant competition at the abstract and motor levels during each trial, without the possible confound of strategic/learned task recoding at the block level. Additionally, the introduction of random switches allowed to perform a direct test of the situated social cognition perspective versus the abstractionist perspective by contrasting the gender categories (bound together) with the domain categories (bound together). In this endeavor, we adapted the recoding-free IAT (Rothermund et al., 2009). Half of the trials of this recodingfree gender-domain IAT were the same as the double-categorization trials of the typical IAT of study 1 (but for the 26

27 fact that there was no block structure, but only random switches). The other half of the trials included the same gender and domain categories, but the gender categories were bound together on one side of the computer screen (top-left or top-right) and contrasted with the domain categories, bound on the opposite side. As previously stated, this binding allows a direct test of the situated social cognition perspective versus the abstractionist perspective (e.g., Greenwald et al., 2002): Either participants categorize with relative ease (i.e., smaller deviations) stimulus words when Female-Male is contrasted with Math-Language, or this binding increases deviation. If smaller deviations are observed, findings would be congruent with the assumption that social categorization is also highly dependent on features of the sensorimotor apparatus and experimental design. If, instead, an increase in deviations is observed, this would suggest a fundamental opposition between female and male at the abstract level sufficiently strong to severely impact the mouse trajectories. Study 4 Method Participants Forty seven (32 female) psychology and 29 (15 female) math undergraduates took part in the study in exchange for course credit or monetary compensation. Participants attended the same university but evolved in different departments. Data collection was part of a larger study. Sample sizes were somewhat unequal, as psychology students were more used to take part in laboratory studies than math students. Procedure and materials Participants were tested individually. The present recoding-free gender-domain stereotype IAT shared many features with study 1 classical IAT: Category labels and stimulus words were those previously used (i.e., with male, female, math, and language being again the target categories), double-category bindings were presented at the topleft and top-right corners of the screen for half of the trials, whereas in the other trials, genre categories were contrasted with domain categories (changing the binding logic as compared to the classical IAT doublecategorization blocks). Following the recoding-free IAT principle, the major change was that instead of using the block structure of typical IATs, target categories switch randomly during the task. The advantage is that it jeopardizes within-block recoding or learning processes, hence ensuring that on each trial participants have to focus on and to 27

28 truly categorize each stimulus word. Participants have to determine on which side of the screen the associated target category is, at the trial level, and not block level as in studies 1 to 3. This paradigm, although quite demanding for participants, provides a stringent test of the parallel competition scenario: If the self-congruency factor explains variation in AUC while sensorimotor features of the task are changing all the time, there would be strong support in favor of the central role of the self in the implicit social cognition dynamics at stake here. The inclusion of trials with Female-Male bindings contrasted with Math-Language bindings allows testing the instantiation of trial-dependent opposition based on the position of the categories on the screen. If responses are possible - and even facilitated - with this responses configurations, this would demonstrate the non-fundamental opposition within gender categories (and within domain categories). All target categories configurations that enforced the alignment of the gender category labels (respectively domain category labels) either vertically or horizontally were exploited, with 24 different stimuli for each configuration. The total of 192 trials were then randomized, ensuring that the position of the target category could not be guessed by the participant (the left-right and top-left position of each category being fully balanced across trials). Fig. 12b provides an illustration of the setup. Mouse-tracking setup was the same as in previous studies, with participants being instructed to click a START button at the bottom center of the screen to start each trial and to categorize each stimulus word by hovering over the chosen category with the computer mouse. Results and Discussion Data preparation relied on the same criteria as study 1 (plus seven participants for whom response patterns reflected fatigue or demotivation given the increased difficulty of the recoding-free IAT, as reflected in a sudden and stable increase in error rates for instance). Analyses were performed using two mixed-effects regression models, with AUC values regressed on category of stimuli, type of trial, stereotype congruence, and relevant interactions for the first model, and category of stimuli, type of trial, self-congruence, and relevant interactions for the second model. For the first model, only a main effect of type of trial was found, B = -0.01, t( ) = -1.99, p <.05, 95% CI [-0.02,-0.001], which signals that participants deviated less when the categorization contrasted Female-Male with Math-Language categories, as compared to classical IAT bindings (e.g., Female-Math versus Male-Language). In addition, and although not of primary importance here, the effect of stereotype-congruency approached 28

29 conventional levels of significance, B = 0.02, t( ) = 1.89, p =.06, 95% CI [-0.01, ]. This effect might be related to the fact that in the present study, stereotypical group members (i.e., non-stem women) were overrepresented. Regarding the second model with the self-congruency factor, results showed again a main effect of type of trial, B = -0.01, t( ) = -2.01, p <.05, 95% CI [-0.01,-0.006], signaling larger deviation when Math- Language related stimuli were categorized. A main effect of self-congruence was also found, B = 0.04, t( ) = 2.82, p <.01, 95% CI [0.01, 0.06], signaling smaller deviation when self-congruent stimuli were categorized (as compared to self-incongruent stimuli). This main effect was qualified by an interaction effect, B = -0.07, t( ) = -2.61, p <.01, 95% CI [-0.01, -0.02], signaling that the self-congruence effect was more pronounced for Math- Language stimuli. Using a recoding-free IAT, findings from study 4 speak in favor of a self-congruence reconceptualization in implicit social cognition. This finding is consistent with results from studies 1, 2, and 3, already supporting the central role of the self. Of interest however is the fact that in study 4, this result was obtained while using a recoding-free IAT, which is a task where bindings are switched randomly, hence increasing task-completion constraints. In study 4, unlike study 3, results were obtained without the inclusion of the self category. A further addition of study 4 consisted in contrasting the typical stereotypical versus counter-stereotypical double-categorization task (as in classical IATs) with the gender versus domain categorization task. Findings support a situated social cognition perspective, as categorization was facilitated (i.e., smaller deviations) when gender and domain were contrasted, as compared to the typical stereotypical versus counter-stereotypical double-categorization task. Thus, task-related constraints can override a fundamental opposition posited at the abstract level (i.e., opposition of female and male categories). Meta-analysis of studies 1, 3, and 4 We conducted a small-scale meta-analysis on the human participants studies (Study 1, 3 and 4), with a focus on the main effect of self-congruency on mean AUC values. We used the mean differences in AUC between selfcongruent and self-incongruent trials to compute a standardized mean difference for each study, along with 95% confidence intervals. Positive values for this effect size indicator signal a smaller AUC for self-congruent trials compared to self-incongruent trials. As can be seen on Fig. 13, which displays the corresponding forest plot, the 29

30 overall meta-analytic effect size for the critical self-congruency effect is estimated at Effect sizes for study 1, 3, and 4, were respectively of 1.10, 0.51, and Additionally, none of the confidence intervals included the value of zero. Based on this meta-analysis, we subsequently performed a power study. Results of this power study indicate that all studies performed on human participants had power of near.90 to detect the self-congruency effect. A fuller description of this power study, along with a figure illustrating the power curves is provided in the Supplemental Material. Together, results of the meta-analysis and the power study suggest that, when using the mouse-tracking methodology, the self-congruency effect is a rather robust, non-trivial effect, and that none of the present studies is underpowered. General discussion In the present research, we relied on different methodologies - empirical studies and computational modeling - to investigate social group-related specificities pertaining to implicit gender-domain stereotypes, as measured by a mouse-tracking adapted IAT(-like) implicit measure. Adopting a situated social cognition perspective, we aimed at testing whether, rather than social group differences per se, a determining factor underlying the emergence of implicit gender-domain stereotypes was whether associations were congruent with the self or not. If so, this would imply that binding between the self and group/domain concepts is a factor that continuously influences decision making processes in IAT(-like) tasks. Our second and related aim was to test whether part of the variance on the types of implicit social cognition measures used in the present research could be accounted for by visuospatial features of the task and subsequent competition at the motor level, variance that cannot be accounted for by competition at the abstract level alone. If confirmed, our findings would complement existing models of implicit social cognition (e.g., Freeman & Ambady, 2011a; Greenwald et al., 2002) that place competition at the abstract level only, and speak in favor of a (strong) situated social cognition perspective on implicitly measured, implicit stereotypical associations. Findings of four studies support the assumption that, in a given situation, the decision dynamics underlying the completion of mouse-tracking adapted IAT(-like) tasks encompass not only what the individual is in the situation and what he/she has learned through socialization, but also the very features of the sensorimotor apparatus and experimental design. 30

31 In studies 1 and 2, we relied on a mouse-tracking adapted IAT to investigate the dynamical processes underlying implicit gender-math associations among stereotypical and counter-stereotypical social groups, in both human and simulated artificial participants. We expected competition - at both the abstract and motor levels, that is, a dual conflict typically conceptualized at the abstract level only in social cognition - between self-congruent trials and selfincongruent trials. In accordance with expectations, results from study 1 showed specificities at a very fine-grained implicit level between stereotypical and counter-stereotypical groups. Counter-stereotypical groups displayed straighter trajectories for incongruent trials (those congruent with the self), whereas the reverse pattern was observed for stereotypical group members, with deviations being smaller for congruent trials (those congruent with the self). In study 2, to generate (simulated) mouse trajectories for different social groups on the basis of the computational model, the motor level had to be integrated into the decision-making process. Of importance, without abstract-level and motor-level competition, no human participants-like trajectories could be generated, suggesting implicit social cognition must be situated. Consistent effects were observed in both human and simulated data, and were particularly salient in the latter, since the computational model only accounted for theorized differences and sources of variability (which was done in order to maximize the explanatory power of the model while keeping it minimalistic). The advantage of computational modeling here is that it permits testing mechanistic hypotheses on the underlying decision-making processes for the specific groups of participants that were the focus here. In particular, the fact that main results were correctly simulated signals the importance of integrating motor actions into decision making to generate the required dynamical outputs. This aspect was absent from previous connectionist models on social categorization (Freeman & Ambady, 2011a; Greenwald et al., 2002). The use of a combined empirical and computational approach enabled to account for social group differences in implicit associations at least for the specific groups under investigation - as observed in human data and explained by the central role of the self in the computational model, and confirmed in our subsequent studies. Indeed, study 3 supports the relevance of the selfcongruency factor when contrasted with the stereotype-congruency factor in accounting for participants decision making dynamics in an IAT-like task. Specifically, participants deviated less when categorization was congruent with 31

32 the self than when it was congruent with cultural gender stereotypes. This effect was obtained in a categorization task that actually included the self category, a category that was not directly present in studies 1 or 2. Consistent with the self-congruency hypothesis, studies 1, 2, and 3 consistently suggest that a determining factor underlying the emergence of implicit gender-domain stereotypes is whether associations are (in-)congruent with the self rather than (in-)congruent with cultural stereotypes per se. Study 4 confirmed these findings and provided even further, complementary evidence in favor of a situated social cognition perspective: Social categorization was facilitated (i.e., smaller deviations) when gender and domain were contrasted, as compared to when stereotypical versus counter-stereotypical bindings were contrasted. This suggests that task-related constraints can at least override a fundamental opposition posited at the abstract level (i.e., opposition of female and male categories). It also suggests that the time may be ripe to reconsider some elements of Unified Theory. Although not initially the focus of the present research, in addition to the evidence in favor of the self-congruency factor, findings show a consistent effect of category of stimuli throughout the human participant studies: Larger deviations were observed when domain-related stimuli were categorized, as compared to gender-related stimuli. We consider this non-hypothesized (though consistent) finding to be relevant for our general situated social cognition approach, as it suggests that yet another part of the context - different types of categories and related stimuli - generate more or less competition at the abstract and motor levels. It also suggests, at the analytical level, the importance of including this factor in the models. As we relied on linguistic stimuli only, it must be highlighted that the observed effect may not generalize to other types of stimuli (e.g., pictures). Future research may explore this generalizability issue, along with a thorough understanding of the observed asymmetry, so as to not consider this stimulus-related variability as contextual noise (e.g., Smith & Semin, 2007), but as a cognitive process worth indepth investigation. To summarize, findings are consistent with previous gender-domain IAT studies (Nosek & Smyth, 2011; Smeding, 2012; Stout et al., 2011), while offering evidence in favor of a situated social cognition rather than an abstractionist perspective per se. Supporting the relevance of the mouse-tracking measure and the associated modeling, the present findings demonstrate that the influence of congruency starts very early and spreads to the whole decisionmaking process, albeit not in the same direction for all social groups. Regarding computational modeling, using a 32

33 few conceptual nodes, context dependent binding, and competition dynamics, we were able to qualitatively replicate the complex trajectories produced by humans. Furthermore, the hypothesized construction of (counter- )stereotypical associations via the self and its effect on decision dynamics for the different social groups has been rigorously reproduced using a minimal connectionist model. As demonstrated by the human data and the computational study, associations with the self and specifically their self-congruent versus self-incongruent modalities - have the potential to override stereotypical associations, in spite of continuous reinforcement of stereotypes through culture and throughout the life of individuals. The pattern for counter-stereotypical individuals suggests the construction of self-domain associations through socialization, and sets the stages for a longitudinal examination of these processes. Consistent with a situated cognition view of social representations such as stereotypes, IAT effects cannot merely be understood as resulting from competition between abstract categories, but also from competition emerging from the sensorimotor constraints of the task. Limitations Would results have been the same if we had conducted the present series of studies among other counterstereotypical or stereotypical social groups (e.g., academically successful African-American students, unsuccessful Asian-American students)? Our studies being focused, at the participant level, on female and male STEM and humanities students, and at the task level on domain and gender categories, generalizability of our findings to other social groups and categories remains an open question. Indeed, some may suggest that there are reasons to believe that our female STEM participants have a particular personal and academic history that uniquely accounts for the present findings, raising the possibility that the relevance of the self-congruency factor is restricted to this social group. Although our research cannot directly address this issue, there are reasons to suspect that our findings are not restricted to some peculiarities of female STEM students and may be relevant more broadly. First, as far as our empirical data are concerned, when focusing on intergroup differences, male humanities students displayed a very similar pattern to that of female STEM students, and for the same reasons. Building on this, it may sound reasonable to expect some similar processes to be at play among counter-stereotypical social groups in the academic realm. Second, it is important to remember that, reflecting general knowledge of cultural stereotypes, it is hypothesized 33

34 (and consistently implemented in the computational model) that all social groups have identical stereotype knowledge. The only differences were those related to the strengths of associations between self and gender, as well as between self and domains. Neither our human or artificial participants are thus assumed to evolve in a social and cultural vacuum. It is assumed, however, that social representations related to gender and domains here under investigation, in the present context, with the specific groups of participants, are dynamically driven by selfcongruency. Third, all hypotheses and computational model parameters were derived from sound and complementary theoretical approaches. Therefore, maybe one way to look at the present findings is to consider them being a proof of concept: Although they cannot directly address the generalizability issue, they indicate that the present findings and underlying processes are possible under the defined conditions. As a consequence, it may be important for implicit social cognition research to consider - and subsequently test - under what (other) defined conditions the self-congruency hypothesis holds. Conclusion Although central from a situated cognition perspective, the conception of social cognition as concomitant, dynamic, integration of high-level abstract and low-level sensorimotor processes has yet to be fully explored. The present research aims at contributing to this endeavor. It is of importance for social categorization and social cognition research more broadly as findings demonstrate that performance on classical implicit social cognition tasks (i.e., IAT-like, mouse-tracking adapted tasks) cannot fully be conceptualized by only positing competition between concepts at the abstract level. As is particularly evident in the computational study, this competition alone lacks flexibility as it does not take into account the immediate contextual features of the task. Consequently, to fully understand participants behavior when performing (implicit) social categorization tasks, particularly (but not only) when using a mouse-tracking device, it seems urgent to conceptualize competition both at the conceptual and motor levels. It is only under this condition that more abstract models from social psychology (Freeman & Ambady, 2011a; Greenwald et al., 2002) will be compatible with models of the sensorimotor aspects of mouse-tracking tasks (Lepora & Pezzulo, 2015; Quinton et al., 2014), hence allowing a more complete and situated understanding of human (social) cognition. 34

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39 Table 1: Hypothetized congruency (+) and incongruency ( ) of IAT associations (rows) for different social groups (columns), based on stereotypicality (outside parentheses) and self-congruency (inside parentheses) (derived from Greenwald et al., 2002) Engineering Humanities Math-male +(++) Math-female (++) Language-male (++) Language-female (++) M ath Female incongruent trials Language Male Uncle congruent trials START Figure 1: Setup used in both experimental and computational studies. After clicking on the START button, a word stimulus is presented centrally. The task consists in categorizing it as fast as possible by pointing on the top-left or top-right targets (here with counter-stereotypical associations). Measuring mouse kinematics permits to unfold the decision in time and space, as illustrated here by trajectories generated for congruent and incongruent trials (with an amplified effect). 39

40 Mean Area Under the Curve (AUC) TRACKING AND SIMULATING DYNAMICS IN SOCIAL COGNITION Stereotype-congruent trials Stereotype-incongruent trials 0 Engineering male Engineering female Humanities male Humanities female Figure 2: Mean Area Under the Curve (AUC) as a function of congruency and social group (human participants data from study 1). Incongruent trials Incongruent trials Incongruent trials Incongruent trials Congruent trials Congruent trials Congruent trials Congruent trials (a) Female engineering students (b) Male engineering students (c) Female humanities students (d) Male humanities students Figure 3: Average mouse trajectories for congruent and incongruent trials for each social group separately (human participants data). 40

41 Figure 4: Set of trajectories produced for all congruent vs. incongruent trials by two human participants from the study (differing on trajectory variability). Significant bifurcation Congruent trials Incongruent trials Time (ms) (a) X-speed profiles for all participants Congruent trials Incongruent trials Time (ms) (b) X-speed profiles for male engineering students Congruent trials Incongruent trials Tmin Vmin Time (ms) (c) X-speed profiles for female engineering students Figure 5: X-speed profiles for all human participants, as well as for male and female engineering students separately. Vmin corresponds to the x- speed minimum value, at corresponding time Tmin. The profiles illustrate partially reversed dynamics between stereotype congruent and incongruent trials, along with a stronger initial attraction toward the counter-stereotypical answer for stereotype congruent trials for female engineering students only. 41

42 Time (ms) Figure 6: Graphical representation of the bifurcation dynamics of the trajectories for all participants taken together. Upper graph represents, for each timestep, the x-speed difference between congruent and incongruent trials (B regression parameter, black line) and associated standard errors (shaded surfaces). Lower graph shows the p-values obtained from the regression analysis performed at each timestep. The positive bump between 250 and 400ms is significant for counter-stereotypical groups, but is here attenuated by the stereotypical participants who do not display a similar pattern. Figure 7: Set of trajectories produced for all congruent vs. incongruent trials by two simulated participants from the computational study (differing on trajectory variability). 42