Self-beneficial belief updating as a coping mechanism for stress-induced negative affect

Being confronted with social-evaluative stress elicits a physiological and a psychological stress response. This calls for regulatory processes to manage negative affect and maintain self-related optimistic beliefs. The aim of the current study was to investigate the affect-regulating potential of self-related updating of ability beliefs after exposure to social-evaluative stress, in comparison to non-social physical stress or no stress. We assessed self-related belief updating using trial-by-trial performance feedback and described the updating behavior in a mechanistic way using computational modeling. We found that social-evaluative stress was accompanied by an increase in cortisol and negative affect which was related to a positive shift in self-related belief updating. This self-beneficial belief updating, which was absent after physical stress or control, was associated with a better recovery from stress-induced negative affect. This indicates that enhanced integration of positive self-related feedback can act as a coping strategy to deal with social-evaluative stress.


Results
After exposure to social-evaluative stress (SOC, Trier Social Stress Test), non-social, physical stress (PHY, Cold Pressor Test) or a no stress control condition (CON, reading) participants performed the LOOP task 21 , which was covered as a measure of cognitive estimation skills (see Fig. 1). The central idea of the LOOP task is to create a performance context and provide manipulated positive or negative feedback in comparatively neutral domains in which people have only vague prior assumptions. By this means, individuals form a concept about their own abilities over the course of the experiment. In a previous study, we showed that this process of self-related belief updating can be described best by a computational prediction error learning model (adapted from Rescorla and Wagner 58 ) with two separate learning parameters for positive and negative prediction errors 21 . During the LOOP task, participants were asked to answer estimation questions in two different estimation domains (e.g. estimating the weight of animals and the height of buildings) and received manipulated performance feedback implying a rather good performance in one category and a rather bad performance in the other one (high vs. low ability condition). In the beginning of each trial participants saw a cue indicating the estimation category and had to rate their expected performance for the upcoming estimation question in this category. A manipulated feedback on their estimation performance in relation to an alleged reference group was presented afterwards. Saliva cortisol as well as negative affect, including perceived stress, embarrassment, anger, and frustration, were assessed several times during the experiment. Pre-stress baseline measures (T1 AFF/CORT ) were taken after a 10-min-period of rest in the beginning of the session. Post-stress negative affect was rated immediately after the stress exposure or control task (T2 AFF ) to calculate the mean change of negative affect (ΔAFF). Post-stress cortisol samples were taken after another 10-min period of rest (T2 CORT ) to calculate the mean cortisol change (ΔCORT). After performing the LOOP task, saliva samples and negative affect were again obtained (T3 AFF/CORT , for a detailed description see methods).
Cortisol response and negative affect. Cortisol change. The stress manipulation was effective and social-evaluative stress, as well as physical stress, led to a stronger increases of cortisol levels from baseline T1 CORT to post-stress T2 CORT Table S1). There was no statistically significant difference between the two stress groups (SOC vs. PHY: z = 1.56, p = 0.355; baseline cortisol levels did not significantly differ between groups H 2 = 1.74, p = 0.419 controlled for TIME, see Forming self-related beliefs over time. In a model free behavior analysis we replicated previous findings regarding the LOOP task which indicates self-related belief updating in response to the feedback 21 . Over the time of 30 trials, participants adapted their performance expectation ratings (EXP) towards the positive and negative feedback of the two ability conditions, i.e. they updated their self-related beliefs (Fig. 3c Fig. 3b; protected exceedance probability for the whole sample pxp total > 0.999, Bayesian omnibus risk BOR total < 0.001 as well as separately for the three groups pxp SOC = 0.985, BOR SOC = 0.019, pxp PHY > 0.999 , BOR PHY < 0.001, pxp Control > 0.999 , BOR Controll < 0.001; see Table 1 and Supplementary Table S3 for more details on model comparisons). This model, with two separate learning rates for positive PEs (α PE+ ) and negative PEs (α PE-) across ability conditions, assumes that learning differs depending on the valence of prediction errors. Learning parameters from the Valence Model were used for further analysis.
The modeled performance expectations of our winning model predicted the performance expectation ratings on the individual subject level within each ability condition with R 2 = 0.33 ± 0.24 (M ± SD). Repeating the model  To better capture biased learning behavior, a valence bias score was computed (valence bias score = (α PE+α PE− )/(α PE+ + α PE− )) 21,61,62 , which represents updating after positive compared to negative prediction errors. More positive valence bias scores indicate more self-beneficial belief updating, while negative valence bias scores speak for stronger self-related belief updating after negative feedback.
Negative affect and cortisol change predict subsequent self-beneficial belief updating. To further assess which aspect of the stress response is associated with self-beneficial belief updating, we correlated negative affect and cortisol with the valence bias scores across all three experimental groups. While both stress groups (SOC and PHY) only differ significantly in terms of an increase in negative affect but not cortisol levels, both measures indicates that a bias towards increased updating in response to negative prediction errors (α PE-) in contrast to positive prediction errors (α PE+ ) is absent in the social-evaluative stress group. (d) Rank-based regression plot of valence bias score predicting the recovery from negative affect (REC, ratings T2 AFF − T3 AFF ) in the subsample of the social-evaluative stress group (n = 29) controlled for the stress-induced change in negative affect (ΔAFF, ratings T2 AFF − T1 AFF ), i.e., residuals of the valence bias score and the recovery predicted by ΔAFF are plotted. More self-beneficial belief updating (higher valence bias score) is associated with a better recovery from stressinduced negative affect. www.nature.com/scientificreports/ show large variance within and across groups (see Fig. 2) that could explain differences in self-related belief updating that is only partially captured by the group effect. We found that a stronger increase in negative affect (ΔAFF = T2 AFF − T1 AFF ) predicted more self-beneficial belief updating (b ΔAFF = 0.100, t 86 = 2.066, p = 0.042, rank regression 63 of the valence bias score predicted by ΔAFF for the whole sample). Also, a higher increase in cortisol levels (ΔCORT = T2 CORT − T1 CORT ) predicted more self-beneficial belief updating (b ΔCORT = 0.020, t 85 = 2.377, p = 0.020, rank regression 63 controlled for TIME for the whole sample, for further information see Supplementary Results and Supplementary Table S6).
Learning bias and affective recovery. A more positive valence bias score predicted better recovery from stressinduced negative affect during learning in the social-evaluative stress group, the only group with significantly increased levels of negative affect after stress ( Fig Table S7).

Discussion
After being devalued for example at work or school we need to empower ourselves in order to uphold or boost our self-image. Research has shown that the ability to adopt a positive attitude towards oneself after receiving criticism is central to positive affect and good mental health outcomes in the long run 11,53,64 . In the current study we investigated how people apply self-beneficial belief updating during a performance feedback situation as a means to counter their negative affect. Using computational modelling, we provide a mechanistic explanation on how individuals engage in more self-beneficial updating of ability beliefs after experiencing a threat to their social image and how this shift in social learning of self-related information predicts recovery from stress-induced negative affect. The positive shift of self-related updating of ability beliefs after social-evaluative stress, going along with a better recovery from negative affect, fits nicely to the notion of a belief 's own value as recently posited by Bromberg-Martin and Sharot 15 . In their revised framework, general belief updating is not solely driven by external outcomes like rewards or punishments but also by the agent's motivation to optimize internal states like positive affect 15,65 . In the present study we show this direct link between self-related belief updating and a change in the affective state indicating that self-related belief updating might be motivated by the wish to uphold or even recover a positive affective state. This is in line with the idea of motivated cognition, i.e. the assumption that cognitive processes like attention, information processing and decision making are not neutral on their own, but are always shaped by needs, feelings and desires of the individual 66 . Especially when processing information that challenges one's self-image, self-related belief updating is not only informed by the history of previous feedback, as it has often been assumed in classical reinforcement learning tasks, but also by various self-relevant needs and goals 67 . Transferred to the present study, this implies that the motivation to restore an endangered self-image and to regulate one's affect back to a set point directly impacts self-related information processing. The pattern of an active counter-regulation of negative affect by self-beneficial belief updating can be described as a striving for homeostasis 11 . To better capture the fluctuation of the affective state and its involvement in the trial-by-trial self-related belief updating loop, following the framework by Bromberg-Martin and Sharot 15 , future studies should consider repeated assessments of affective states during the task to predict the empowering potential of shifts in learning on the single trial level.  www.nature.com/scientificreports/ Since negative self-related beliefs are at the core of psychiatric conditions like depression 54 , this study targets clinically highly relevant processes. Depression is associated with seeking negative feedback which confirms negative self-related beliefs 68 and seeking negative feedback in combination with a stressful life event can further increase depressive symptoms 69 . Furthermore, depression is associated with a weaker stress recovery mediated by an attentional bias towards negative feedback. Understanding the mechanisms of how people form self-related beliefs in a context mimicking everyday performance settings and linking these to the regulation of negative affect after stress has important implications for understanding the etiology of depressive symptoms. The present study set-up, including a social-evaluative stress induction followed by a social-evaluative performance situation also addresses one of the fundamental fears of individuals with social anxiety: being devalued by others. Since both depression and social anxiety are associated with negatively biased updating behavior in response to self-related feedback 12,21,55,70 , we assume that the affect-regulating and empowering potential of self-beneficial belief updating after social-evaluative stress would be less pronounced in depression or social anxiety and would thereby possibly exacerbate the symptomatology in a self-fulfilling way. Future studies with similar experimental set-ups and clinical samples could examine the relationship between self-beneficial belief updating and affect regulation in more detail and develop potential intervention strategies based on empowering individuals on their way to processing newly incoming information.
Replicating a previous study of ours 21 , self-related belief updating was negatively biased in the control condition in which participants were not exposed to any stress. In the prior study, this negativity bias has been shown to be specific for self-related belief updating in comparison to belief updating about another person 21 . In the present study, we found that after physical stress participants also exhibited a negativity bias in forming self-related beliefs, i.e. participants tended to make greater updates in response to negative prediction errors in contrast to positive prediction errors. The negativity bias stands in contrast to other studies reporting a positivity or optimism bias in feedback-based learning e.g. when receiving feedback about the chance to encounter negative life events 20,71 , about one's intelligence 17 or about one's personality 18,19 (for a review see 16 ). There are several possible explanations for the motivation behind the negativity bias in context of the LOOP task in contrast to the reported positivity biases of other studies which was, however, not the focus of the present study (for a discussion on the negativity bias see 21 ). In order to test for the specificity of self-beneficial belief updating after social-evaluative stress, it would be interesting to test if this effect also accounts for experiments that typically yield a positivity bias (e.g. for life events, IQ or personality) in feedback-based learning tasks.
Here, we demonstrated that both, negative affect and cortisol stress responses, go along with a shift in selfrelated belief updating. It has been shown before that experiencing social emotions (e.g. embarrassment or shame) is related to increased cortisol levels in situations which threaten one's social image, like the socialevaluative stress induction 6 . Cortisol has been linked to reward processing and feedback-based learning in the stress triggers additional reward salience-STARS-model which proposes that stress and the associated release of cortisol modulates the dopamine system, resulting in an increased salience of rewards, thus biasing learning towards rewarding feedback 43,72 . The current results, however, suggest that the quality of stress (here, social vs. physical) might make a difference, and the STARS model, based on a rather unspecifically triggered cortisol response, cannot fully explain the present stress effect on self-related belief updating after social but not physical stress.
Although both groups showed a significantly greater increase in cortisol compared to control, this effect was less pronounced in the physical stress group. While the Cold Pressor Test is known to elicit a strong sympathetic activity, studies reported only low to moderate cortisol effects 73 , that were weaker than after the Trier Social Stress Test 74,75 . Our alteration of the Cold Pressor Test, to remove the social element of the conductor, might have even further reduced stress effects as compared to the original Cold Pressor Test protocol. We did find an association of the negative affect response (i.e. self-evaluative emotions like embarrassment), which is typically specific for social-evaluative stress and rather absent during physical stress, with shifts in learning behavior in our study. But also cortisol as a rather unspecific stress component was associated with shifts in learning behavior. Thus, we cannot rule out that a more intense physical stress protocol with higher cortisol responses would have led to similar effects on learning rates. A more detailed recording of negative affect and a comparison between different negative affective states as well as more detailed recording of the physiological stress response might help in future studies to better differentiate between different stress qualities and understand specific effects of social-evaluative stress on self-beneficial belief updating.
To summarize, our results indicate a shift towards more self-beneficial belief updating after social-evaluative but not physical stress. This shift goes along with a better recovery from stress-induced negative affect. Linking self-related belief updating to affect is an important step in understanding biases in self-related learning and its relation to affect regulation. The special feature of the present study was the study-set that allowed to examine a link between negative affect and self-related belief updating. By introducing a performance context with consecutive self-related feedback, corresponding to real-life school or work-related performance situations, individuals can form beliefs about their own abilities over time and potentially use this formation process as a means to regulate their affect. With this approach we aimed to increase the ecological validity of the study in order to trigger and investigate motivational processes that might be less relevant in more abstract study settings. Since social evaluation represents a constant stressor in every-day life, the question of an appropriate coping strategy to regulate negative affect is of great importance when handling everyday social situations.

Materials and methods
Participants. Eighty . From the initially recruited N = 96 subjects, seven had to be excluded-five because they did not believe the cover story and two due to technical problems. All included participants were fluent in German, non-smokers with a body-mass index between 18.5 and 30. They were not diagnosed with acute or chronic psychiatric conditions or diseases affecting the hormone system and did not take psychiatric drugs or medication affecting the hormone system (except hormonal contraceptives). Participants had normal or corrected-to-normal vision and did not study psychology to avoid previous experience with experiments using cover stories. Additional exclusion criteria for participants who underwent the physical stress protocol were cardiovascular diseases, frequent fainting or seizures and current hand injuries. For more details on the sample characteristics see Supplementary Table S9a. All participants gave written informed consent prior to the participation and received monetary compensation for their participation. They were naive to the background of the study during the session and debriefed about the cover story afterwards. The study was conducted in compliance with the ethical guidelines of the American Psychological Association (APA) and was approved by the ethics committee of the University of Lübeck.
Manipulation procedure. Social-evaluative stress. Social-evaluative stress was induced by a public speech similarly to the Trier Social Stress Test 3 . Participants were instructed to prepare a short self-presentation for an application for a scholarship, which had to be presented in front of a selection committee who would allegedly assess the participant's verbal skills and body language. The selection committee consisted of the experimenter, who was passive during the speech, a second experimenter, who was allegedly responsible for measuring verbal skills, and a passive camera assistant, who pretended to videotape the speech. Before starting the 10-min preparation period, participants briefly visited the room with the selection committee. After the preparation time was over, participants were asked to come back to this room and present their speech. Talking time was 5 min (M = 4.9 min, SD = 0.16) with a minimum of 3 min of uninterrupted speech. If the participant finished the speech before the time was over, the second experimenter waited for at least 15 s with a motionless face and then asked the participant to continue. If the participant stopped speaking again and the 3 min of free speech had passed, the second experimenter asked standardized questions until the 5 min of talking time were over ("Explain why it is important for you to achieve a good performance. ", "Do you think it is important to improve yourself throughout your life?", "Do you consider yourself a person who values his/her independence?"). Average social-evaluative stress duration (start subsequent rest period − start speech preparation) was M = 16.4 min, SD = 1.2.
Physical stress. Physical stress was induced by an exposure to ice water according to the Cold Pressor Test protocol 57,76 . Participants were asked to dip their non-dominant hand in cold water (water tempera- . The water was kept in motion with a small electrical pump to prevent the water temperature from rising around the participant's hand. To control for the procedure of the social-evaluative stress condition, participants visited the room with the cold pressor apparatus first, had a 10-min preparation period and came back into the room for the stress exposure. During the preparation time, participants were asked to imagine dipping their hands in a freezing cold environment and write down their associations. To make the stress exposure less social, the experimenter was not present in the room but waited in an adjacent room. If the participant took out their hand before the 3 min were over, they had to signal this immediately by ringing a bell. The experimenter could roughly observe the participant in the reflection of the glass door, thus ensuring that she/he dipped the hand into the water. Average physical stress duration (including preparation period) was M = 16.2 min, SD = 1.5.
No stress control condition. In the control condition, participants performed a reading task that was described to them as measuring reading speed. They had 10 min to rehearse two different texts about applying for a scholarship. Afterwards, they were guided to the other room with nobody present and were asked to measure their reading time, while reading the two texts aloud at a natural speed. Average control duration was M = 15.3 min, SD = 1.3.

Manipulation checks.
Cortisol. Three saliva samples were collected during the experiment for cortisol analysis (see Fig. 1a). The first sample (baseline T1 CORT ) was taken after a 10 min period of rest immediately before starting the instruction for the stress manipulation (mean time between T1 CORT and start of the SOC, PHY or CON preparation phase: M = 3.7 min, SD = 1.4). The post-stress cortisol sample T2 CORT was collected after another 10 min resting period following the stress manipulation and the last sample (T3 CORT ) was collected after the learning task (M = 45.6 min (SD = 3.3) post stress). The stress-induced cortisol change (ΔCORT) was determined by subtracting the cortisol levels of T2 CORT − T1 CORT . Saliva was collected with Salivettes (Sarstedt, Nümbrecht, Germany), stored at − 30 °C and sent to the bio-psychological lab at TU Dresden, Dresden, Germany for analysis (here stored at − 20 °C until analysis). Salivary free cortisol levels were determined using a chemoluminescence immunoassay (IBL International, Hamburg, Germany).
Negative affect. We assessed negative affect by means of a short pen and paper questionnaire, covering the emotions embarrassment, anger, frustration, as well as the perceived stress with one rating each. The questionnaires were handed out at baseline (T1 AFF ) as well as at the very end of the experiment (T3 AFF ). The post-stress negative affect was measured immediately after the stress manipulation (T2 AFF ; see Fig. 1). Ratings were averaged for each measurement point to get a composite measure of negative affect (see Supplementary Fig. S1  www.nature.com/scientificreports/ scores). The change in negative affect after stress (ΔAFF) was determined by subtracting T1 negative affect from T2 (T2 AFF − T1 AFF ). The recovery from negative affect (REC) was determined by subtracting T3 negative affect from T2 (T2 AFF − T3 AFF ).
Behavioral task. Learning of own performance task. The Learning of own performance (LOOP) task 21 ( Fig. 1b) allows to measure self-related belief updating through trial-by-trial performance expectation ratings and subsequent performance feedback. The task included estimation questions in two different estimation categories (heights of houses and weights of animals) and was presented to the participants as a measure of estimation abilities. To make participants learn about their estimation ability the two estimation categories were paired with manipulated performance feedback implying high ability for one category and low ability for the other (e.g. heights of houses = high ability and weights of animals = low ability, estimation categories were counterbalanced between ability conditions). The assignment of the categories to the ability conditions was independent of the participants' actual performance and their performance expectation ratings. Thus, participants could learn over the course of the experiment that they were good in one estimation category and rather bad in the other one. Each trial began with a cue displaying the category of the next estimation question followed by a performance expectation rating for this question. Afterwards, the estimation question was presented together with a picture for 10 s. Continuous response scales below the pictures determined a range of plausible answers for each question, and participants indicated their responses by navigating a pointer on the response scale with a computer mouse. Subsequently, feedback indicating the estimation accuracy as percentiles compared to an alleged reference group of 350 university students was presented for 5 s (e.g. "You are better than 72% of the reference participants. "). The order of the two estimation categories/ability conditions was intermixed with a maximum of two consecutive trials of the same condition and 30 trials per condition in total. The estimation questions were randomized within the estimation category/ability conditions. A fixed sequence of ability conditions and feedback was presented for all participants. In the low ability condition, feedback was approximately normally distributed around the 35th percentile (SD ≈ 16; range 1-60%) and in the high ability condition around the 65th percentile (SD ≈ 16; range 40-99%). The task started with detailed instructions and three test trials. All stimuli were presented using MATLAB Release 2015b (The MathWorks, Inc.) and the Psychophysics Toolbox 77 .
Procedure. To minimize noise in the cortisol saliva samples, participants were asked to follow behavioral rules prior to the experimental session. These were in detail: no alcohol on the evening before the experiment and bed rest at about 10 p.m. (ideal case eight hours of sleep); one hour before the session: no sport, no smoking, no drinks containing caffeine or theine, no food (including bonbons and chewing gums) and no juices. Upon arrival at the laboratory, participants read the participant information including the cover story regarding the stress manipulation and the LOOP task. After signing the consent form, they were asked to fill out a questionnaire checking the adherence to the behavioral rules. Participants rested for 10 min before the baseline measurement, including saliva cortisol and negative affect, was obtained (T1 AFF/CORT ). During the resting period, they filled out a short personality questionnaire (not included in this study). Subsequently, participants of the social and physical stress groups were challenged with a stress protocol while participants of the control group did the control reading task. Directly afterwards, participants rated their affective state (T2 AFF ) followed by another 10 min resting period, which was terminated with a saliva sampling (T2 CORT ). In the second part of the experiment participants performed the LOOP task. Finally, another cortisol sample and affective ratings were collected (T3 AFF/CORT ). After completing a post-experimental interview, including additional questionnaires, participants were debriefed about the cover story. The experimental sessions were run between 10.00 a.m.-12.00 p.m., 1.00-3.00 p.m. or 3.45-5.45 p.m. The allocation to the time slots did not differ between the experimental groups (Pearson's Chi-squared test p = 0.867, see Supplementary Table S9b). See Fig. 1a for a graphical illustration of the procedure.

Statistical analysis. Stress manipulation.
To test whether the stress manipulation was effective, the stressinduced changes in cortisol as well as affect were compared between the three experimental groups. Due to the stress manipulation, the variance of the cortisol and negative affect responses were unequal between the three experimental groups (Levene test ps < 0.05). Since the distributions of the cortisol and affective stress response were skewed in some groups (Lilliefors-corrected Kolmogorov-Smirnov normality test ps < 0.05 for the cortisol change in the control group and for the change in negative affect in all groups) non-parametric tests were used. Since cortisol levels are known to underlie circadian fluctuations 78  www.nature.com/scientificreports/ models of the model space with one or two learning rates modeled separately for each participant (see Fig. 3a). The first model (Unity Model) included a single learning rate for the whole time course (EXP t+1 = EXP t + α Uni PE t ).
The second model (Ability Model) contained two separate learning rates for the two ability conditions allowing to capture a difference in expectation updating when receiving feedback in a high ability context (α High ability ) or low ability context (α Low ability ). The third model (Valence Model) with two separate learning rates for positive PEs (α PE+ ) and negative PEs (α PE-) across ability conditions allows to model learning that differs depending on the valence of prediction errors rather than different ability conditions. The three models were compared to a Mean Model with two performance expectations means reflecting the assumption of stable expectations for each ability condition without learning over time. In addition to the learning rates, we fitted two parameters for the initial belief about the participant's performance, separately for both ability conditions (see Table 1).
Model fitting. For model fitting we used the RStan package 79 , which uses Markov chain Monte Carlo (MCMC) sampling algorithms. All learning models of the model space were fitted separately for each subject. To sample posterior parameter distributions, a total of 2400 samples were drawn after 1000 burn-in samples (overall 3400 samples; thinned with a factor of 3) in three MCMC chains. Convergence of the MCMC chains to the target distributions was assessed by R values 80 for all model parameters. One subject was excluded due to implausible model parameters, i.e. mean learning rate of almost 1, as well as R values of 1.1 and low effective sample sizes (n eff , estimates of the effective number of independent draws from the posterior distribution) for some model parameters of the valence model. Otherwise the effective sample sizes were greater than 1000 (> 1400 for most parameters). Posterior distributions for all parameters for each of the participants were summarized by their mean resulting in a single parameter value per subject that we used to calculate group statistics.
Bayesian model selection and family inference. To select the model that describes the participants' updating behavior best, we estimated pointwise out-of-sample prediction accuracy for all fitted models separately for each participant by approximating leave-one-out cross-validation (LOO) 60 . To this end, we applied Pareto-smoothed importance sampling (PSIS) using the log-likelihood calculated from the posterior simulations of the parameter values as implemented by Vehtari et al. 60 (loo R package 81 ). Sum PSIS-LOO scores for each model as well as information about k values, the estimated shape parameters of the generalized Pareto distribution, indicating the reliability of the PSIS-LOO estimate, are depicted in Table 1. As summarized in Table 1 very few trials resulted in insufficient parameter values for k and thus potentially unreliable PSIS-LOO scores (on average 0.20% of trials per subject with k > 0.7). Bayesian model selection on PSIS-LOO scores was performed on the group level accounting for group heterogeneity as described by Stephan et al. 59,82 . This procedure provides the protected exceedance probability for each model (pxp), indicating how likely a given model has a higher probability explaining the data than all other models, as well as the Bayesian omnibus risk (BOR), the posterior probability that model frequencies for all models are all equal to each other 82 . Additionally, difference scores of PSIS-LOO for all models in contrast to the winning model were computed, which can be interpreted as a simple 'fixedeffect' model comparison 60 (see Table 1).

Posterior predictive checks.
To test whether the predicted values of the winning model could capture the variance in the performance expectation ratings a regression analysis (EXP ~ pred. values) was performed for each subject separately for the two ability conditions. R-squared statistic was determined and averaged. In addition, the model free analysis of the expectation ratings was repeated with the predicted values of the winning model to assess if the predicted data captured the effects that were present in the data of the expectation ratings.
Analysis of learning parameters. Learning rates for positive (α PE+ ) and negative prediction errors (α PE-, factor PE-Valence) were compared between the three groups in a linear mixed model with the factors PE-Valence and group (split into the contrasts SOC vs. [PHY, CON] and PHY vs. CON). Additional post-hoc tests for the PE-Valence within each stress group were performed with the Wilcoxon test. To test whether the variance in affective response and the cortisol response created by our stress manipulation is related to a bias in the updating behavior, we calculated a normalized learning rate valence bias score (valence bias score = (α PE+ − α PE− )/ (α PE+ + α PE− )) 21,53,54 and tested whether the affective response and the cortisol response predicted this bias. Since the distribution of the cortisol and affective response is left-skewed due to the experimental manipulation and thus absence of the response in parts of the subjects (valence bias score is normally distributed in the whole sample as well as all subgroups) we used rank regressions following Kloke et al. 63 . In case of the cortisol response, time of the day was additionally included in the regression analysis as a control variable to take into account circadian fluctuations of cortisol levels. To test whether the learning bias is associated with the recovery from negative affect elicited by stress (change in affective ratings post-stress T2 AFF − post-learning T3 AFF ), rank regressions with the valence bias score predicting the recovery were computed with the stress-induced increase in negative affect as an additional control variable to take into account regression to the mean. This was computed within the three experimental groups as well as for the whole sample, here with the additional variable group (split into the contrasts SOC vs. [PHY, CON] and PHY vs. CON) as well as the interaction bias x group to test whether the correlation differs between the three experimental groups. Data was analyzed in with the software R version 3.6.0 83 and plots were made with the R package gglpot2 84 .