Fig 1.
Experimental paradigm and trial-by-trial behavioural responses. A) On each trial, participants were presented with a blue and orange cup and had to choose one of them, receiving either a coin as positive feedback or a red ‘x’ as negative feedback. B) Probability of choosing one of the cups (denoted here as Cup A) across time in the full sample (Experiment 1; N = 80). Vertical lines represent reversals in contingency, with three reversals occurring in the low volatility condition and seven reversals for high volatility. Dashed yellow line represents the underlying true contingency in each miniblock. Trial-by-trial responses are shown for all four experimental conditions. Confidence intervals are ± 1 SEM around the group mean.
Table 1.
Experiment 1 - Behavioural results for the full sample (N = 80). Average accuracy, reaction time (RT), win-stay, and lose-shift behaviour is shown per condition – low volatility with low noise (LVLN), low volatility with high noise (LVHN), high volatility with low noise (HVLN), high volatility with high noise (HVHN). Differences in behavioural measures for low vs. high noise and low vs. high volatility are also displayed. Numbers in brackets represent ±1 SD.
Fig 2.
Experiment 1 - Behavioural results.
Accuracy, win-stay responses, and lose-shift responses per condition in (A) the full sample (N = 80) and (C) low (N = 28) and high (N = 27) ANX groups. Differences in these measures for low vs. high noise and low vs. high volatility are shown in (B) the full sample and (D) low and high ANX groups. (A, B) Results demonstrate a visible effect of noise level on behaviour, with better task performance, more win-stay behaviour, and less lose-shift behaviour under low compared to high noise conditions (all p < .001 in full sample). Participants showed more win-stay responses for high compared to low volatility in the context of low noise, and less win-stay behaviour for high compared to low volatility under high noise (p < .001 in full sample). Note that volatility-induced change in the three behavioural measures is minor compared to noise-induced change. (C, D) The high ANX group had significantly more win-stay responses than the low ANX group under low (pbonf = .015) but not high noise (pbonf = .962) (see inset in D). The high ANX group also showed significantly more lose-shift responses in the high compared to low noise conditions (pbonf < .001) whereas the low ANX group did not display meaningful noise-related differences in lose-shift behaviour (pbonf = 0.132). LVLN: low volatility with low noise, LVHN: low volatility with high noise, HVLN: high volatility with low noise, HVHN: high volatility with high noise. Error bars are ± 1 SEM.
Fig 3.
Experiment 1 - Relationship between learning and STAI traits in full sample (N = 80). A) Significant positive correlation between anxious traits and general win-stay behaviour (p = .019; left panel); a positive, trend-only relationship between anxious traits and win-stay behaviour in low compared to high noise conditions (p = .061; middle panel); and a significant positive relationship between anxious traits and lose-shift responses in high compared to low noise conditions (p = .021; right panel). B) No relationship between anxious traits and lose-shift behaviour in high compared to low noise conditions under high volatility (p < .1; left panel), but crucially, a significant positive correlation between anxious traits and lose-shift behaviour in high compared to low noise conditions under low volatility (LVHN – LVLN, p = .009; middle panel); and a positive, trend-only relationship between anxious traits and negative learning rate for the same comparison (LVHN – LVLN, p = .069; right panel). Grey bands represent 95% confidence intervals.
Table 2.
Experiment 1 - Behavioural results for low ANX (N = 28) and high ANX (N = 27) groups. Average accuracy, reaction time (RT), win-stay, and lose-shift behaviour is shown per condition. Differences in behavioural measures for low vs. high noise and low vs. high volatility are also displayed. Numbers in brackets represent ±1 SD.
Table 3.
Experiment 1 – Comparisons between Bayesian model group-level posterior distributions across conditions. The highest density interval (HDI) represents the 89% probability region of the difference probability distribution. Intervals that do not overlap zeros indicate a meaningful difference between distributions, i.e., between conditions.
Fig 4.
Experiment 1 - Individual-level and group-level model parameters of the winning hierarchical Bayesian model.
(A) Model parameters of the full sample (N = 80), showing median individual-level parameters (upper panel) and group-level posterior distributions (lower panel). The least uncertain LVLN condition (in green) can be seen to engender a reduced positive learning rate compared to both HVLN (in orange) and LVHN (in yellow), i.e., there is both a volatility- and noise-induced difference in positive learning rate. A similar volatility-induced increase in negative learning rate can also be seen from LVLN to HVLN. (B) Model parameters for the low (N = 28) and high (N = 27) ANX groups. Crucially, negative learning rate for the LVHN condition (in yellow) overlaps with the LVLN condition in the low ANX group, i.e., distributions are similar for high versus low noise under low volatility, but is shifted to higher values and overlaps the HVHN condition in the high ANX group. Value sensitivity distributions are higher in general for high compared to low ANX groups. Note that analyses of condition differences according to ANX group are carried out on group-level distributions only. (C) Full sample group-level condition differences in three model parameters; with a higher positive learning rate and higher negative learning rate in high compared to low volatility under low noise (left and middle panel, respectively) and greater value sensitivity for low compared to high noise under high volatility (right panel). (D) Group-level distribution differences for low and high ANX groups. The LVHN condition is significantly lower than HVHN in the low ANX group (left panel) whereas there is full overlap of these conditions in the high ANX group (right panel). ANX group differences are seen in the value sensitivity parameter, with higher values for the high ANX group in each of the LVLN, HVLN, and HVHN conditions (lower panel). Red bar across the x-axis represents the 89% highest density interval (HDI); HDIs that don’t overlap zero signify a meaningful difference.
Table 4.
Experiment 1 - Differences in ANX groups model parameter posterior distributions. 89% highest density intervals (HDI) on group and condition parameter posterior distribution differences, showing the lower and upper bounds of the 89% HDI. HDI that does not overlap 0 indicates a meaningful difference between distributions. Between-group HDI per condition (top), and between-condition HDI for each group (middle: Low ANX, bottom: High ANX).
Table 5.
Experiment 2 - Behavioural results for the full sample (N = 152). Average accuracy, reaction time (RT), win-stay, and lose-shift behaviour is shown per condition – low volatility with low noise (LVLN), low volatility with high noise (LVHN), high volatility with low noise (HVLN), high volatility with high noise (HVHN). Differences in behavioural measures for low vs. high noise and low vs. high volatility are also displayed. Numbers in brackets represent ±1 SD.
Fig 5.
Experiment 2 – Behavioural results.
Accuracy, win-stay, and lose-shift responses per condition in (A) the full sample (N = 152) and (C) low (N = 78) and high (N = 74) ANX groups. Differences in these measures for low vs. high noise and low vs. high volatility are shown in (B) the full sample and (D) low and high ANX groups. (A, B) Main effects of noise on behaviour seen in Experiment 1 (see Fig 2) were replicated, with greater task performance, more win-stay behaviour, and less lose-shift behaviour under low compared to high noise conditions (all p < .01 in full sample).There was a volatility*noise interaction on accuracy (p = .001), with higher accuracy in low compared to high volatility under low noise, but similar levels under high noise across the volatility conditions. There was also a volatility*noise interaction on win-stay behaviour (p = .001), with more win-stay for high compared to low volatility under low noise but less win-stay for high compared to low volatility under high noise, replicating Experiment 1. There were more lose-shift responses under high compared to low volatility (p < .001). (C, D) A three-way interaction between volatility, noise and ANX group on win-stay behaviour was found (p = .022). Although both ANX groups show more win-stay responses for low compared to high noise conditions (also captured across the full sample), this effect is heightened in the low ANX group, whereas the high ANX group show elevated win-stay behaviour for low vs. high volatility, compared to the low ANX group. Note that volatility-induced change in win-stay behaviour is minor (also seen in the full sample) compared to noise-induced change, also seen in Experiment 1. Error bars represent ± 1 SEM.
Fig 6.
Experiment 2 (N = 152) – Replication attempt. Relationships between learning measures and anxious traits from Experiment 1 (Fig 3) were not replicated. All associations were insignificant (p > .1).
Fig 7.
Experiment 2 – Interaction between volatility, noise and anxious traits on win-stay behaviour.
There were similar reductions in win-stay behaviour for higher anxious traits under LVLN, LVHN, and HVLN conditions, but no change in win-stay behaviour according to anxious traits in the HVHN condition. This three-way interaction was verified by a repeated-measures ANOVA (p = .039) and LME regression model on stay/switch behaviour (p = .014).
Table 6.
Experiment 2 - Comparisons between Bayesian model group-level posterior distributions across conditions. The highest density interval (HDI) represents the 89% probability region of the difference probability distribution. Intervals that do not overlap zeros indicate a meaningful difference between distributions, i.e., between conditions.
Fig 8.
Experiment 2 – Individual-level and group-level model parameters of the winning hierarchical Bayesian model.
(A) Model parameters of the full sample (N = 152), showing median individual-level parameters (upper panel) and group-level posterior distributions (lower panel). As in Experiment 1 (see Fig 4), there was a volatility-induced higher negative learning rate in the HVLN compared to LVLN condition. A higher value sensitivity was also seen in the HVLN condition compared to both the LVLN and HVHN conditions. (B) Model parameters for the low (N = 78) and high (N = 74) ANX groups. Note that the overlap of negative learning rate LVLN (in green) and LVHN (in yellow) distributions according to ANX group is not the same as was found in Experiment 1. (C) The same full sample group-level condition difference distributions as seen in Fig 4C are shown. Unlike in Experiment 1, there was no meaningful difference between LVLN and HVLN in positive learning rate in Experiment 2 (left panel). Like in Experiment 1, however, negative learning rate was significantly higher in the HVLN compared to LVLN condition, and value sensitivity was also higher in the HVLN compared to HVHN condition. (D) Group-level distribution differences for low and high ANX groups. Anxiety-based differences were generally found in be different in Experiment 2; here we present meaningful ANX-group level differences in Experiment 2. For positive learning rate, the high ANX group had a higher positive learning rate in the HVHN condition than the low ANX group (upper left panel). In the high ANX group only, positive learning rate was also found to be higher in the HVHN compared to HVLN condition (upper right panel). In the low ANX group, negative learning rate was found to be higher in the HVLN than LVLN condition (lower left panel), replicating Experiment 1 (see Fig 4D). Finally, in contrast to Experiment 1, negative learning rate was higher in the HVHN than LVHN condition in the high ANX group (lower right panel). Red bar across the x-axis represents the 89% highest density interval (HDI); HDIs that don’t overlap zero signify a meaningful difference.