Perception is rich and probabilistic

Evidence that reported distributions incorporate imprecision

To explore the extent to which participants’ bets captured representational noise, we first examined whether betting distribution predicted performance. To maximize performance, a participant should place bets narrowly when shape representation is low accuracy and spread bets wide when accuracy is low. Indeed, we found significant positive correlations (pr= 0.392). These individual correlations were transformed by Fisher (mean z= 0.434, 95% CI=[0.029, 0.899]) and one you -test revealed that this distribution was significantly different from zero (you (39) = 11.75, pz= 0.343) or the interquartile range22 (mean z = 0.333) of the uncertainty profile.

Evidence that profiles reflect trial-specific probability

This analysis demonstrates that the way bets are placed reflects the error in participants’ first response. But how well do the uncertainty profiles reported in the trials match the inter-trial error of the participants, as assessed by the uncertainty profile of the error in the first responses between the trials? If participants accurately recreated their internal representations by sampling them to derive early responses, the error distributions across trials would match the average of the uncertainty profiles reported in a single trial. We examined this using two Kolmogorov–Smirnov samples (KS) tests23 to compare the distribution of errors between trials (error of the first answer versus the correct answer) to the average uncertainty profile of the trial for each participant. The uncertainty profiles were shifted in a circle to align the target shapes and averaged at each integer value of the shape space (eg, at 360 discrete points). In 32 of the 40 participants, the D -value (the KSstatistic that measures the maximum difference between the two empirical cumulative distribution functions) was low (average D= 0.045, South Dakota= 0.025) and not significant (p > 0.05), highlighting that the reported average uncertainty profiles were not significantly different from the inter-trial error of the first response (Fig. 2a). This analysis suggests that participants have access to rich probabilistic information and can report it. The way participants allocate their bets is likely constrained by their internal representations.

Figure 2

Comparison of the error distribution of the first answer between the trials (red) and established uncertainty profiles (after the six bets) averaged between the trials (blue), for each participant. (a) The 40 participants in the main study. (b) 20 participants from a control study where participants were given the opportunity to cancel a response.

Moreover, if participants simply used confidence plus a memorized discrete percept15 rather than having access to a rich internal distribution, we would expect the drawn distributions to be roughly symmetric with respect to bet 1. Therefore, if we invert the uncertainty profiles before comparing them to the distribution errors between trials, this should not significantly affect the KStest results. However, this translates to only 11 of the participants (compared to 32 in the original analysis) whose two distributions are not significantly different (mean D= 0.098, South Dakota= 0.064). Comparing this to the original analysis, these D-the values ​​are significantly different (you(39) = 5.05, p

Proof that the bets contain more information than found in the first answer

The previous analyzes show that uncertainty profiles convey rich information about internal representations. But do they also contain information about what is in memory beyond what is captured by the initial response or first response plus a separate notion of trust15? If participants have an internal distribution from which to make multiple responses, it is possible that the cumulative error on bets will be more accurate than any single bet, even the first (see Supplementary Material). An example of how this could work is if the participants have an internal representation but can only draw one sample from it at a time (e.g. one different sample per bet), which makes the initial bet suboptimal . This is different from a discrete or discrete + confidence model, where the cumulative error can only get worse (especially if we assume there is a memory component that causes the betting information to degrade).

We analyzed the placement of the individual bets, as well as the cumulative circular average of the bets (for example, if the first bet was a 10° clockwise shape and the second was 4° clockwise anti-clockwise, the cumulative average would be 3° clockwise). As shown in Figure 3, the placement of the first bet is the most accurate, with a relatively monotonic decline in individual bet accuracy throughout the trial (when considering the center of bets in isolation). To examine this, we subjected betting to a one-way ANOVAwith the six bet order levels as a within-subjects factor. Errors generally increase with bet number (bet 1 = 14.9°, bet 6 = 20.3°), F(5195) = 17.76, pη2= 0.313. This result is not surprising given that the first response was worth double the points of subsequent responses and that subsequent responses came after increasing delays and potential interference from previous responses.

picture 3
picture 3

Individual response errors (red) and cumulative errors (blue) based on response order. Cumulative errors are calculated as the error of the mean of the responses. For example, the cumulative error for answer 3 would be influenced by answer 2 and answer 1, while the individual answer error for answer 3 is solely determined by this bet. (a) Errors for Experiment 1. (b) The equivalent errors for Experiment 2.

Although less specific than the first answers, subsequent answers may still contain additional and unique information about the target item. To test this, we examined whether additional bets provided new information not contained in the first response by testing whether the center of the uncertainty profile approximated the true shape with repeated bet placements. We submitted the average bet placement to one way ANOVAand we found that performance improved with additional bets (bet 6 = 14.1°), F(5195) = 3.71, p= 0.003, η2= 0.087, despite the fact that the average error trended much worse for the latest bets. This suggests that the combination of responses contains more information than any individual response, including the first response.

Proof that the average of the advantages is not caused by wrong first answers

As a precautionary measure, we wanted to make sure that the effects were not due to participants making a mistake in bet 1 (eg a wrong click) but with correct returns in the following bets. The paradigm of this control study was virtually identical to Experiment 1, except that for a given trial, participants had the option of clearing a bet by right-clicking the mouse. For example, if they made a mistake for bet 1, they can go back before confirming their bet 2. Similarly, a participant can cancel bet 5 before confirming bet 6. not used this feature in the first 20 tries received a reminder of this feature. All participants were also reminded of this between main practice/trials and at each break.

Participants rarely used the undo feature (mean = 2% of trials), despite constant reminders. Pointing error rates show a speed-accuracy trade-off24; therefore, a low correction rate was to be expected given the non-accelerated nature of the task. These canceled bets were generally of a greater magnitude of error (average error = 70°) and in line with random clicks (odds error = 90°) compared to the bets that replaced them (average = 16°) , indicating that they were erroneous. clicks rather than real answers. Use of the void feature was evenly distributed across bets, for example, it was used as frequently to void bet 1 as it was for bets 2, 3, 4 or 5. you-test on Bet 1 error magnitudes for experiment 2 (M= 18.2°, South Dakota= 1.3°) was slightly higher than that of Experiment 1 (M= 14.9°, South Dakota= 0.9°), (you(58) = 1.82, p= 0.074, η2= 0.05) despite being able to erase an incorrect answer, suggesting that Experiment 1 did not suffer from many of these false clicks.

Otherwise, the results of this control study mirror those of the main study. Significant positive correlations (pr= 0.440). When comparing the distribution of first-response errors between trials and the uncertainty profiles (after the six bets) averaged between trials (Fig. 2b), in 14 of 20 participants, the KStest D-the value was low (medium D= 0.055, South Dakota= 0.016) and not significant (p> 0.05). Errors also generally increased with bet number (bet 1 = 18.2°, bet 6 = 24.2°), F(5.95) = 11.82, pη2= 0.384, while the cumulative betting error (bet 6 = 17.0°) decreased, F(5.95) = 2.51, p= 0.035, η2= 0.12 (Fig. 3b). Therefore, we see no evidence that the improvement in later responses is caused by participants realizing after making an incorrect response.

Comments are closed.