Perceptual confidence has near perfect access to the existence of discrete representations, but only weak access to precision

Abstract

Perceptual confidence describes the degree to which we believe our internal perceptual representations reflect the external stimuli that caused them. How confidence is derived from internal representations is currently debated, but answering this question is made difficult because the nature of internal representations is also an ongoing debate. Here we leverage recent findings regarding how global motion is internally represented to test the prominent hypothesis that confidence is derived from internal representations. Participants estimated the global motion direction of two types of random-dot stimuli. In Experiment 1 a stimulus was used which induces discrete, all-or-none segmentation of signal and noise dots. Confidence nearly perfectly tracked whether or not these discrete representations existed, but had no relationship with their precision despite some representations being more precise than others. In Experiment 2 a motion stimulus was used which induces continuous local motion pooling characterized by large differences in response precision. Although confidence tracked the precision of these continuous representations, the relationship between confidence and precision was much weaker, suggesting that meta-knowledge of precision is highly error prone. This dissociation was also present when both discrete and continuous motion stimulus were presented intermixed in Experiment 3, suggesting that it is not merely driven by task set. Instead, the way in which confidence is derived from motion representations depends on whether they arose from a discrete or continuous encoding process. These results support theories which posit that confidence is generally derived from internal perceptual representations, but has only limited access to the precision of those representations.

Shortly after pioneering work began to characterize differences between the physical world and our conscious perception of it (Fechner, 1860; Weber, 1834) a natural question arose: to what degree are we consciously aware of our own mental processes? A now standard approach for measuring this metacognition is to have people rate how confident they are in their decisions during a task (Peirce & Jastrow, 1885). Confidence ratings have been used in many areas of cognitive psychology, often with the goal of understanding whether internal representations are continuous or discrete in nature. For example, in recognition memory confidence ratings are sometimes taken as evidence that long-term memory is a continuous signal-detection process, such that all stored memories have some level of latent memory strength (Egan, 1958; D. M. Green & Moses, 1966; Kintsch, 1967; Wixted & Mickes, 2010). However, confidence ratings have also been taken to imply that continuous memory strength is not sufficient for explaining memory, and that there must also be a discrete process whereby memories either occur with very high precision or not at all (Yonelinas, 1994). More recently, confidence ratings were used to argue that such an all-or-none discrete process alone is sufficient to explain recognition memory: you either remember something or you do not (Province & Rouder, 2012). Confidence ratings have also been used to examine whether visual working memory is a continuous or discrete process, but with similar contradictory conclusions (e.g. Adam & Vogel, 2017; Van den Berg et al., 2017). In the study of basic perceptual processes, confidence ratings have sometimes been used to reject Fechner’s idea that perception of faint signals occurs in an all-or-none manner, and that instead perception is a continuous signal detection process (e.g. D. M. Green & Swets, 1966). Although understanding the nature of perceptual and mnemonic representations is fundamental to psychological science, and despite the promise and continued use of confidence ratings to shed light on these representations, such endeavors seem to have made little progress across multiple fields of study.

One caveat in the use of confidence judgments is that it is not clear how they are derived from the underlying perceptual representations. For example, prominent theories including signal detection (D. M. Green & Swets, 1966) and various ideal observer models (Ma et al., 2006) assume that confidence is computed directly from the internal representation of a stimulus (Adler & Ma, 2018; Galvin et al., 2003). However, confidence is often found to be less informative about performance than would be expected if it were computed directly from internal evidence (Shekhar & Rahnev, 2021b). Some contemporary models have accounted for such imperfect metacognitive performance by proposing the presence of noise in confidence computations (Mueller & Weidemann, 2008; Shekhar & Rahnev, 2021a). Alternatively, experimental studies have shown that confidence may not be based on the internal representation itself, but is derived indirectly from other information that is diagnostic of performance such as response time (Baranski & Petrusic, 1994), variability in task difficulty (Rahnev & Fleming, 2019), perceived stimulus variability (Boldt et al., 2017), or subjective cues (Koriat, 2000, 2011). Moreover, even if confidence reports are derived directly from internal representations, it is mathematically impossible to identify the functional form of this mapping, since the relationship between them is non-linear and the representations are latent (Rouder et al., 2010).

There is currently little consensus regarding the nature of internal representations (vision, memory or otherwise), nor a consensus regarding how confidence ratings might be derived from those representations. Whereas attempting to solve these two problems often occupies different literatures (e.g. studies of memory versus studies of metacognition), we propose here that the ongoing debates in one area are a natural consequence of our current lack of understanding in the other. That is, many studies seek to make inferences about underlying mental representations by examining confidence ratings, but without knowing how confidence ratings are derived from those representations there is no way to see through the ratings to learn about the representations without relying on strong, often untestable assumptions. Likewise, trying to understand how confidence ratings are derived from the internal representations cannot be accomplished unless we already know the basic nature of those representations. This is like trying to solve an equation with too many unknowns (e.g., x + y = 3), such that progress will require either knowing something about how confidence judgments arise and then studying the representations from which they are derived, or knowing something about the representations and then examining how confidence judgments map onto them. Here we take the latter approach, leveraging recent results regarding continuous and discrete perceptual processes, and examining how confidence judgments map onto perceptual performance for these very different types of representations.

Our starting point is to consider the perception of global motion, which is the overall motion direction of an object that must be inferred from the object’s many local motion signals. For example, a dog running past you from left to right has a rightward global motion direction. But at any given moment each part of the dog has various levels of motion energy in different directions: its tail might be moving upwards; its leg might be moving leftwards. But our visual system creates the perception of a coherent object with a coherent global motion trajectory (see Nishida et al., 2018, for a review). Most theories of global motion perception suggest that doing so relies on a pooling process whereby local motion signals are combined into a global direction (Heeger, 1987; Van Santen & Sperling, 1984), which is thought to occur in mid-level cortical visual areas (Britten et al., 1992). However, such local-to-global pooling must also be highly selective so that signals arising from different objects are not erroneously pooled together. For example, if the dog is running past a bush it is critical that any movement of the bush’s leaves is not pooled along with the parts of the dog, even though they occupy similar parts of space. Therefore, many theories suggest that in addition to pooling, global motion perception includes a segmentation process which ensures that local motion energy is pooled within an object, but that multiple objects are segmented from one another in part based on their global motion energy (Braddick, 1993).

One stimulus that is often used to test theories of global motion perception (e.g., Shadlen & Newsome, 1996; Williams & Sekuler, 1984) consists of signal dots that all move in the same direction, mixed with noise dots that move in different random directions (Figure 1A). The percentage of coherently moving signal dots determines the strength of the global motion signal, and decreasing motion coherence leads to a decrease in motion direction identification performance. The perception of this motion stimulus is often referred to as transparent motion because the subset of coherently moving dots appears as a transparent moving surface with the noise dots appearing to move behind it. Such transparent motion perception is thought to reflect the motion segmentation process, whereby the signal dots are bound together as a single object that is perceived as being separate from the noise dots despite their shared spatial location (Schütz et al., 2010). In a recent study we demonstrated that this segmentation process is discrete (M. L. Green & Pratte, 2022). Participants were asked to report the global direction of transparent motion stimuli and identification errors were analyzed across several coherence conditions using a mixture-model approach (Zhang & Luck, 2008). This model assumes that global motion is sometimes perceived and the precision of direction reports (SD) can vary across conditions, or global motion perception fails altogether and participants are forced to guess (producing a uniform distribution of errors). Motion direction errors (Figure 1B) strongly indicated a discrete process: Response distributions appeared to be a mixture of pure guessing and highly accurate reports, and across coherence conditions the rate of pure guessing varied substantially while the precision of non-guess responses remained constant (Figure 1C). This pattern is consistent with an all-or-none segmentation process such that on some trials you segment signal dots from noise, and if you do the direction of this subset is trivially easy to identify, but on other trials segmentation does not occur and you fail to perceive a global direction altogether.

Figure 1.

Transparent and Gaussian motion. A) Transparent motion stimuli are composed of noise dots that move randomly and signal dots that move in the same direction. B) Motion direction errors for transparent motion vary across several levels of motion coherence. C) Manipulating coherence for transparent motion affects guess rates but not precision. D) For Gaussian motion the dot motion directions are sampled from a circular Gaussian distribution. E) Motion direction errors for Gaussian motion vary across several levels of coherence. F) Manipulating coherence for Gaussian motion causes substantial changes in precision. Data are from Green and Pratte (2022).

But whereas transparent motion stimuli elicit the segmentation of signal dots from noise dots, other stimulus types may not trigger such a process (Scase et al., 1996; Schütz et al., 2010). For example, rather than choosing dot directions from easily separable signal and noise distributions, in Green and Pratte (2022) a global motion stimulus was built by generating dot directions from a (circular) Gaussian distribution. The mean of this distribution defines the global direction and the concentration around the mean defines the coherence of the global motion signal. But whereas in transparent motion all signal dots move in the same direction, in this Gaussian motion stimulus (Figure 1D) no two dots move in precisely the same direction, such that segmentation may not be initiated despite there still being an average global direction. In support of this difference, there was far less guessing for Gaussian motion (Figure 1E), and manipulating coherence now primarily affected the precision of reports rather than the rate of guessing (Figure 1F). Taken together these results imply a striking dissociation in how different types of global motion are represented: Transparent motion perception is discrete as it either occurs with very high accuracy or not at all, whereas Gaussian motion is represented continuously such that the precision of reports tracks the strength of the global motion signal.

Here we leverage the dissociation between discrete and continuous motion perception to examine how confidence ratings arise from these substantially different representational forms. In Experiment 1 confidence tracked the existence or absence of transparent motion representations with near perfect accuracy. However, confidence had no relationship with the precision of these representations beyond their all-or-none status, despite there clearly being trial-to-trial variability in precision. However, in Experiment 2 confidence did track the precision of motion representation arising from a Gaussian motion stimulus to some degree, suggesting that when stimulus representations are continuous rather than all-or-none confidence has some access to their precision. This dissociation persisted in Experiment 3 in which both transparent and Gaussian motion were presented in a mixed design, suggesting that these differences are not due to overall task differences, but instead result from fundamental differences in how these different types of motion stimuli are represented.

Experiment 1

Method

Participants

Sixty-one adult undergraduate college students participated in Experiment 1 in exchange for research participation credit. Participants were included in further analyses if they met either of two inclusion criteria: 1) a Kolmogorov-Smirnov test rejected the null hypothesis that errors on trials with non-random motion were uniformly distributed, which would indicate chance performance, and 2) a Kolmogorov-Smirnov test rejected the null hypothesis that confidence on trials with non-random motion were similarly distributed as confidence on random motion trials, which would indicate unreliable confidence ratings. Three participants were excluded because their errors were uniformly distributed, ten were excluded because their confidence did not differ from confidence on random motion trials, and six more were excluded because they failed to meet both inclusion criteria. In total, 42 participants were included in further analyses. Details of the inclusion criteria analyses are reported in the Supplemental Material. For all experiments herein the procedures were performed in compliance with relevant laws and institutional guidelines and were approved by the Mississippi State University Institutional Review Board (Date: March 7, 2019; Ref: 16–316). Informed consent was obtained from all participants before they began the experiment.

Stimuli

Stimuli were displayed on 24-inch LCD monitors using the Psychophysical Toolbox (Kleiner et al., 2007) for Octave (Eaton et al., 2023) running on the Linux operating system. Transparent motion stimuli were comprised of small round white dots spanning approximately 0.1° visual angle with anti-aliasing. Dots were presented on a black background within an annulus spanning 1° – 9° visual angle radially from a central fixation. Each stimulus display had an average density of 3 dots/deg². Individual dots moved at a rate of 5 deg/sec. The lifetime of each dot was 200 ms (with random initial life time) before vanishing and being re-positioned at a new random location. Dots that reached the edge of the stimulus region were repositioned to the opposite side of the annulus. Each dot followed a linear trajectory, with a motion direction that could be one of two types: signal dots all moved in the same global motion direction, whereas noise dots moved in random, uniformly distributed directions (see Figure 1A). Motion coherence is defined as the percentage of signal dots, such that higher coherence yields a stronger global motion signal. Whereas the motion direction of each dot was generated randomly on each trial as is done in most studies, here the exact same motion displays were shown to all participants and in the same order across trials. This design allowed systematic differences across particular dot motion stimuli to be measured.

Procedure

The structure of a trial is shown in Figure 2A. Each trial began with a motion stimulus that was displayed for 500 ms. Following this stimulus the mouse cursor was positioned at fixation and a response region appeared comprised of a ring with inner (3°) and outer (5°) circular boundaries. Participants were required to move the cursor into the response region, after which the cursor was replaced by an arrow (4°) originating from fixation. Participants positioned the direction of the arrow using the computer mouse to indicate the global motion direction perceived in the stimulus. Following a mouse click to confirm their motion direction estimate, the cursor was repositioned at fixation and participants were required to move the cursor into the confidence rating region (8° length × 2° height) at the top center of the display (9° above fixation) to report their confidence in their motion direction estimate. The words “Low confidence” and “High confidence” were presented to the left and right sides of the response region, respectively. Participants were instructed to select a position along this continuum that reflects how confident they were that they accurately reported the true global motion direction. Once the cursor was moved into the confidence rating region the cursor was replaced by a vertical line indicating position on the confidence scale, and participants made a mouse click to confirm their confidence rating. Confidence ratings were recorded on a scale ranging from 0 to 1.

Figure 2.

Structure of a trial for Experiments 1–3. All experiments had similar designs but differed in the type of motion stimulus.

On each trial the global motion direction was randomly sampled from a uniform distribution (0 – 2π). Motion coherence was manipulated across four levels (0, 22, 33, and 50%), sampled with even frequency and randomly ordered across trials, with 150 trials at each coherence level. Participants completed 20 practice trials followed by 600 experimental trials, in which a break was provided every 80 trials. The 0% coherence condition, which has no global motion energy, provided the distribution of confidence ratings when no global motion is perceived and was used primarily for the inclusion criteria. The main analyses were conducted on the 450 trials from the three coherent motion conditions. Data and analysis code are available from the Open Science Framework (https://osf.io/abe8r/)

Results

Coherence Condition Effects

Figure 3A shows histograms of errors in reported motion directions. A repeated-measures analysis of variance (ANOVA) confirmed that the average (absolute) magnitude of errors increased as coherence was decreased (F (2, 82) = 105.60, p < .001, ${\eta }_P^2=.72$, BF₁₀ = 9.4 × 10¹⁹). To characterize how performance changes across conditions the Zhang and Luck (2008) mixture model was fit to the errors for each participant and each condition using standard maximum likelihood estimation techniques (for details see Standard Mixture Model in the Supplemental Material). This model assumes that pure guessing occurs at an estimated rate, and errors arising from guessing necessarily follow a uniform distribution because the true global motion direction is sampled uniformly from a circular space. Response errors that are not guesses follow a von Mises distribution (similar to a circular Gaussian) centered at zero with an estimated standard deviation (SD) which measures the precision of non-guess trials. Models fit to the subject-averaged data are shown as lines in Figure 3A, suggesting that they provide an accurate account of the error distributions.

Figure 3.

Error distributions for transparent motion in Experiment 1. A) Errors were aggregated across participants and models were fit to these averaged distributions (lines) for display purposes. B) Fitting the model to individuals suggests that guess rates increase substantially as coherence is lowered. C) The standard deviation of non-guessing responses is nearly invariant across conditions. D) Confidence increased as motion coherence is increased. All error bars denote standard errors of the mean.

Figure 3 shows the resulting parameter estimates for each condition. Guess rates (Figure 3B) varied substantially across coherence conditions (F (2, 82) = 50.03, p < .001, ${\eta }_P^2=.55$), whereas the standard deviation of non-guess responses (Figure 3C) did not differ significantly across conditions (F (2, 82) = .07, p = .93, ${\eta }_P^2=.002$). A Bayes Factor ANOVA with default priors (Rouder et al., 2012) also suggests an effect of condition on guess rate (BF₁₀ = 7.0 × 10¹¹) and no effect of condition on SD (BF₀₁ = 12.5). However, this approach of applying ANOVA to model-based estimates suffers from several potential problems. For example, assumptions of ANOVA are violated because the parameter estimates are typically not normally distributed nor have homogeneity of variance across conditions. Moreover, there are known biases in the mixture model parameters such as parameter trade-off between guess rates and SD (Sutterer & Awh, 2016), and applying an ANOVA to biased estimates can not take those biases into account. For example, in simulation studies (see Supplemental Material) we found that the ANOVA reliably identified a significant effect of condition on guess rate in all simulations, but had an inflated Type-1 error rate indicating a significant effect on precision (SD) in 14.5% of simulations in which there was no such effect.

For these and other reasons, previous work has advocated for a formal model comparison approach rather than applying ANOVAs to parameter estimates (Prins & Kingdom, 2018). Fortunately, the simulation studies here demonstrate that formal model comparison using the Bayesian Information Criterion (BIC, Schwarz, 1978) provides for a highly reliable way to assess whether mixture-model parameters do or do not vary across conditions. To do so, a fixed-guess model was constructed which forced guess rates to be the same across conditions and allowed only SD to vary. But the full model, which allowed both the guess rate and SD to vary across conditions, was preferred to the fixed-guess model (ΔBIC = 6), implying that guessing behavior varied across conditions. Alternatively, a fixed-precision model forced SD to be invariant across conditions but allowed the guess rate to vary, and it was preferred to both the full model (ΔBIC = 9) and the fixed-guess model (ΔBIC = 15) suggesting that precision was invariant across conditions. These model comparison results concur with the ANOVA analysis, and similar results were found when using Akaike Information Criterion (AIC, Akaike, 1973) to compare models. Taken together, these results replicate the previous finding that, for transparent motion, manipulating coherence affects the rate of guessing but not the precision of non-guess responses (M. L. Green & Pratte, 2022).

Conditional Analysis

Mean confidence ratings (Figure 3D) varied across coherence conditions as expected (F (2, 82) = 117.30, p < .001, ${\eta }_P^2=.74$, BF₁₀ = 2.0 × 10²¹). However, confidence can track performance across conditions for several reasons, such as the stimulus serving as a clue to being in a high or low coherence condition, rather than reflecting knowledge about the precision with which global directions were identified (Spence et al., 2016). Critically, correlations between confidence ratings and absolute errors in motion reports were calculated for each participant in each condition, and suggest that confidence tracks performance from trial-to-trial within the low (ρ = −.29, t(41) = 9.45, p < .001), moderate (ρ = −.29, t(41) = 10.09, p < .001) and high (ρ = −.26, t(41) = 7.59, p < .001) coherence conditions. Our goal is to determine how confidence tracks performance on a trial-by-trial basis. To do so we follow a procedure developed by Rademaker et al. (2012) which we term the conditional analysis. The error data were conditioned on different levels of confidence and differences in these errors were analyzed with the mixture model , providing a reliable test of whether variability in confidence ratings is related to variability in guess rates or precision across trials (see Model Recovery Simulations in the Supplemental Material). Confidence ratings were first binned into quartiles separately for each participant, thereby characterizing confidence on each trial as “very low”, “low”, “high”, or “very high”. Figure 4A shows errors in motion direction separately for each level of confidence and coherence condition, and the fitted mixture models (lines) provide accurate fits to the conditional data.

Figure 4.

Conditional analysis of transparent motion perception in Experiment 1. A) Error distributions of the data aggregated across participants (points) were fit with the full model (lines) for display purposes. B) Estimated guess rates from fitting the full model to individual participants. C) Estimated precision from the full model.

A full model with guess rate and precision parameters was fit to each coherence condition and confidence level separately. A 3 × 4 repeated measures ANOVA applied to the resulting guess rates (Figure 4B) suggests significant main effects of coherence (F (2, 82) = 28.23, p < .001, ${\eta }_P^2=.41$, BF₁₀ = 4, 485) and confidence (F (3, 123) = 27.32, p < .001, ${\eta }_P^2=.39$, BF₁₀ = 5.8 × 10²²) but no interaction (F (6, 246) = .91, p = .49, ${\eta }_P^2=.02$, BF₁₀ = .01). Alternatively, an ANOVA on estimates of SD (Figure 4C) suggests no main effect of confidence (F (3, 123) = 1.62, p = .19, ${\eta }_P^2=.04$, BF₁₀ = .21) and no main effect of coherence on SD (F (2, 82) = .43, p = .65, ${\eta }_P^2=.01$, BF₁₀ = .04). Although there was marginal evidence for an interaction between coherence and confidence (F (6, 246) = 1.9, p = .08, ${\eta }_P^2=.04$), the Bayes factor ANOVA provides strong evidence against an interaction (BF₀₁ = 16.7). For the model comparison approach, fifteen unique models that varied in whether they allowed guessing, precision or both parameters to vary across coherence, confidence, or both factors, were compared to determine how guess rate and precision varied with coherence and confidence. The preferred model (ΔBIC >= 9, preferred for N = 32/42 participants) allowed guess rate to vary across confidence levels but not across coherence levels, and included only a single precision value for all coherence and confidence levels (see supplementary Table S3 for detailed results).

The model comparison again suggests that there is little-to-no variability in precision across coherence levels, supporting the results on error data reported above. However, the model further suggests that guess rates were identical across coherence conditions. At first glance this result seems to suggest that there is no effect of coherence, and in fact the error histograms look nearly identical across coherence conditions when they are conditioned on confidence (Figure 4A). However, this pattern in the conditioned data does not imply that guess rates do not vary with coherence. Indeed, guess rates vary substantially across coherence conditions when the data are not conditioned on confidence level (Figure 3B). Instead, the effects of coherence are masked when the data are conditioned on confidence level, as these conditioned histograms do not show how much data exists within each confidence level. For example there are more “very low” confidence responses and fewer “very high” confidence responses in the low coherence condition compared to the high coherence condition. But critically, the fact that the substantial effects of coherence can be largely removed by conditioning error data on confidence level implies a conditional independence: the confidence rating on a trial can be used to accurately predict the corresponding error distribution, even without knowing the motion coherence condition of that trial. This conditional independence therefore implies that confidence ratings provide a nearly perfect indication of guessing behavior on individual trials. That is, confidence ratings accurately tracked whether a person made a guessing response or accurately reported the motion direction on individual trials, suggesting that people have nearly perfect meta-awareness of whether a global motion direction was represented or failed to be encoded altogether.

Systematic Trial Variability

Although the conditional analysis suggests that confidence closely tracks guess rate but does not track response precision across trials, this pattern could merely reflect a lack of trial-to-trial variability in precision. Whereas many theories assume that precision should vary from trial to trial due to fluctuations in internal noise, it was recently suggested that most (Pratte et al., 2017) or even all (Shen & Ma, 2019) such variability instead reflects systematic stimulus-driven factors. Those studies analyzed orientation perception, but there are reasons to expect similar effects in motion identification. In particular, it has been shown that motion perception exhibits an oblique effect whereby some motion directions are easier to perceive than others (Gros et al., 1998). The patterns of these effects can be quite complex and may depend on several aspects of the stimulus (Ezzo et al., 2023), but the result is systematic variability across particular motion stimuli. There are several other effects that might drive some trials to be easier than others, such as better performance on a trial when the stimulus value is similar to that on the previous trial (Pratte & Green, 2023), or even particular configurations of local dots that make the global motion salient on some trials more so than others. In order to characterize such stimulus effects in global motion perception, in a manner that is agnostic to their cause, the random-dot stimuli in Experiment 1 were identical across participants. That is, every participant saw the exact same display of moving dots on a given trial. This design allows for the data to be aggregated across participants, providing error distributions for individual displays. If there are displays with systematically higher or lower precision, the critical question is whether confidence ratings track these precision effects.

The data were aggregated over participants and the resulting error distributions for each trial were fit with the mixture model, providing estimates of guess rate and precision for each trial. The top row in Figure 5 shows guess rates as a function of average confidence for each trial. The degree of systematic variation across trials is surprisingly large: Even within the same condition there are trials in which over 90% of participants guessed, and other trials where nearly nobody guessed. To assess the reliability of these effects 95% confidence intervals were estimated for each guess rate (obtained from the Hessian matrix in likelihood estimation), and the extent to which they do not overlap with the average guess rate for that condition implies that some trials have systematically higher or lower guess rates than others. In the low, moderate, and high coherence conditions 48%, 40%, and 35% of trials, respectively, have confidence intervals that do not overlap with the average guess rate (see Figure S1,A–C in the Supplemental Material). Critically, this substantial variability in guess rate is strongly related to average confidence ratings for individual trials. Pearson’s correlations confirm that guess rates were correlated with confidence in the low (ρ = −.71,p < .001), moderate (ρ = −.79,p < .001) and high (ρ = −.82,p < .001) coherence conditions. These high correlations further suggest that performance differences across trials are not merely due to noise, but reflect systematic differences that make some trials easier than others. There are probably several factors that cause guess rates to be systematically high on some trials and low on others (Pratte & Green, 2023), and these results suggest that participants are aware of these differences in their guessing behavior.

Figure 5.

Individual trial analysis of transparent motion perception (Experiment 1). Upper panels (A-C) show the estimated guess rates and mean confidence on each trial for the low (A), medium (B), and high (C) coherence conditions. Lower panels (D-F) show estimates of precision and mean confidence on each trial for the low (D), medium (E), and high (F) coherence conditions. Pearson correlations (ρ) are noted within each panel.

The bottom row of Figure 5 shows estimates of SD as a function of the average confidence rating for each trial. Although precision did not vary across motion coherence conditions, there was substantial variability across trials within each condition. Confidence intervals on SD did not overlap with mean SD far more often than would be expected by chance (40%, 36% and 45% of trials in the low, moderate, and high coherence conditions respectively) suggesting that precision is higher for some dot-motion displays than others (see Figure S1, D–F in the Supplemental Material). However, there was not a significant correlation between precision and confidence in the low coherence (ρ = −.15,p = .07) or the moderate coherence conditions (ρ = .12,p = .13). Confidence and precision were somewhat correlated in high coherence conditions (ρ = .25,p = .002), but the correlation is positive which would imply that participants were more confident on trials with worse performance. Taken together these results suggest an extremely strong relationship between guessing and confidence on individual trials, but no reliable relationship between precision and confidence. These trial-specific results therefore mirror the conclusions of the conditional analysis, and further show that the lack of relationship between precision and confidence is not merely due to a lack of trial-to-trial variability in precision.

Discussion

The results of Experiment 1 replicate the finding that perception of a transparent motion stimulus reflects a discrete, all-or-none segmentation process (M. L. Green & Pratte, 2022). Critically, confidence ratings tracked whether or not these discrete representations existed with remarkable accuracy, but there was no evidence for a relationship between confidence ratings and the precision of non-guess reports. However, it is possible that the results of Experiment 1 — that confidence tracks guess rates but has no relationship with precision — are specific to the transparent motion stimulus by virtue of the representations arising from a discrete segmentation process. In particular, it is possible that the segmentation process provides a point estimate of the global motion direction of the segmented dots, but no information about the precision of that estimate. Such a process is in line with typical phenomenological experiences of moving objects: You simply see an object moving in a particular direction; you do not experience a myriad of possible true directions that might have caused your current perceptual state (Block, 2018).

However, whereas a segmentation of the world into discrete visual objects may describe the majority of motion perception under natural conditions, M. L. Green and Pratte (2022) found that not all types of global motion perception relies on discrete segmentation. In particular, in a Gaussian motion stimulus no two dots share exactly the same direction but all share a common average. This stimulus is like a flocks of birds or bubbles rising through water, where all of the elements share a common global direction even if no two elements are moving in precisely the same manner. M. L. Green and Pratte (2022) found that manipulating the coherence of a Gaussian motion stimulus primarily affected response precision (see Figure 1E), suggesting that for this type of motion participants derive a global direction by averaging over all or most of the dot direction on every trial. This is a substantially different encoding process than the discrete segmentation of signal and noise dots for transparent motion stimuli, and in Experiment 2 we examine whether confidence ratings therefore have a different type of access to the resulting perceptual representation. For example, if the global direction of Gaussian motion is computed from an average of local motion directions, then the precision of this average may be a natural consequence of how those signals are encoded and combined in mid-level visual areas (Jazayeri & Movshon, 2006). If so, then confidence ratings should track the precision of global motion when it arises from a Gaussian motion stimulus.

Experiment 2

Method

Participants

Sixty adult undergraduate college students participated in Experiment 2. Eight participants were excluded for failing to use the confidence ratings appropriately, using the same exclusion criteria as in Experiment 1. Further analyses were conducted on data from the remaining fifty-two participants who met the inclusion criteria.

Stimulus and Procedure

Experiment 2 was identical to Experiment 1 with the following exceptions. Whereas in Experiment 1 the motion direction of each dot was designated as either signal or noise, in Experiment 2 the motion direction of each dot was sampled from a wrapped Gaussian distribution (Figure 1D, see Watamaniuk et al., 1989). The mean of this sampling distribution determined the global motion direction on each trial, and its concentration around this mean determined motion coherence. Coherence was defined as the mean resultant length of the distribution (R), which is related to the variance of the underlying Gaussian distribution $(R=e^{-{\sigma }^2/2})$. Coherence was manipulated across four levels (R = 26°, 35°, 43° and random motion) which were chosen in pilot experiments to provide similar overall performance as the coherence conditions in Experiment 1.

Results

Coherence Condition Effects

Figure 6A shows error histograms for each level of coherence. Fitting the full model and applying repeated measures ANOVAs to the estimates confirms that, like transparent motion, guess rates decreased as coherence was increased (Figure 6B, F (2, 102) = 63.48, p < .001, ${\eta }_P^2=.55$, BF₁₀ = 5.3 × 10¹⁵). But unlike transparent motion, for this Gaussian motion stimulus the SD of non-guess responses (Figure 6C) also decreased significantly with increasing motion coherence (F (2, 102) = 96.64, p < .001, ${\eta }_P^2=.65$, BF₁₀ = 8.2 × 10²⁰). Formal model comparison supports the effect of coherence on precision, with BIC preferring a model in which only SD varied with coherence over a model in which only guessing varied (ΔBIC = 16), and over the full model which allowed both guess rate and SD to vary with coherence (ΔBIC = 3). However, AIC suggested that the full model was preferred to the fixed-SD model (ΔAIC = 21) as well as the fixed-guess model (ΔAIC = 5), mirroring the ANOVA results and suggesting that both SD and guess rate varied across coherence conditions. Taken together these results replicate the previous finding in M. L. Green and Pratte (2022) that guess rates may vary somewhat with coherence for Gaussian motion, but critically, that precision varies substantially across coherence conditions.

Figure 6.

Error distributions for Gaussian motion perception in Experiment 2. A) Errors were aggregated across participants and models were fit to these averaged distributions (lines) for display purposes. B) Fitting the full model to individuals suggest that guess rates vary somewhat with coherence, and C) the precision of non-guessing responses varies substantially with coherence. D) Confidence increased as motion coherence is increased.

Conditional Analysis

Mean confidence ratings (Figure 6D) varied with coherence for Gaussian motion (F (2, 102) = 107.10, p < .001, ${\eta }_P^2=.68$, BF₁₀ = 2.5 × 10²²) to a similar degree that they did for transparent motion in Experiment 1 (Figure 3D). And critically, confidence was again correlated on average with motion report errors in the low (ρ = −.24, t(51) = 16.89, p < .001), moderate (ρ = −.23, t(51) = 14.41, p < .001) and high (ρ = −.15, t(51) = 7.61, p < .001) coherence conditions, suggesting that confidence tracks performance on a trial-by-trial basis even within conditions. The conditional analysis (Rademaker et al., 2012) was therefore used to explore how motion identification performance varied across levels of confidence.

Figure 7A shows report errors conditioned on binned confidence ratings, separately for each coherence condition. A 3 × 4 repeated measures ANOVA on guess rates (Figure 7B) suggests a main effect of coherence (F (2, 102) = 46.85, p < .001, ${\eta }_P^2=.48$, BF₁₀ = 6.9 × 10¹¹) and a main effect of confidence (F (3, 153) = 31.98, p < .001, ${\eta }_P^2=.39$, BF₁₀ = 4.4 × 10²⁰). Although the interaction was significant (F (6, 306) = 3.58, p = .002, ${\eta }_P^2=.07$) the Bayes factor ANOVA provided little evidence for or against an interaction (BF₁₀ = 1.6). These rates of guessing are far lower than those seen in Experiment 1, but the conditional analysis suggests that again confidence ratings closely track guessing behavior, although perhaps not as closely as it did for transparent motion. Alternatively, the precision of non-guess responses (Figure 7C) shows a different pattern than Experiment 1. An ANOVA suggests a significant main effect of coherence (F (2, 102) = 123.60, p < .001, ${\eta }_P^2=.71$, BF₁₀ = 2.3 × 10³⁸) and a main effect of confidence on SD (F (3, 153) = 15.55, p < .001, ${\eta }_P^2=.23$, BF₁₀ = 6.5 × 10⁵). There was marginal evidence for an interaction between coherence and confidence (F (6, 306) = 2.22, p = .04, ${\eta }_P^2=.04$), but the Bayes Factor suggested evidence against an interaction (BF₀₁ = 5.6). That SD varies with confidence level implies that confidence tracks the precision of responses for this Gaussian motion stimulus, whereas there was no such relationship for transparent motion in Experiment 1.

Figure 7.

Conditional analysis of Gaussian motion perception in Experiment 2. A) Error distributions (points) were aggregated across participants and fit with the full model (lines) for display purposes. B) Estimated guess rates from fitting the full model to individual participants. C) Estimates of precision from the full model.

A factorial model-comparison approach was performed using the same models as in Experiment 1 (see supplemental Table S5 for details). The preferred model by BIC (ΔBIC >= 13, N = 21/52) included a single guess rate for all confidence and coherence levels, and whereas precision was free to vary across coherence conditions in this model it was fixed across confidence levels. Although this model implies that precision does not vary with confidence, the evidence for this model was relatively weak, being preferred for only 40% of subjects. In total, the best-fitting model by BIC for 33 out of the 52 participants (63%) included the restriction that precision was constant across confidence levels, suggesting that perhaps precision does not track confidence despite the ANOVA result to the contrary. However, AIC did not clearly identify a single winning model. Instead, the four top-performing models had similar AIC values (ΔAIC < 3), and three of these four models allowed SD to vary across confidence levels. Taken together, the ANOVA, BIC and AIC results suggest that in Experiment 2 confidence tracked response precision to some degree, but the relationship was weak. This conclusion is supported by the fact that precision varies substantially with coherence conditions in Experiment 2, even when conditioning on confidence (Figure 7A). That is, in Experiment 1 conditioning on confidence removed nearly any difference across conditions, implying that confidence ratings contained complete information about which condition a piece of data arose from. But the failure to condition out the effect of condition Experiment 2, and the fact that the effect of coherence on precision was similar regardless of whether the data were conditioned on confidence ratings (Figure 7C) or not (Figure 6C) implies that confidence ratings only weakly track trial-to-trial performance when identifying Gaussian motion.

Systematic Trial Variability

The Gaussian motion stimuli were identical and presented in the same order for all participants, such that aggregating the data across individuals for each trial provided distributions of errors and confidence ratings for each specific motion stimulus. The mixture model was fit to the error distributions for each stimulus, and in Figure 8 the resulting parameter estimates are plotted as a function of mean confidence for that stimulus. Like the transparent motion stimuli in Experiment 1, performance varied substantially across particular Gaussian motion stimuli in Experiment 2. But whereas this variability was larger in guess rates for transparent motion, for Gaussian motion the variability appears to be larger in precision. In particular, for guess rates 28%, 26%, and 39% of estimates in the low, moderate, and high coherence conditions, respectively, had confidence intervals below or above the mean guess rate (Figure S3A–C). For SD, 35%, 59%, and 56% of estimates in the low, moderate, and high coherence conditions, respectively, had confidence intervals below or above the mean SD (Figure S3D–F). Finally, whereas trial-specific estimates of SD in Experiment 1 range from about 5 to 20, in Experiment 2 they range from about 5 to 60 (note that the y-axes differ across the bottom panels of Figures 5 and 8). Taken together, these results suggest that the Gaussian stimuli in Experiment 2 had more variability in precision compared with the transparent motion stimulus, potentially increasing our ability to find relationships between precision and confidence should they exist.

Figure 8.

Individual trial analysis of Gaussian motion perception (Experiment 2). Upper panels (A-C) show the estimated guess rates and mean confidence on each trial for the low (A), medium (B), and high (C) coherence conditions. Lower panels (D-F) show estimates of precision and mean confidence on each trial for the low (D), medium (E), and high (F) coherence conditions. Pearson correlations (ρ) are noted within each panel.

However, despite the substantial variability in precision, there was again not a consistent relationship between precision and confidence (Figure 8D–F). Confidence was not correlated with precision in either the moderate (ρ = .06,p = .47) or high (ρ = .03,p = .69) coherence conditions, but confidence was moderately correlated with precision in the low coherence condition (ρ = −.24,p = .003). In contrast, confidence was again correlated with guess rates in the low (ρ = −.27,p < .001), moderate (ρ = −.33,p < .001) and high (ρ = −.25,p = .002) coherence conditions, even though guessing was far less prevalent for the Gaussian motion stimulus in Experiment 2 (Figure 8A–C), and these moderate correlations were much smaller than the extremely large correlations in Experiment 1. Overall, these results again suggest that confidence has some access to the precision of Gaussian motion representations on a trial-by-trial basis, but that this relationship is inconsistent and highly error prone.

Discussion

Experiment 2 replicates M. L. Green and Pratte (2022) in that the precision with which the average direction of Gaussian motion is reported decreases as motion coherence is decreased, suggesting a pooling process in which local motion signals are combined into an average direction. The dissociation between discrete segmentation of transparent motion in Experiment 1 and continuous pooling of Gaussian motion in Experiment 2 is striking given that the motion-identification task is equivalent and the stimuli appear so similar. Critically, this dissociation was also observed in confidence ratings: For transparent motion confidence has near perfect access to whether or not a global motion signal is represented, but no access to the precision of those representations. Alternatively, for Gaussian motion, confidence rates do track the precision of motion reports, albeit only weakly.

The different ways in which confidence ratings have access to global motion representations may reflect something fundamental about how they are represented, such as transparent motion undergoing an all-or-none segmentation process and Gaussian motion being the result of averaging local motion. However, an alternative possibility is that differences in how these stimuli are perceived caused participants to adopt different strategies for making confidence ratings across Experiments 1 and 2. For example, if participants realize that their perception of transparent motion in Experiment 1 was either very accurate or completely absent, they might adopt a coarse-grained strategy in using the confidence ratings, such that their confidence ratings failed to track more nuanced differences in precision. Therefore, in order to more directly assess this dissociation, in Experiment 3 both transparent and Gaussian motion stimuli were presented and intermixed randomly across trials. Because participants couldn’t know which type of motion stimulus would appear on a given trial until it began to move, this mixed design should discourage any strategies that are particular to one type of motion stimulus and allow for a more direct comparison across stimulus types.

Experiment 3

Method

Participants

Fifty-one adult undergraduate college students participated in Experiment 3. One participant was excluded from analysis because their errors were uniformly distributed, nine were excluded because their confidence did not differ from confidence on random motion trials, and two more were excluded because they failed to meet both inclusion criteria. In total, 39 participants were included in further analyses. These exclusion rates are similar to those in Experiment 1, which were somewhat higher than those in Experiment 2 and which could have caused differences across those experiments. However, the mixed design of Experiment 3 ensures that differences across transparent and Gaussian motion can not be caused by different exclusion rates.

Stimuli and Procedure

Experiment 3 was similar to Experiments 1 and 2 with the following exceptions. Each trial consisted of either a transparent motion stimulus or a Gaussian motion stimulus. Motion coherence was either low or high for transparent motion (15% or 33% signal dots) and Gaussian motion (26° or 43° mean resultant length). These coherence levels match the second-to-lowest and second-to-highest conditions from Experiments 1 and 2, with the goal of observing robust coherence effects for both stimulus types. Stimulus type and coherence level were counterbalanced in a 2×2 factorial design and presented in random order, with 150 trials for each of the four conditions (600 total). An additional random motion condition (150 trials at 0% coherence) was included to test whether confidence ratings were reliable for each participant. Unlike Experiments 1 and 2 in which all participants saw the same motion displays, in Experiment 3 the dot locations and directions for each stimulus were chosen randomly on each trial, as was the global motion direction. Although this design does not allow for performance to be compared across particular displays, it ensures that the results are not an artifact of using the same stimuli across participants.

Results

Coherence Condition Effects

Figure 9A shows the resulting response error distributions, and visual inspection suggests that the differential effects of coherence across stimulus types was replicated: for transparent motion (top) coherence primarily affected the rate of guessing, seen as a rise in the long flat tails, whereas for Gaussian motion (bottom) coherence affected SD, seen as a widening of the central part of the distribution. This dissociation was supported by an ANOVA on estimates of SD, which revealed an interaction between stimulus type and coherence on SD (F (1, 38) = 10.22, p = .003, ${\eta }_P^2=.21$, BF₁₀ = 5.9 × 10¹⁶, BF₁₀ = 1.3 × 10¹⁵). Follow-up t-tests indicate that precision is invariant across coherence levels for transparent motion condition (t(38) = 1.86, p = .07, BF₁₀ = .82), but precision increases substantially from the low to high coherence conditions for the Gaussian motion condition (t(38) = 8.85, p < .001, BF₁₀ = 1.1 × 10⁸). This pattern of results replicates the findings in Experiments 1 and 2 that precision is invariant for transparent motion but varies with stimulus coherence for Gaussian motion. An ANOVA on guess rates revealed main effects of stimulus type (F (1, 38) = 213.8, p < .001, ${\eta }_P^2=.85$, BF₁₀ = 1.7 × 10²⁴) and coherence condition (F (1, 38) = 68.08, p < .001, ${\eta }_P^2=.64$, BF₁₀ = 161), suggesting again that guessing may vary with coherence in both stimulus conditions. The interaction was marginally significant (F (1, 38) = 3.6, p = .065, ${\eta }_P^2=.09$) but the Bayes factor ANOVA indicated little evidence for an interaction (BF₁₀ = 1.2). But follow-up t-tests indicate that guessing was strongly affected by coherence in the transparent motion condition (t(38) = 6.2, p < .001, BF₁₀ = 54, 633), and was also affected by coherence for the Gaussian stimulus though to a lesser degree (t(38) = 3.8, p = .0004, BF₁₀ = 63). These results were supported by formal model comparisons, such that BIC identified a model in which coherence only affected guess rates for transparent motion and only SD for Gaussian motion (see Supplementary Materials for details). But a model in which guess rate was additionally allowed to vary with coherence for both motion types performed nearly as well, confirming that guess rates are somewhat affected by coherence even for the Gaussian stimulus. Overall these results replicated the dissociation observed across Experiments 1 and 2, that manipulating the coherence of a transparent motion stimulus primarily affects the rate of guessing, but manipulating the coherence of a Gaussian motion stimulus also affects the precision of reports.

Figure 9.

Error distributions from Experiment 3. The top panels (A) show errors for transparent motion with low (left) and high coherence (right). Bottom panels (B) show error for Gaussian motion with low (left) and high (right) coherence. The selective-influence model (dashed line) only allowed guess rate to vary across transparent motion conditions (A) and only allowed precision to vary across Gaussian motion conditions (B), yet fit nearly as well as the full model (solid line) which allowed both guess rate and precision to vary across coherence levels for both stimulus types.

Conditional Analysis

The error data were conditioned on confidence (Figure 10) and mixture model parameters were analyzed across levels of stimulus, coherence and confidence. For guess rates the three-way interaction between stimulus type, coherence, and confidence was not significant (F (3, 114) = .80, p = .50, ${\eta }_P^2=.02$, BF₀₁ = 250), nor was the two-way interaction between coherence and confidence (F (3, 114) = .54, p = .66, ${\eta }_P^2=.01$, BF₀₁ = 50) or the two-way interaction between stimulus type and coherence (F (1, 38) = .35, p = .56, ${\eta }_P^2=.009$, BF₀₁ = 6.25). There was a two-way interaction between stimulus type and confidence (F (3, 114) = 5.83, p = .001, ${\eta }_P^2=.13$, BF₁₀ = 20). The main effect of coherence was also significant (F (1, 38) = 186.3, p < .001, ${\eta }_P^2=.54$, BF₁₀ = 249.6) and together with the lack of interactions involving coherence suggests that this effect was similar across both stimulus types and across confidence conditions. Separate one-way ANOVAs on the effect of confidence for each stimulus type suggested that the interaction arises from a larger effect of confidence in the transparent motion condition (F (3, 114) = 37.0, p < .001, ${\eta }_P^2=.49$, BF₁₀ = 2.4 × 10¹⁹) than in the Gaussian motion condition (F (3, 114) = 18.2, p < .001, ${\eta }_P^2=32$, BF₁₀ = 3.0 × 10⁸). This pattern of results replicates the relationships between confidence and guess rate observed across Experiments 1 and 2.

Figure 10.

Conditional analysis of transparent and Gaussian motion perception in Experiment 3. Error distributions for transparent motion (A) and for Gaussian motion (B) are shown as points. Lines show the best-fitting full model which allowed guess rate and SD to vary across coherence and confidence.

Applying an ANOVA to the SD parameters suggests that there is again not a three-way interaction (F (3, 114) = 1.59, p = .20, ${\eta }_P^2=.04$, BF₀₁ = 3333.3), nor a two-way interaction between coherence and confidence (F (3, 114) = 1.39, p = .25, ${\eta }_P^2=.04$, BF₁₀ = .09), or between stimulus type and confidence (F (3, 114) = .91, p = .44, ${\eta }_P^2=.02$, BF₁₀ = .05) or between coherence and stimulus type (F (1, 38) = 2.03, p = .16, ${\eta }_P^2=.05$, BF₁₀ = .36). The main effect of stimulus type was also not significant (F (1, 38) = .16, p = .70, ${\eta }_P^2=.004$, BF₀₁ = 10). However, both the main effect of coherence (F (1, 38) = 20.76, p < .001, ${\eta }_P^2=.35$, BF₁₀ = 1, 626) and confidence were significant (F (3, 114) = 7.3, p = .0002, ${\eta }_P^2=.16$, BF₁₀ = 29.23). The lack of a main effect of stimulus type along with no interactions suggests that precision varies across confidence conditions in both stimulus conditions. However, follow-up tests indicate that for transparent motion the effect of coherence and confidence is being driven by the singular SD estimate in the Low Coherence, Very Low Confidence condition which is significantly larger than the SD in all of the High Coherence conditions (ts >= 2.25, ps <= .002), but it does not vary from any other estimates within the Low Coherence condition (ps > .05), and all of the estimates in the High Coherence condition are invariant (ps > .05). These results largely mirror the relationships between confidence and precision observed across Experiments 1 and 2 in that there is very little variability of precision in the transparent motion condition, but for Gaussian motion precision varies across coherence conditions and confidence ratings.

Given the complexity of the design in Experiment 3, rather than a fully factorial model comparison we directly compare the two models for each stimulus condition which test the hypotheses that confidence tracks guessing in the transparent motion condition, and that confidence tracks precision in the Gaussian motion condition. For transparent motion the model in which precision was fixed across coherence and confidence conditions, and guess rate varied only with confidence, was preferred over a fixed precision model in which guess rate varied only with coherence by both BIC (ΔBIC = 28, N = 28/39) and AIC (ΔAIC = 37, N = 35/39). This finding supports the ANOVA result that confidence tracks guess rates for transparent motion. For the Gaussian motion condition a model in which guess rate was fixed across conditions and precision varied only with coherence was marginally identified by BIC in half of participants (ΔBIC = 2, N = 20/39). However, AIC indicated a model in which SD additionally varied with confidence (ΔAIC = 7, N = 23/39) in 58% of participants. Overall, these model comparison results are highly similar to the results across Experiments 1 and 2, and taken together with the ANOVA results suggest that confidence has near perfect access to guessing for a transparent motion stimulus, and has weak access to the precision of Gaussian motion representations. Critically, replicating this dissociation in the mixed design of Experiment 3 suggests that something fundamental about these motion stimuli drives different levels of access to precision, rather than merely a different strategy or task set.

General Discussion

Many theories assume that visual confidence is computed directly from the internal representation of a stimulus, yet the nature of these internal representations is itself not yet fully understood. Here we leveraged recent findings that the internal representations of global motion differ markedly across different types of motion stimuli (M. L. Green & Pratte, 2022) to explore how confidence tracks various aspects of these representations. The results of Experiment 1 suggest that confidence has nearly perfect access to the existence of motion representations that arise from a discrete segmentation process, but no access to the precision of those representations. Alternatively, Experiment 2 suggests that when global motion perception results from a continuous pooling process of local motion direction, confidence has some access to the precision of the resulting representation. In Experiment 3 both stimulus types were presented in a mixed design, and confidence again perfectly tracked the existence of discrete motion representations and tracked the precision of continuous motion representations to some degree. Taken together, these results support the hypothesis that visual confidence is computed directly from the internal representations of a stimulus, but reveal that the information available for computing confidence depends greatly on the type of stimulus representation.

Most contemporary theories of perception assume that stimulus features like motion direction are represented by a population of neurons, such as global motion being encoded as population activity in localized patches of the medial temporal lobe (Britten et al., 1992). Moreover, this population activity is thought to represent the degree to which the feature value of a stimulus is known, in the form of probability distributions over possible feature values (Pouget et al., 2003). However, the degree to which we have conscious access to the information contained within this population activity has enjoyed years of debate. Some work suggests that we have full access to these internal probability distributions, including knowledge of uncertainty (Geurts et al., 2022; Honig et al., 2020; Van den Berg et al., 2017). Alternatively, others have argued that awareness of the precision of representations can be ruled out a priori simply based on our subjective experiences. For example, Block (2018) notes that neurons in the medial temporal lobe have broad motion tuning functions, and in the face of a moving object both individual neurons and the population response will have energy at many possible motion directions. Nonetheless, we do not consciously experience this distribution of energy, we merely see an object moving in a particular direction. The results of Experiment 1 support this lack of access to feature-tuned population responses beyond their peak, as confidence ratings had little relationship to fine changes in the precision of behavioral reports, but confidence did closely track the all-or-none state of motion representations such that you know when you perceived coherent global motion and when you did not. This pattern suggests a limited access account whereby you know when there is a representation, but don’t necessarily know with great acuity how accurately it reflects properties of the distal stimulus.

The transparent motion stimulus in Experiment 1 is representative of typical motion in real life, where there are many sources of external motion and the visual system must use these patterns of motion to segment the visual scene into discrete objects. The implication of Experiment 1 is that the result of this discrete segmentation into representations of coherently moving objects does not permit access to the precision of the resulting motion directions. This finding supports Block’s (2018) assertion that we typically do not enjoy access to the precision of our representations. In contrast, the results of Experiment 2 suggest that under some circumstances confidence can reflect changes in the precision of internal perceptual representations. In particular, when global motion arises from a collection of dots that do not share an identical direction, but on average cluster around one direction, there is some access to the precision of the resulting average. There are no discrete collections of dots in this stimulus (unlike the signal and noise dots in transparent motion), and the error data suggest that the global direction is derived by averaging over the local motions rather than forming sub-sets that have highly similar motion directions. Although we are quite accurate at doing so, this is a far less ecologically valid motion stimulus except perhaps in cases such as observing the heading direction of a school of fish or flock of birds. It therefore seems that, in the case of motion perception, typical visual processes such as segmentation produce representations without corresponding information about the precision of those representations. However the results of Experiment 2 suggest that there are visual encoding processes which produce representations along with consciously accessible information about the precision of those representations. This discrepancy may exist for a variety of visual stimuli, suggesting that conclusions drawn from studies of how confidence reflects precision may only be applicable to the specific type of stimulus used in that study, such that broad claims about access to precision or a lack of it are not possible.

Whereas we found that on a trial-by-trial basis confidence strongly tracks guessing behavior for discrete motion but only weakly tracks precision for continuous motion, confidence increased with manipulations of motion coherence similarly for both discrete and continuous stimulus types. However we hesitate to interpret how confidence changes across gross manipulations of coherence as there are many factors that may drive confidence to vary across conditions, including those that do not arise from the internal representations at all. For example, confidence judgments may reflect some aspect of the stimulus (Bertana et al., 2021; Boldt et al., 2017; Desender et al., 2018) or task (e.g. Rahnev & Fleming, 2019) that is predictive of performance to some degree. In particular, knowing you are in an easy condition (such as detecting high motion coherence) may increase confidence on average across trials, even if the internal representation for any particular stimulus is imprecise (Spence et al., 2016). It is likely that confidence judgments arise from both the nature of an internal representation and stimulus information such as coherence level, and possibly other sources of information as well (e.g. Koriat, 2011). Due to this lack of knowledge regarding how confidence ratings map onto internal states we have avoided interpreting changes in confidence ratings across conditions. Instead, leveraging the conditional analysis (Rademaker et al., 2012) and fixing stimuli across participants (Brady & Alvarez, 2015; Pratte & Green, 2023) provided reliable approaches for examining confidence on a trial-by-trial level. Critically, neither approach relied on strong assumptions about the distribution of confidence ratings or how those ratings map onto behavior.

Recent studies have taken a variety of approaches to examine the relationship between confidence and performance, and some have suggested that confidence ratings clearly track the precision of responses. These studies examined the perception of simple visual features such as orientation Rademaker et al. (2012) and Van den Berg et al. (2017) and color (Honig et al., 2020), and it is possible that the extent to which precision tracks confidence depends on the stimulus. For example, weak global motion information can be processed and affect behavior even when participants are not aware of the motion energy (Watanabe et al., 2001), suggesting that a great deal of motion information may not be available for conscious access. More generally, we may have conscious access to the precision of simple visual feature representations like the motion of individual dots during local pooling, whereas other representations like a coherent motion pattern segmented from noise might provide only a point estimate. However, our results suggest that confidence may not invariably track precision for all stimulus types, and we worry that these previous conclusions about how confidence is derived from internal representations may have been driven by unmet assumptions. For example, using a model comparison approach Van den Berg et al. (2017) suggested that confidence tracks the precision of representations in working memory as well as guessing behavior, similar to our Gaussian motion condition. However, the confidence reports were binned and the models assumed that guesses always led to the lowest confidence bin, and several studies have suggested that this assumption is incorrect and problematic (Bröder & Schütz, 2009; Dube & Rotello, 2012; Province & Rouder, 2012). For example, the guessing model misfit the data exactly as would be expected if guesses do not always result in the lowest confidence report: the rate of lowest-confidence reports was over-estimated, the rate of low (but not lowest) confidence reports was under-estimated, and memory performance for these lower confidence reports was overestimated (see Figure 8 in Van den Berg et al., 2017). This pattern suggests the possibility that there is more guessing in the error data than can be accounted for by the prevalence of lowest-confidence responses. But because the model is forced to assume guessing only occurs for the lowest-confidence responses it must compromise by underestimating guessing and overestimating the prevalence of very low confidence. With this model-based approach, strong assumptions about how confidence ratings map onto guessing and precision may have driven the conclusion of Van den Berg et al. (2017) that confidence closely tracks the precision of working memory representations.

In another recent study (Honig et al., 2020) suggested that confidence tracks the precision of working memory representations of color by asking participants to place “confidence bands” around the reported colors. This task is much like a betting game where the goal is to ensure that the true color is contained within the confidence band. They observed a correlation between the size of confidence bands and behavioral accuracy, suggesting that participants know the accuracy of their internal color representations. A similar relationship is found between betting distributions and accuracy (Jabar & Fougnie, 2022). But because there was evidence of pure guessing in the behavioral reports, and such guessing might explain why confidence is related to behavioral accuracy, a modeling approach was used to disentangle whether confidence really tracked the precision of color reports or merely reflected guessing. The model comparison results suggested that confidence tracked the precision of behavioral reports in addition to tracking guessing behavior. However, as in Van den Berg et al. (2017) the model assumed that guessing was equivalent to having zero precision, and as such assumed that confidence bands would always be large when a guess occurred. The distribution of confidence ratings that arose from guessing was determined by model parameters, as the lowest possible confidence ratings (i.e. confidence bands that spanned nearly the entire color space) were rare in the data even with the clear presence of guessing. We find a similar result here whereby guesses correspond to low but not necessarily zero confidence, confirming that confidence ratings arise from complex decision processes. For example, modeling work implicates several sources of information that can result in suboptimal confidence, including choice consistency across tasks or across trials (Boundy-Singer et al., 2022; Rahnev et al., 2015), and even subjective evaluations of the qualities of alternative choices on a given trial (Li & Ma, 2020). Because confidence clearly arises from many types of information and does so in complex ways, simplifying assumptions such as forcing guessing to always produce very low confidence might drive conclusions, particularly by pushing some of the variability between confidence and guessing into other parameters like precision.

In addition to potentially tenuous assumptions about how latent states map onto confidence, assumptions about confidence rating distributions themselves may be problematic. For example, using a modeling approach for confidence ratings in a 2-alternative forced choice task Province and Rouder (2012) concluded that in long-term memory confidence mapped only to guessing behavior but not latent memory strength (which is similar to precision as used here). Their proposal was that a discrete guessing model predicts bi-modal confidence distributions comprised of a low-confidence component arising from guesses and a high-confidence component arising from non-guesses, and that changes across conditions should only cause changes in the proportion of responses arising from each of these components. Alternatively, a continuous model predicts that the center of confidence distributions should shift up and down as performance changes. However, our motion identification data suggests that such assumptions may be unwarranted. Figure 11 shows distributions of confidence ratings. For transparent motion (left) the distributions look bimodal, and it seems that changing coherence leads to different proportions of responses in the high and low modes with no change in the location of those components. This pattern in confidence ratings is exactly as would be expected if these conditions differ only in the rate of guessing, as is also suggested by the behavioral data here and in previous work (M. L. Green & Pratte, 2022). However, for Gaussian motion the behavioral data clearly shows a substantial difference in precision across conditions, but the distributions of confidence ratings also appear to be bi-modal for Gaussian motion stimuli, and show only very subtle differences in the locations of the modes (Figure 11, right). This failure to find a dissociation between transparent and Gaussian motion in the distributions of confidence ratings suggests that these distributions may not be diagnostic of the underlying processes. For example, even if confidence judgments track the continuous latent strength of a given stimulus it is possible that people place a threshold on their internal precision, essentially transforming a continuous space into low or high confidence response depending on whether precision is above or below the threshold. As such, we worry that previous studies which used a modeling approach to suggest a link between precision and confidence (Honig et al., 2020; Van den Berg et al., 2017) and models proposing a link between guessing and confidence (Province & Rouder, 2012) may suffer from assumptions about the link between internal representations and confidence judgments.

Figure 11.

A) Confidence distributions for transparent motion in Experiment 1 are bimodal. As motion coherence is increased, the proportion of low confidence ratings decrease and the proportion of high confidence ratings increase. B) A similar pattern in confidence distributions is seen for Gaussian motion, even though the behavioral data suggests that manipulating coherence primarily affects the precision of responses rather than guess rates.

Our approach to analyzing behavioral errors did make parametric assumptions by using the (Zhang & Luck, 2008) mixture model to characterize how guessing and precision manifest in behavioral errors. Despite the widespread use of this model and its underlying theory in the study of visual working memory (e.g. see Luck & Vogel, 2013), several alternatives have been proposed that make substantially different assumptions. Many of these models eschew the existence of guessing altogether, and instead explain the long tails in error distributions as reflecting very low precision on some trials (e.g. Bays, 2014; Schurgin et al., 2020; Van den Berg et al., 2012). In working memory studies the precision of reports is often relatively low, making it difficult to discern whether large errors arise from pure guessing or low precision. However, for the transparent motion task (Experiment 1) the data provide compelling evidence for a mixture of highly accurate responses tightly centered around zero error, and pure guessing reports that follow a uniform distribution and that increase in prevalence when motion coherence is lowered. Moreover, the finding that coherence affects guess rates for transparent motion but primarily affects precision for Gaussian motion provides a clear dissociation (see also M. L. Green & Pratte, 2022), suggesting that guess rate and precision can not be reduced to a single process as is assumed in alternative models. But even though the Zhang & Luck mixture model provides an excellent fit to the motion identification data, it is certainly possible that more accurate models of error distributions could be developed and used to better characterize how performance changes with confidence. Ideally such measurement models would be motivated by theories of global motion perception, and the pattern of results showing stark differences in how transparent and Gaussian motion is perceived provides a great deal of constraint for developing such theoretical approaches.

We have proposed that lowering the coherence of a Gaussian motion stimulus lowers precision by interfering with the pooling of location motion signals into an overall mean direction, a process that is often at the heart of models of global motion perception (Heeger, 1987; Jazayeri & Movshon, 2006; Van Santen & Sperling, 1984). With more noise in each local element, the average of these elements over space will naturally be less precise, producing more error in reports of the average heading direction. Alternatively, the all-or-none perception of transparent motion may reflect the success or failure of a motion segmentation process, whereby highly similar local motion signals are bound together to form the percept of a single moving object (Braddick, 1993; Grossberg et al., 2001; Tlapale et al., 2010). But when this grouping fails the perception of global motion is completely absent, as if the perceptual system decides that there is not enough evidence to warrant building an object from a few noisy motion signals. Surprisingly, such failures are common even at moderately high motion coherence levels, suggesting that the success or failure to build a coherent global motion is not dictated by a perceptual threshold in the Fechnarian sense. That is, transparent motion does not simply go undetected at low coherence levels but is easily detected once coherence passes some threshold. Instead, motion segmentation appears to be similar to other high-level cognitive phenomena that are thought to exhibit all-or-none categorical perception (see e.g. Goldstone & Hendrickson, 2010). A classic example is phoneme perception, whereby utterances that fall halfway between /be/ and /ge/ are not perceived as such, but instead are clearly heard as one of the phonemes or the other (Liberman et al., 1957). It seems reasonable that just as you should perceive a language that is made up of discrete phonemes in an all-or-none manner, in a world comprised of discrete moving objects you would benefit from strictly carving up local visual elements as either belonging to particular objects completely or not at all.

In most studies the data are aggregated across trials within a condition, as we do here to analyze the overall effects of motion coherence. But if there are systematic differences in performance across trials, whereby motion is more easily identified for some particular stimuli than others, then averaging can distort the results whether using a signal detection analysis of 2AFC tasks (Rouder & Haaf, 2019), discrete confidence ratings to draw ROCs (Pratte et al., 2010), or collecting continuous reports (Pratte et al., 2017). Very few studies look at how performance varies across particular random dot motion displays, but the results of our trial-wise analysis demonstrate that there is substantial variability. Studies of orientation perception suggest that all such variability might be driven by stimulus-specific factors such as the oblique effect (Shen & Ma, 2019) whereby performance is worse for oblique versus cardinal orientations (Appelle, 1972). Similar oblique effects have been observed in motion perception (Ezzo et al., 2023; Gros et al., 1998) and appear to drive at least some of the trial-to-trial variability observed here (see supplementary Figures S2 and S4). However, in other domains we have observed substantial sources of trial-to-trial variability that are not due to such stimulus parameters. For example, in a working memory task performance was markedly improved if the tested feature on a trial was the same as that on the previous trial (Pratte & Green, 2023). Such carryover effects could occur in simple perceptual tasks if, for example, similar true motion directions are presented back to back. Similarly here, for random-dot stimuli like the transparent motion stimulus, properties of the visual system have been shown to cause motion reports 180° from the true motion direction (Bae & Luck, 2022), which can be seen to some degree in Experiments 1 (Figure 3A) and 3 (Figure 9A), and result in high confidence. Although such systematic opposite direction errors occur infrequently, they nonetheless contribute to some of the trial-to-trial variability in transparent motion performance. However, the trial-specific analyses do not clearly indicate any particular conditions under which these errors occur (such as frequently confusing leftward and rightward motion), suggesting that these illusory motion reversals may be driven by internal processes rather than particular stimulus conditions. Substantial modeling work would be necessary to accurately model these 180° responses along with the numerous other sources of the trial-specific effects observed here, but doing so could provide a window into the mechanisms that govern global motion perception.

Across three studies, confidence perfectly tracked guessing behavior when motion perception arose from a discrete, all-or-none segmentation process, and to some degree tracked precision when motion perception arose from a continuous local-to-global pooling process. Although we suspect that this pattern would hold for other stimulus domains and tasks where discrete and continuous processes can be dissociated, it is possible that confidence does track precision more closely with other stimuli (e.g. color) or in other domains like working memory tests where multiple items are shown simultaneously. It is also possible that alternative approaches to measuring confidence, such as having participants draw confidence bands or place wagers, would be more sensitive to precision than confidence ratings and reveal a stronger relationship with precision. However, our results suggest that even if such a relationship does exist between confidence and precision across trials, it would be far weaker than the nearly perfect relationship between confidence and guessing. The majority of previous studies of motion perception (and perception more broadly) have relied on two-alternative forced choice tasks, but such designs do not allow for guessing behavior to be distinguished from the precision of responses that are not guesses. Going forward, we propose that a lot could be gained by using paradigms like continuous report, and by developing models that can link such data to theoretical models of perception.