Noise Increases Anchoring Effects

We introduce a theoretical framework distinguishing between anchoring effects, anchoring bias, and judgmental noise: Anchoring effects require anchoring bias, but noise modulates their size. We tested this framework by manipulating stimulus magnitudes. As magnitudes increase, psychophysical noise due to scalar variability widens the perceived range of plausible values for the stimulus. This increased noise, in turn, increases the influence of anchoring bias on judgments. In 11 preregistered experiments ( N = 3,552 adults), anchoring effects increased with stimulus magnitude for point estimates of familiar and novel stimuli (e.g., reservation prices for hotels and donuts, counts in dot arrays). Comparisons of relevant and irrelevant anchors showed that noise itself did not produce anchoring effects. Noise amplified anchoring bias. Our findings identify a stimulus feature predicting the size and replicability of anchoring effects—stimulus magnitude. More broadly, we show how to use psychophysical noise to test relationships between bias and noise in judgment under uncertainty.

High Contrast Allows the Retina to Compute More Than Just Contrast

The goal of sensory processing is to represent the environment of an animal. All sensory systems share a similar constraint: they need to encode a wide range of stimulus magnitudes within their narrow neuronal response range. The most efficient way, exploited by even the simplest nervous systems, is to encode relative changes in stimulus magnitude rather than the absolute magnitudes. For instance, the retina encodes contrast, which are the variations of light intensity occurring in time and in space. From this perspective, it is easy to understand why the bright plumage of a moving bird gains a lot of attention, while an octopus remains motionless and mimics its surroundings for concealment. Stronger contrasts simply cause stronger visual signals. However, the gains in retinal performance associated with higher contrast are far more than what can be attributed to just a trivial linear increase in signal strength. Here we discuss how this improvement in performance is reflected throughout different parts of the neural circuitry, within its neural code and how high contrast activates many non-linear mechanisms to unlock several sophisticated retinal computations that are virtually impossible in low contrast conditions.

Age-Related Differences in Time Reproduction Reflect Attentional Control but not Stimulus Magnitude

Research on age-related differences in time perception are mixed, with the strongest results indicating that age group differences are magnified based on the cognitive complexity of the specific task design. This raises the possibility that age-related differences in time perception may reflect downstream effects of ‘non-temporal’ factors such as stimulus magnitude, selective attention, and memory requirements. The current study explored this possibility with two experiments conducted on both younger and older adults that systematically varied stimulus magnitude and attentional demands. The first experiment was a focused–attention time reproduction task in which participants reproduced the temporal duration of a white rectangle with an embedded four-digit number. The stimulus magnitude varied from small (1000–3999) to medium (4000–6999) to large (7000–9999) digits. The second experiment was a divided-attention variant of the first experiment, where the participant either reported the temporal duration or recalled the number sequence embedded in the stimulus. Analyses indicated minimal age group differences under focused-attention conditions, but under divided-attention conditions there were age-related decreases in time estimates and temporal precision. Stimulus magnitude operated as predicted by the number–time association (NTA) effect, in which larger stimulus magnitudes induce longer duration estimates. Surprisingly, the NTA effect was evident similarly for both age groups and across both experiments. Exploratory analyses found evidence for age group equivalence in the positive influence of short-term memory on time reproduction, but age-related differences in the correlative link with cognitive processing speed. We conclude that age-related differences in our time reproduction task reflects attentional control factors but not stimulus magnitude.

Limitations of Proposed Signatures of Bayesian Confidence

The Bayesian model of confidence posits that confidence reflects the observer's posterior probability that the decision is correct. Hangya, Sanders, and Kepecs ( 2016 ) have proposed that researchers can test the Bayesian model by deriving qualitative signatures of Bayesian confidence (i.e., patterns that one would expect to see if an observer were Bayesian) and looking for those signatures in human or animal data. We examine two proposed signatures, showing that their derivations contain hidden assumptions that limit their applicability and that they are neither necessary nor sufficient conditions for Bayesian confidence. One signature is an average confidence of 0.75 on trials with neutral evidence. This signature holds only when class-conditioned stimulus distributions do not overlap and when internal noise is very low. Another signature is that as stimulus magnitude increases, confidence increases on correct trials but decreases on incorrect trials. This divergence signature holds only when stimulus distributions do not overlap or when noise is high. Navajas et al. ( 2017 ) have proposed an alternative form of this signature; we find no indication that this alternative form is expected under Bayesian confidence. Our observations give us pause about the usefulness of the qualitative signatures of Bayesian confidence. To determine the nature of the computations underlying confidence reports, there may be no shortcut to quantitative model comparison.

Intact Dynamic Visual Capture in People With One Eye

Observing motion in one modality can influence the perceived direction of motion in a second modality (dynamic capture). For example observing a square moving in depth can influence the perception of a sound to increase in loudness. The current study investigates whether people who have lost one eye are susceptible to audiovisual dynamic capture in the depth plane similar to binocular and eye-patched viewing control participants. Partial deprivation of the visual system from the loss of one eye early in life results in changes in the remaining intact senses such as hearing. Linearly expanding or contracting discs were paired with increasing or decreasing tones and participants were asked to indicate the direction of the auditory stimulus. Magnitude of dynamic visual capture was measured in people with one eye compared to eye-patched and binocular viewing controls. People with one eye have the same susceptibility to dynamic visual capture as controls, where they perceived the direction of the auditory signal to be moving in the direction of the incongruent visual signal, despite previously showing a lack of visual dominance for audiovisual cues. This behaviour may be the result of directing attention to the visual modality, their partially deficient sense, in order to gain important information about approaching and receding stimuli which in the former case could be life-threatening. These results contribute to the growing body of research showing that people with one eye display unique accommodations with respect to audiovisual processing that are likely adaptive in each unique sensory situation.

Limitations of proposed signatures of Bayesian confidence

The Bayesian model of confidence posits that confidence is the observer’s posterior probability that the decision is correct. It has been proposed that researchers can gain evidence in favor of the Bayesian model by deriving qualitative signatures of Bayesian confidence, i.e., patterns that one would expect to see if an observer was Bayesian, and looking for those signatures in human or animal data. We examine two proposed qualitative signatures, showing that their derivations contain hidden assumptions that limit their applicability, and that they are neither necessary nor sufficient conditions for Bayesian confidence. One signature is an average confidence of 0.75 for trials with neutral evidence. This signature only holds when class-conditioned stimulus distributions do not overlap and internal noise is very low. Another signature is that, as stimulus magnitude increases, confidence increases on correct trials but decreases on incorrect trials. This signature is also dependent on stimulus distribution type. There is an alternative form of this signature that has been applied in the literature; we find no indication that it is expected under Bayesian confidence, which resolves an ostensible discrepancy. We conclude that, to determine the nature of the computations underlying confidence reports, there may be no shortcut to quantitative model comparison.