Grouping-Induced Numerosity Biases Vary with Autistic-Like Personality Traits

Individuals with autism spectrum disorder are thought to have a more local than global perceptual style. We used a novel paradigm to investigate how grouping-induced response biases in numerosity judgments depend on autistic-like personality traits in neurotypical adults. Participants judged the numerosity of clouds of dot-pairs connected by thin lines, known to cause underestimation of numerosity. The underestimation bias correlated strongly with autism-spectrum quotient (r = 0.72, Bayes factor > 100), being weaker for participants with high autistic traits. As connecting dots probably activates global grouping mechanisms, causing dot-pairs to be processed as an integrated whole rather than as individual dots, the results suggest that these grouping mechanisms may be weaker in individuals self-reporting high levels of autistic-like traits.

Do estimates of numerosity really adhere to Weber’s law? A reexamination of two case studies

Both humans and nonhuman animals can exhibit sensitivity to the approximate number of items in a visual array or events in a sequence, and across various paradigms, uncertainty in numerosity judgments increases with the number estimated or produced. The pattern of increase is usually described as exhibiting approximate adherence to Weber’s law, such that uncertainty increases proportionally to the mean estimate, resulting in a constant coefficient of variation. Such a pattern has been proposed to be a signature characteristic of an innate “number sense.” We reexamine published behavioral data from two studies that have been cited as prototypical evidence of adherence to Weber’s law and observe that in both cases variability increases less than this account would predict, as indicated by a decreasing coefficient of variation with an increase in number. We also consider evidence from numerosity discrimination studies that show deviations from the constant coefficient of variation pattern. Though behavioral data can sometimes exhibit approximate adherence to Weber’s law, our findings suggest that such adherence is not a fixed characteristic of the mechanisms whereby humans and animals estimate numerosity. We suggest instead that the observed pattern of increase in variability with number depends on the circumstances of the task and stimuli, and reflects an adaptive ensemble of mechanisms composed to optimize performance under these circumstances.

Peer influence on conformity and confidence in a perceptual judgment task

Undergraduate college students were presented with two arrays of dots varying in numerosity on a computer screen and asked to indicate if the arrays differed in number. They also rated their level of confidence in their responses. Trials varied in difficulty based on the size of the arrays. On half of the trials, participants were shown the ostensible responses of confederates to test the effect of peer influence on numerosity judgments and participant confidence. On the other half of the trials, participants received no information about the responses of the confederates to provide a measure of baseline performance. Higher levels of conformity were observed for the difficult trials, on which participants were both less accurate and less confident. However, confidence ratings were influenced by peer judgments for easy trials but not for difficult trials. These data suggest that task difficulty influences conformity when making perceptual judgments.

Repulsive Serial Effects in Visual Numerosity Judgments

We investigated how the approximate perceived numerosity of ensembles of visual elements is modulated by the numerosity of previously viewed ensembles depending on whether the first ensemble is held in visual working memory or not. We show that the numerosity of the previously seen ensemble has a repulsive effect, that is, a stimulus with high numerosity induces an underestimation of the following one and vice versa. This repulsive effect is present regardless of whether the first stimulus is memorized or not. While subtle changes of the experimental paradigm can have major consequences for the nature of interstimulus dependencies in perception, generally speaking the fact that we found such effects in a visual numerosity estimation task confirms that the process by which human observers produce estimates of the number of elements bears analogies to the processes that lead to the perception of visual dimensions such as orientation.

Why try saving the ANS? An alternative proposal

Leibovich et al. propose that continuous magnitudes and a number sense are used holistically to judge numerosity. We point out that their proposal is incomplete and implausible: incomplete, as it does not explain how continuous magnitudes are calculated; implausible, as it cannot explain performance in estimation tasks. We propose that we do not possess a number sense. Instead, we assume that numerosity judgments are accomplished by weighing the different continuous magnitudes constituting numerosity.

The direct octaves rule: Testing a scene-analysis interpretation

A venerable rule of traditional Western part writing is the so-called Direct Octaves Rule (also known as Hidden or Exposed octaves), whereby similar pitch motion (i.e., two or more voices moving in the same direction) to a perfect octave should be avoided unless step motion is used. A number of interpretations have been offered as to why musicians might follow this rule. A traditional account (Fux, 1725/1966) exhibits several inconsistencies. A modern interpretation based on auditory scene analysis appears to have merit. However, this interpretation has yet to be tested empirically. Three experiments test the scene-analysis account using numerosity judgments for complex chords as the dependent measure. In Experiment 1, musician listeners show decreasing accuracy in numerosity judgments when an octave is present in the sonority – as predicted. In experiments 2 and 3, chords were preceded by a single neighboring or distant tone. It was hypothesized that neighboring primes would increase the accuracy of numerosity judgments for octave-containing chords more than distant primes – consistent with the Direct Octaves rule. However, no such facilitation was observed. Nevertheless, a post-hoc test showed improved accuracy when the octave was approached by step motion in highest voice compared with step-approach to the lowest voice. This latter finding is consistent with the most restrictive formulations of the direct octaves rule.