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.

The psychophysics of number arise from resource-limited spatial memory

People can identify the number of objects in small sets rapidly and without error but become increasingly noisy for larger sets. However, the cognitive mechanisms underlying these ubiquitous psychophysics are poorly understood. We present a model of a limited-capacity visual system optimized to individuate and remember the location of objects in a scene which gives rise to all key aspects of number psychophysics, including error-free small number perception and scalar variability for larger numbers. We therefore propose that number psychophysics can be understood as an emergent property of primitive perceptual mechanisms --- namely, the process of identifying and representing individual objects in a scene. To test our theory, we ran two experiments: a change-localization task to measure participants' memory for the locations of objects (Experiment 1) and a numerical estimation task (Experiment 2). Our model accounts well for participants' performance in both experiments, despite only being optimized to efficiently encode where objects are present in a scene. Our results demonstrate that the key psychophysical features of numerical cognition do not arise from separate modules or capacities specific to number, but rather from lower-level constraints on perception which are manifested even in non-numerical tasks.

Nighttime wind and scalar variability within and above an Amazonian canopy

Nocturnal turbulent kinetic energy (TKE) and fluxes of energy, CO2 and O3 between the Amazon forest and the atmosphere are evaluated for a 20-day campaign at the Amazon Tall Tower Observatory (ATTO) site. The distinction of these quantities between fully turbulent (weakly stable) and intermittent (very stable) nights is discussed. Spectral analysis indicates that low-frequency, nonturbulent fluctuations are responsible for a large portion of the variability observed on intermittent nights. In these conditions, the low-frequency exchange may dominate over the turbulent transfer. In particular, we show that within the canopy most of the exchange of CO2 and H2O happens on temporal scales longer than 100 s. At 80 m, on the other hand, the turbulent fluxes are almost absent in such very stable conditions, suggesting a boundary layer shallower than 80 m. The relationship between TKE and mean winds shows that the stable boundary layer switches from the very stable to the weakly stable regime during intermittent bursts of turbulence. In general, fluxes estimated with long temporal windows that account for low-frequency effects are more dependent on the stability over a deeper layer above the forest than they are on the stability between the top of the canopy and its interior, suggesting that low-frequency processes are controlled over a deeper layer above the forest.

Severing Scale Structure from the Adjective

The scale structure of adjectives, whether an adjective measures on an open or closed scale, has certain grammatical consequences and is traditionally captured by encoding scale structure into an adjective’s lexical representation and projecting it into the grammar. However, adjectives can exhibit scalar variability, suggesting that scale structure is not projected from the lexicon, but instead is constructed by the adjective’s structural environment. I review a recent analysis of adjectival scale structure, observing that an economy condition with a single pos morpheme requires polysemy for these variable-behavior adjectives, and propose that splitting the pos morpheme and severing scale structure from the adjective captures scalar variability within a unified lexical entry without economy.

Episodic temporal generalization: A developmental study

Groups of 5-year-olds, 10-year-olds, and adults completed either an episodic temporal generalization task, in which no stimuli were repeated, or a repeated standard temporal generalization task, in which there was a fixed standard that was repeated on every trial. Significant developmental improvements were found on both tasks. In both tasks, gradients of performance over two different stimulus ranges superimposed well when plotted on the same relative scale. Performance was similar for the adults and 10-year-olds across tasks, but the 5-year-olds performed better on the repeated standard task. These findings suggest that perceptual processes are a source of scalar variability in timing, and that there are developmental changes in levels of such variability.

Cognitive euroscience: Scalar variability in price estimation and the cognitive consequences of switching to the euro

The present paper examines the ability to evaluate prices in a familiar currency (French francs, Portugese escudos, or Irish punt) and in an unfamiliar currency (euro). Participants evaluated prices for different items either by selecting the most appropriate price from a set of alternatives (in a timed or not-timed version) or by directly producing a price estimate for each item. The results followed Weber's law: The standard deviation of estimated prices was proportional to their mean. The Weber fraction was stable for the familiar currency in different countries, but was significantly higher for the unfamiliar currency. We suggest that price estimation relies on a learned mapping between items and their prices as represented by distributions of activation on an internal number line. The observed Weber fraction reflects the degree of expertise with a given currency as well as a minimal variability intrinsic to the number line itself.