Are People Naïve Probability Theorists? A Further Examination of the Probability Theory + Variation Model

Two experiments tested predictions derived from the Probability Theory + Variation (PTV) model. PTV model assumes that judgments follow probability theory, but systematic errors arise from noise in the judgments. Experiment 1 compared the PTV model to a configural weighted averaging model in joint probability judgment and found more support for the PTV model in diagnostic cases. Specifically, noise was negatively correlated with semantic coherence and conjunction and disjunction fallacies increased when order effects produced more noise in conjunctions and disjunctions. Consistent with both models, judgments adhered stochastically to the addition law. Contrary to the integration rules of the PTV model, we failed to find increased noise in disjunctions compared to conjunctions. Experiment 2 tested predictions of the PTV model for conditional probability judgment. Consistent with the PTV model, noise was negatively correlated with semantic coherence in conditional probabilities and judgments adhered stochastically to Bayes' theorem. Conversion errors were generally more prevalent than conditional reversals, a finding that is not fully consistent with the PTV model. In general, the quantitative fit of the PTV model was relatively better for overlapping and subset problems compared to identical, independent and mutually exclusive problems, especially for semantic coherence. Copyright © 2014 John Wiley & Sons, Ltd.     

Lost in the supermarket: Quantifying the cost of partitioning memory sets in hybrid search

The items on a memorized grocery list are not relevant in every aisle; for example, it is useless to search for the cabbage in the cereal aisle. It might be beneficial if one could mentally partition the list so only the relevant subset was active, so that vegetables would be activated in the produce section. In four experiments, we explored observers’ abilities to partition memory searches. For example, if observers held 16 items in memory, but only eight of the items were relevant, would response times resemble a search through eight or 16 items? In Experiments 1a and 1b, observers were not faster for the partition set; however, they suffered relatively small deficits when “lures” (items from the irrelevant subset) were presented, indicating that they were aware of the partition. In Experiment 2 the partitions were based on semantic distinctions, and again, observers were unable to restrict search to the relevant items. In Experiments 3a and 3b, observers attempted to remove items from the list one trial at a time but did not speed up over the course of a block, indicating that they also could not limit their memory searches. Finally, Experiments 4a, 4b, 4c, and 4d showed that observers were able to limit their memory searches when a subset was relevant for a run of trials. Overall, observers appear to be unable or unwilling to partition memory sets from trial to trial, yet they are capable of restricting search to a memory subset that remains relevant for several trials. This pattern is consistent with a cost to switching between currently relevant memory items.     

Semantic Coherence and Inconsistency in Estimating Conditional Probabilities

Two studies examined semantic coherence and internal inconsistency fallacies in conditional probability estimation. Problems reflected five distinct relationships between two sets: identical sets, mutually exclusive sets, subsets, overlapping sets, and independent sets (a special case of overlapping sets). Participants estimated P(A), P(B), P(A|B), and P(B|A). Inconsistency occurs when this constellation of estimates does not conform to Bayes' theorem. Semantic coherence occurs when this constellation of estimates is consistent with the depicted relationship among sets. Fuzzy‐trace theory predicts that people have difficulty with overlapping sets and subsets because they require class‐inclusion reasoning. On these problems, people are vulnerable to denominator neglect, the tendency to ignore relevant denominators, making the gist more difficult to discern. Independent sets are simplified by the gist understanding that P(A) provides no information about P(B), and thus, P(A|B) = P(A). The gist for identical sets is that P(A|B) = 1.0, and the gist of mutually exclusive sets is that P(A|B) = 0. In Study 1, identical, mutually exclusive, and independent sets yielded superior performance (in internal inconsistency and semantic coherence) than subsets and overlapping sets. For subsets and overlapping sets, interventions clarifying appropriate denominators generally improved semantic coherence and inconsistency, including teaching people to use Euler diagrams, 2 × 2 tables, or relative frequencies. In Study 2, with problems about breast cancer and BRCA mutations, there was a strong correlation between inconsistency in conditional probability estimation and conjunction fallacies of joint probability estimation, suggesting that similar fallacious reasoning processes produce these errors. Copyright © 2012 John Wiley & Sons, Ltd.     

Digital Piracy: An Examination of Three Measurements of Self-Control

Research has shown a link between digital piracy and self-control. However, the research focuses on only one version of self-control theory. The purpose of the present study is to examine the link between self-control and digital piracy. Using data from 358 college students, this study shows that all 3 measures of self-control help us understand the link between self-control and digital piracy. The results indicate that illuminating the factors that could be inhibitions and developing strong social bonds can reduce the likelihood of digital piracy.     

Auditory and visual memory in musicians and nonmusicians

Numerous studies have shown that musicians outperform nonmusicians on a variety of tasks. Here we provide the first evidence that musicians have superior auditory recognition memory for both musical and nonmusical stimuli, compared to nonmusicians. However, this advantage did not generalize to the visual domain. Previously, we showed that auditory recognition memory is inferior to visual recognition memory. Would this be true even for trained musicians? We compared auditory and visual memory in musicians and nonmusicians using familiar music, spoken English, and visual objects. For both groups, memory for the auditory stimuli was inferior to memory for the visual objects. Thus, although considerable musical training is associated with better musical and nonmusical auditory memory, it does not increase the ability to remember sounds to the levels found with visual stimuli. This suggests a fundamental capacity difference between auditory and visual recognition memory, with a persistent advantage for the visual domain.     

When categories collide: accumulation of information about multiple categories in rapid scene perception

Experiments have shown that people can rapidly determine if categories such as "animal" or "beach" are present in scenes that are presented for only a few milliseconds. Typically, observers in these experiments report on one prespecified category. For the first time, we show that observers can rapidly extract information about multiple categories. Moreover, we demonstrate task-dependent interactions between accumulating information about different categories in a scene. This interaction can be constructive or destructive, depending on whether the presence of one category can be taken as evidence for or against the presence of the other.     

Signal detection evidence for limited capacity in visual search

The nature of capacity limits (if any) in visual search has been a topic of controversy for decades. In 30 years of work, researchers have attempted to distinguish between two broad classes of visual search models. Attention-limited models have proposed two stages of perceptual processing: an unlimited-capacity preattentive stage, and a limited-capacity selective attention stage. Conversely, noise-limited models have proposed a single, unlimited-capacity perceptual processing stage, with decision processes influenced only by stochastic noise. Here, we use signal detection methods to test a strong prediction of attention-limited models. In standard attention-limited models, performance of some searches (feature searches) should only be limited by a preattentive stage. Other search tasks (e.g., spatial configuration search for a "2" among "5"s) should be additionally limited by an attentional bottleneck. We equated average accuracies for a feature and a spatial configuration search over set sizes of 1-8 for briefly presented stimuli. The strong prediction of attention-limited models is that, given overall equivalence in performance, accuracy should be better on the spatial configuration search than on the feature search for set size 1, and worse for set size 8. We confirm this crossover interaction and show that it is problematic for at least one class of one-stage decision models.     

How does our search engine “see” the world? The case of amodal completion

This article illustrates a dissociation between the perceived attributes of an object and the ability of those attributes to guide the deployment of attention in visual search. Orientation is an attribute that guides search. Thus, a vertical line will “pop out” amid horizontal distractors. Amodal completion can create perceptually convincing oriented stimuli when two elements appear to form a complete object partially hidden behind an occluder. Previous work (e.g., Rensink &; Enns, Vision Research, 38, 2489–2505, 1998) has shown a preattentive role for amodal completion in search tasks. Here, we show that orientation based on perceptually compelling amodal completion may fail to guide attention. The broader conclusion is that introspection is a poor guide to the capabilities of our internal search engine.     

Assessing semantic coherence and logical fallacies in joint probability estimates

A constellation of joint probability estimates is semantically coherent when the quantitative relationship among estimates of P(A), P(B), P(A and B), and P(A or B) is consistent with the relationship among the sets described in the problem statement. The possible probability estimates can form an extremely large number of permutations. However, this entire problem space can be reduced to six theoretically meaningful patterns: logically fallacious (conjunction or disjunction fallacies), identical sets (e.g., water and H₂O), mutually exclusive sets (e.g., horses and zebras), subsets (e.g., robins and birds), overlapping sets (e.g., accountants and musicians), and inconsistent overlapping sets. Determining which of these patterns describes any set of probability estimates has been automated using Excel spreadsheet formulae. Researchers may use the semantic coherence technique to examine the consequences of differently worded problems, individual differences, or experimental manipulations. The spreadsheet described above can be downloaded as a supplement from http://brm.psychonomic-journals.org/content/supplemental.