Differences between probability and frequency judgments: The role of individual differences in working memory capacity

Most theories of probability judgment assume that judgments are made by comparing the strength of a focal hypothesis relative to the strength of alternative hypotheses. In contrast, research suggests that frequency judgments are assessed using a non-comparative process; the strength of the focal hypothesis is assessed without comparing it to the strength of alternative hypotheses. We tested this distinction between probability and frequency judgments using the alternative outcomes paradigm (Windschitl, Young, & Jenson, 2002). Assuming that judgments of probability (but not judgments of frequency) entail comparing the focal hypothesis with alternative hypotheses, we hypothesized that probability judgments would be sensitive to the distribution of the alternative hypotheses and would be negatively correlated with individual differences in working memory (WM) capacity. In contrast, frequency judgments should be unrelated to the distribution of the alternatives and uncorrelated with WM-capacity. Results supported the hypotheses.     

Probability judgment and subadditivity: The role of working memory capacity and constraining retrieval

In this research, we examined the role that individual differences in working memory (WM) capacity, the strength of alternatives, and time constraints play in probability judgment and subadditivity. With a laboratory-based learning task, Experiment 1 revealed that the degree to which participants’ probability judgments were subadditive was negatively correlated with a measure of WM capacity, even when variance due to short-term memory capacity was removed. In addition, participants were more subadditive when the viable alternatives were all rather weak. Experiment 2 extended the WM-capacity-subadditivity correlation to a population judgment task and revealed that subadditivity increases when the judgment task is performed under time constraints. Results support a model that assumes that people make probability judgments by comparing the focal hypothesis with relevant alternatives retrieved from long-term memory and that people high in WM span include more alternatives in the comparison process. Time constraints are assumed to truncate the alternative generation process, leading to fewer alternatives being recalled from long-term memory.     

Context cue focality influences strategic prospective memory monitoring

Monitoring the environment for the occurrence of prospective memory (PM) targets is a resource-demanding process that produces cost (e.g., slower responding) to ongoing activities. However, research suggests that individuals are able to monitor strategically by using contextual cues to reduce monitoring in contexts in which PM targets are not expected to occur. In the current study, we investigated the processes supporting context identification (i.e., determining whether or not the context is appropriate for monitoring) by testing the context cue focality hypothesis. This hypothesis predicts that the ability to monitor strategically depends on whether the ongoing task orients attention to the contextual cues that are available to guide monitoring. In Experiment 1, participants performed an ongoing lexical decision task and were told that PM targets (TOR syllable) would only occur in word trials (focal context cue condition) or in items starting with consonants (nonfocal context cue condition). In Experiment 2, participants performed an ongoing first letter judgment (consonant/vowel) task and were told that PM targets would only occur in items starting with consonants (focal context cue condition) or in word trials (nonfocal context cue condition). Consistent with the context cue focality hypothesis, strategic monitoring was only observed during focal context cue conditions in which the type of ongoing task processing automatically oriented attention to the relevant features of the contextual cue. These findings suggest that strategic monitoring is dependent on limited-capacity processing resources and may be relatively limited when the attentional demands of context identification are sufficiently high.     

The Δ–∑ hypothesis: How contrast and reinforcement rate combine to generate suboptimal choice

When given a choice between two alternatives, each offering food after the same delay with different but signaled probabilities, pigeons often prefer the low probability alternative. This preference is surprising because pigeons fail to maximize the rate of food intake; they exhibit a suboptimal preference. We advance a new explanation, the Δ–∑ hypothesis, in which the difference in probability of reinforcement within terminal links (Δ) and the overall reinforcement probability rate of each alternative (∑) are the key variables responsible for such suboptimal preference. We tested the Δ–∑ hypothesis in two experiments. In Experiment 1, we manipulated the Δs while maintaining constant all other parameters of the task, in particular the ∑s. We predicted a preference for the alternative with the larger Δ. In Experiment 2, we examined the effect of the overall reinforcement probabilities, the ∑s, while maintaining constant all other parameters of the task, in particular the Δs. We predicted a preference for the larger ∑. The results of both experiments support the Δ–∑ hypothesis.     

Task self-efficacy and task interest as a function of performance on a gender-neutral task

This study experimentally investigates several hypotheses about the relationships between performance on a gender-neutral task and gender, self-efficacy, performance attributions, and task interest. Ninety-two subjects were randomly assigned to a success or failure condition and attempted to solve a series of easy or difficult anagrams. Results indicated that changes in self-efficacy expectations as a result of task success or failure were in accordance with predictions from self-efficacy theory; 2 × 2 × 4 ANCOVAs, with the pretest as the covariate, were conducted on self-efficacy strength, level, and task interest. Subjects decreased their ratings of self-efficacy and task interest as a result of the failure experience, and the same ratings increased as a result of the success experience. Few gender differences were found, supporting the hypothesis that the sex linkage of the task significantly influences gender differences in self-efficacy. Analyses of global verbal and mathematical ability ratings resulted in the same trends. Finally, women in the success condition were significantly more likely than men in that condition to attribute their performance to luck; women in the failure condition were significantly more likely than men or women in any other group to attribute their failure to their lack of ability. Implications of these results for future research on career self-efficacy were discussed.     

Similarity, confusability, and the density hypothesis

Results from several letter- and digit-identification studies have been interpreted (Appelman & Mayzner, 1982; Krumhansl, 1982) as providing support for the hypothesis that psychological similarity is influenced by the local density of items in the stimulus space. This conclusion is questioned on the grounds that density was not directly manipulated in the studies, thus alternative explanations based on other stimulus characteristics cannot be excluded. In the present article six experiments are reported in which stimulus density was manipulated. In three experiments using similarity ratings and two using discrimination confusions, no effect of stimulus density was found. However, the identification counterpart of one of the discrimination studies did provide evidence of an effect of density on response probabilities. It is concluded that stimulus density can affect identification performance through its influence on the choice process implicit in any identification task, but is not an important determinant of psychological similarity.     

Responsibility and obsessive-compulsive disorder: an experimental test

To test the causal status of responsibility in obsessive-compulsive disorder (OCD), an experiment was executed in which responsibility was experimentally manipulated. OCD patients, non-OCD anxiety controls, and non-patients executed a classification task in either a high or a low responsibility (LoRes) condition. Subjective ratings related to danger and responsibility indicated that the manipulation was successful. Subjective OCD-like experiences and checking behaviors were higher in OCD patients in the high responsibility (HiRes) condition than in all other groups. Although the checking subscale of the Padua Inventory correlated with subjective ratings in the OCD patients in the HiRes condition, it was not associated with checking behaviors. The results confirm the hypothesis that responsibility plays a causal role in OCD.     

Likelihood judgment based on previously observed outcomes: the alternative-outcomes effect in a learning paradigm

Previous research has demonstrated that intuitive perceptions of certainty regarding a focal outcome are sensitive to variations in how evidence supporting nonfocal alternatives is distributed, even when such variations have no bearing on objective probability. We investigated this alternative-outcomes effect in a learning paradigm in which participants made likelihood judgments on the basis of their memory for past observations of relevant outcomes. In Experiment 1, a manipulation of evidence (observed frequencies) across alternative outcomes influenced not only intuitive certainty estimates about a focal outcome but also numeric subjective probabilities. Experiment 2 ruled out the possibility that these effects were attributable to the influence of information loss on frequency estimations. The findings were consistent with the heuristic comparison account, which suggests that the judged likelihood of a focal outcome will be disproportionately influenced by the strength (frequency) of the strongest alternative outcome.     

Absolutely relative or relatively absolute: violations of value invariance in human decision making

Making decisions based on relative rather than absolute information processing is tied to choice optimality via the accumulation of evidence differences and to canonical neural processing via accumulation of evidence ratios. These theoretical frameworks predict invariance of decision latencies to absolute intensities that maintain differences and ratios, respectively. While information about the absolute values of the choice alternatives is not necessary for choosing the best alternative, it may nevertheless hold valuable information about the context of the decision. To test the sensitivity of human decision making to absolute values, we manipulated the intensities of brightness stimuli pairs while preserving either their differences or their ratios. Although asked to choose the brighter alternative relative to the other, participants responded faster to higher absolute values. Thus, our results provide empirical evidence for human sensitivity to task irrelevant absolute values indicating a hard-wired mechanism that precedes executive control. Computational investigations of several modelling architectures reveal two alternative accounts for this phenomenon, which combine absolute and relative processing. One account involves accumulation of differences with activation dependent processing noise and the other emerges from accumulation of absolute values subject to the temporal dynamics of lateral inhibition. The potential adaptive role of such choice mechanisms is discussed.     

Too exhausted to remember: Ego depletion undermines subsequent event‐based prospective memory

Past research has consistently found that people are likely to do worse on high‐level cognitive tasks after exerting self‐control on previous actions. However, little has been unraveled about to what extent ego depletion affects subsequent prospective memory. Drawing upon the self‐control strength model and the relationship between self‐control resources and executive control, this study proposes that the initial actions of self‐control may undermine subsequent event‐based prospective memory (EBPM). Ego depletion was manipulated through watching a video requiring visual attention (Experiment 1) or completing an incongruent Stroop task (Experiment 2). Participants were then tested on EBPM embedded in an ongoing task. As predicted, the results showed that after ruling out possible intervening variables (e.g. mood, focal and nonfocal cues, and characteristics of ongoing task and ego depletion task), participants in the high‐depletion condition performed significantly worse on EBPM than those in the low‐depletion condition. The results suggested that the effect of ego depletion on EBPM was mainly due to an impaired prospective component rather than to a retrospective component.     

Early evidence affects later decisions: Why evidence accumulation is required to explain response time data

Models of decision making differ in how they treat early evidence as it recedes in time. Standard models, such as the drift diffusion model, assume that evidence is gradually accumulated until it reaches a boundary and a decision is initiated. One recent model, the urgency gating model, has proposed that decision making does not require the accumulation of evidence at all. Instead, accumulation could be replaced by a simple urgency factor that scales with time. To distinguish between these fundamentally different accounts of decision making, we performed an experiment in which we manipulated the presence, duration, and valence of early evidence. We simulated the associated response time and error rate predictions from the drift diffusion model and the urgency gating model, fitting the models to the empirical data. The drift diffusion model predicted that variations in the evidence presented early in the trial would affect decisions later in that same trial. The urgency gating model predicted that none of these variations would have any effect. The behavioral data showed clear effects of early evidence on the subsequent decisions, in a manner consistent with the drift diffusion model. Our results cannot be explained by the urgency gating model, and they provide support for an evidence accumulation account of perceptual decision making.     

Motivational sources of confirmation bias in criminal investigations: the need for cognitive closure

In two experiments, criminal investigators (N = 50) and undergraduate students (N = 68) read a set of facts from the preliminary investigation of a homicide case. Participants' initial hypothesis regarding the crime was manipulated by providing background information implying that the prime suspect had a jealousy motive or that there might be an alternative perpetrator. Students displayed a framing effect, such that guilt was ascribed to the prime suspect only when a potential motive was presented, whereas investigators did so regardless of hypothesis, thus being less sensitive to alternative interpretations. Investigators' need for cognitive closure (NFC) moderated the effect of the hypothesis on perceptions of the strength of the evidence against the prime suspect; high (v low) NFC investigators were less likely to acknowledge inconsistencies in the material when presented with a potential motive, but were more likely to do so when made aware of the possibility of an alternative perpetrator. Interpretations are somewhat clouded by the fact that dispositional NFC did not seem to affect in a consistent manner participants' motivation toward the experimental task. Copyright © 2005 John Wiley & Sons, Ltd.     

Asymmetrical scepticism towards criminal evidence: The role of goal‐ and belief‐consistency

Previous demonstrations of asymmetrical scepticism (i.e., that investigators perceive evidence inconsistent [vs. consistent] with the focal hypothesis of a case as less reliable) have failed to account for the underlying mechanism. This study examined whether inconsistent evidence is discredited due to its inconsistency with a prior belief or because it conflicts with the goal to reach closure in a case. Police trainees (N = 107) were presented with a homicide case and judged the reliability of incriminating or exonerating evidence while entertaining a ‘guilty’ or ‘innocent’ hypothesis concerning a suspect. Asymmetrical scepticism was observed in the guilty condition, but not in the innocent condition, partially supporting the goal‐consistency explanation. Implications for the organization of criminal investigations are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

The effects of memory trace strength on eyewitness recall in children with and without intellectual disabilities

Children with mild moderate intellectual disabilities (ID) were compared with typically developing peers of the same chronological age (CA) on an eyewitness memory task in which memory trace strength was manipulated to examine whether increased memory trace strength would benefit those with ID more than those without ID. No evidence was found for this claim or for the notion that different mechanisms are implicated in memory processes for children with ID versus CA controls. Fuzzy-trace theory was also used to contrast question types that probed verbatim memory versus gist memory. Manipulations of trace strength, when used with immediate recall (to reduce the impact of decay), were predicted to improve verbatim memory more than gist memory. The results broadly supported the predictions. Performance was not improved in the stronger trace strength condition on measures of recall that tapped gist memory (e.g., open-ended recall), whereas performance was significantly better in the stronger trace strength condition on two of the three measures of recall that tapped verbatim memory (i.e., closed misleading questions, open-ended specific questions). Differences in performance between the groups were quite marked on several question types, supporting previous findings that those with ID have certain vulnerabilities as potential witnesses compared with peers of the same CA.     

Task set induces dynamic reallocation of resources in visual short-term memory

Successful interaction with the environment requires the ability to flexibly allocate resources to different locations in the visual field. Recent evidence suggests that visual short-term memory (VSTM) resources are distributed asymmetrically across the visual field based upon task demands. Here, we propose that context, rather than the stimulus itself, determines asymmetrical distribution of VSTM resources. To test whether context modulates the reallocation of resources to the right visual field, task set, defined by memory-load, was manipulated to influence visual short-term memory performance. Performance was measured for single-feature objects embedded within predominantly single- or two-feature memory blocks. Therefore, context was varied to determine whether task set directly predicts changes in visual field biases. In accord with the dynamic reallocation of resources hypothesis, task set, rather than aspects of the physical stimulus, drove improvements in performance in the right- visual field. Our results show, for the first time, that preparation for upcoming memory demands directly determines how resources are allocated across the visual field.     

Cognitive Control of Attentional Guidance by Visual and Verbal Working Memory Representations

Both visual and verbal information in working memory guide visual attention toward a memory‐matching object. We tested whether: (a) visual and verbal representations have different effects on the deployment of attention; and (b) both types of representations can be used equally in a top‐down manner. We asked participants to maintain a visual cue or a verbal cue at the beginning of each trial, and ended with a memory task to ensure that each cue was represented actively in working memory. Before the memory task, a visual search task appeared where validity was manipulated as valid, neutral, or invalid. We also manipulated the probability of valid trials (20%, 50%, and 80%), which had been told to the participants prior to the task. Consistent with earlier findings, attentional guidance by visual representations was modulated by the probability. We also found that this was true for verbal representations, and that these effects did not differ between representation types. These results suggest that both visual and verbal representations in working memory can be used strategically to control attentional guidance.     

The suppression of q card selections: Evidence for deductive inference in Wason's Selection Task

The results of three experiments investigating the role of deductive inference in Wason's selection task are reported. In Experiment 1, participants received either a standard one-rule problem or a task containing a second rule, which specified an alternative antecedent. Both groups of participants were asked to select those cards that they considered were necessary to test whether the rule common to both problems was true or false. The results showed a significant suppression of q card selections in the two-rule condition. In addition there was weak evidence for both decreased p selection and increased not-q selection. In Experiment 2 we again manipulated number of rules and found suppression of q card selections only. Finally, in Experiment 3 we compared one- and two-rule conditions with a two-rule condition where the second rule specified two alternative antecedents in the form of a disjunction. The q card selections were suppressed in both of the two-rule conditions but there was no effect of whether the second rule contained one or two alternative antecedents. We argue that our results support the claimthat people make inferences about the unseen side of the cards when engaging with the indicative selection task.     

Distorted subjective reports of stimulus onsets under dual-task conditions: Delayed conscious perception or estimation bias?

We investigated whether selecting a response for one task delays the conscious perception of another stimulus (delayed conscious perception hypothesis). In two experiments, participants watched a revolving clock hand while performing two tasks in close succession (i.e. a dual-task). Two stimuli were presented with varying stimulus onset asynchrony (SOA). After each trial, participants separately estimated the onsets of the two stimuli on the clock face. Across two experiments and four conditions, we manipulated response requirements and assessed their impact on perceived stimulus onsets. Results showed that (a) providing speeded responses to the stimuli did lead to greater SOA-dependent misperceptions of both stimulus onsets as compared to a solely perceptual condition, and (b) that response grouping reduced these misperceptions. Overall, the results provide equivocal evidence for the delayed conscious perception hypothesis. They rather suggest that participants’ estimates of the two stimulus onsets are biased by the interval between their responses.