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PubMed2006

Differential effects of the stimulus sequence on CNV and P300.

During the presentation of stimulus sequences in oddball paradigms, participants tend to implicitly evaluate the conditional probability of target occurrence. It is not sure, however, if subjective estimation of conditional probabilities modulates target expectancy and target processing in the same manner. In the present experiment, the amplitudes of CNV and P300 were studied separately to compare preparatory and decision mechanisms and their sensitivity to variations in target probability. Amplitudes of both components were measured at different positions in the stimulus sequence, which modulates target probability as a function of distance from the preceding target. Results showed shorter RTs with increased probability of target occurrence (that is, with longer distance to the previous target). CNV amplitude was low when target probability was zero and maximal when the occurrence of a target was possible, regardless of its probability. Conversely, a gradual increase with augmenting probability was observed for P300 amplitude. Thus, preparatory activity as reflected by the CNV showed an all or nothing response to variations in probability, whereas action closure mechanisms, indexed by P300 components, were found to be more sensitive to subtle differences in stimulus expectancy.

Adult↗
PubMed2005

The effect of numerical distance and stimulus probability on ERP components elicited by numerical incongruencies in mental addition.

In two experiments, we investigated the effect of the numerical distance of incongruous results from correct results and stimulus probability on the N270/N400 event-related brain potential components. In Experiment 1, 12 subjects saw two one-digit addends and a possible solution and signaled if the proposed result (falling in the range of 3-17) was true or false. Incorrect results could deviate by +/-2 or by +/-9 from the correct answer. The probability of correct results was 50%. Twelve subjects carried out a similar task in Experiment 2 without giving behavioral responses. The probability of incorrect results was 20%, 50% or 80% in different conditions. Both raw potentials and incorrect minus correct difference potentials were analyzed. A fronto-central N3 and a centro-parietal dN3 (incorrect-correct difference) were present for incongruous results in both experiments. The amplitude of the dN3 was not sensitive to numerical distance, but the latency of the dN3 was longer when numerical distance was larger. The overall amplitude of the N3 and of the dN3 was not sensitive to the probability manipulation. However, there was a parietally localized effect of probability on N3 amplitude. The dN3 in mental addition is most probably identical to the arithmetic N400 effect reported earlier in mental multiplication. The distance effect in latency may be a correlate of the discrimination of correct vs. incorrect results. A parietally localized probability effect (right greater than left) was found in the N3 amplitude. The dN3 was insensitive to the probability manipulation. In accord with its insensitivity to stimulus probability, the dN3 seems to be more related to the N400 than to the N2b. Posterior attentional processes sensitive to the allocation of attentional resources may have contributed to the topography of the dN3. The N3 is more related to the detection of expectation violation, while the P3 reflects the ease of identifying stimulus categories.

Adolescent↗
PubMed2006

A Bayesian view of covariation assessment.

When participants assess the relationship between two variables, each with levels of presence and absence, the two most robust phenomena are that: (a) observing the joint presence of the variables has the largest impact on judgment and observing joint absence has the smallest impact, and (b) participants' prior beliefs about the variables' relationship influence judgment. Both phenomena represent departures from the traditional normative model (the phi coefficient or related measures) and have therefore been interpreted as systematic errors. However, both phenomena are consistent with a Bayesian approach to the task. From a Bayesian perspective: (a) joint presence is normatively more informative than joint absence if the presence of variables is rarer than their absence, and (b) failing to incorporate prior beliefs is a normative error. Empirical evidence is reported showing that joint absence is seen as more informative than joint presence when it is clear that absence of the variables, rather than their presence, is rare.

Analysis of Variance↗
PubMed2006

The probability of causal conditionals.

Conditionals in natural language are central to reasoning and decision making. A theoretical proposal called the Ramsey test implies the conditional probability hypothesis: that the subjective probability of a natural language conditional, P(if p then q), is the conditional subjective probability, P(q/p). We report three experiments on causal indicative conditionals and related counterfactuals that support this hypothesis. We measured the probabilities people assigned to truth table cases, P(pq), P(p notq), P( notpq) and P( notp notq). From these ratings, we computed three independent predictors, P(p), P(q/p) and P(q/ notp), that we then entered into a regression equation with judged P(if p then q) as the dependent variable. In line with the conditional probability hypothesis, P(q/p) was by far the strongest predictor in our experiments. This result is inconsistent with the claim that causal conditionals are the material conditionals of elementary logic. Instead, it supports the Ramsey test hypothesis, implying that common processes underlie the use of conditionals in reasoning and judgments of conditional probability in decision making.

Analysis of Variance↗
PubMed2005

Complex slow potential generators in a simplified attention paradigm.

We have recently obtained evidence for complex multifocal, individually variable generators of slow cortical potentials, elicited during performance of visual tasks involving expecting attention, comparison and memory [Basile, L.F.H., Ballester, G., Castro, C.C., and Gattaz, W.F., 2002. Multifocal slow potential generators revealed by high-resolution EEG and current density reconstruction. Int. J. Psychophysiol., 45 (3), 227-240; Basile, L.F.H, Baldo, M.V., Castro, C.C., and Gattaz, W.F. 2003. The generators of slow potentials obtained during verbal, pictorial and spatial tasks. Int. J. Psychophysiol., 48, 55-65]. The cue-target aspect of traditional paradigms for attention studies is equivalent to 'warning S1'-'imperative S2' in slow potential designs. We simplified Posner's spatial cueing task [Posner, M.I. 1980. Orienting of attention.Q. J. Exp. Psychol. Feb;32 (1), 3-25; Posner, M.I., Snyder, C.R., Davidson, B.J. 1980. Attention and the detection of signals. J Exp Psychol. Jun; 109 (2), 160-174] to temporal cuing only, by using visual cues to indicate the mere presence, on a known central position, of the eventual target (17 ms duration, +/-0.3 degrees grey circle). We recorded slow potentials on 12 healthy subjects, by 124-channel EEG system (Neuroscan Inc.), and modeled their generators using current density reconstruction (CDR) by L(p) 1.2 norm minimization ("Curry V4.6", Neurosoft Inc.) applied to the target onset time. MRIs were obtained for each subject for constraining source models to individual brain anatomy. Average slow potentials were computed from above 60 artifact-free EEG-epochs (ISI=1.6 s, average ITI=2.5 s). We tabulated individual cortical current distributions by cytoarchitectonic area of Brodmann, after scaling into negligible, low, moderate and strong local density, based on percentile bands with respect to absolute maximum current. Despite the task's simplicity, the main result was individual variability and complexity in both scalp voltage and cortical current distributions. As observed in our previous studies, there was strong intersubject variability in the exact distribution of task-related cortical activity. Only parietal area 7 bilaterally was non-negligibly active in all subjects (currents above 10% maximum). As opposed to drawing conclusions based on group averaged data, we propose that activity by cytoarchitectonic area be ranked and statistically analysed only after being scaled on each individual. Based on the present results, the concept of a universal attention-related set of cortical areas if restricted to common areas across subjects is challenged, since even area 7 may no longer be common when the sample size becomes larger. We discuss the fact that group averaging may de-emphasize weakly but consistently active areas, and emphasize strongly but inconsistently active ones.

Adult↗
PubMedDate not supplied

Class distributions on SOM surfaces for feature extraction and object retrieval.

A Self-Organizing Map (SOM) is typically trained in unsupervised mode, using a large batch of training data. If the data contain semantically related object groupings or classes, subsets of vectors belonging to such user-defined classes can be mapped on the SOM by finding the best matching unit for each vector in the set. The distribution of the data vectors over the map forms a two-dimensional discrete probability density. Even from the same data, qualitatively different distributions can be obtained by using different feature extraction techniques. We used such feature distributions for comparing different classes and different feature representations of the data in the context of our content-based image retrieval system PicSOM. The information-theoretic measures of entropy and mutual information are suggested to evaluate the compactness of a distribution and the independence of two distributions. Also, the effect of low-pass filtering the SOM surfaces prior to the calculation of the entropy is studied.

Artificial Intelligence↗
PubMed2004

Probability effects on the neural correlates of retrieval success: an fMRI study.

Event-related fMRI was employed to investigate the influence of the relative probability of old and new test items on the neural correlates of recognition memory. Twelve subjects undertook three study-test cycles, each consisting of an identical study phase in which a series of words was encoded in an incidental task, followed by a test phase in which yes/no recognition judgments were made to a mixture of studied (old) and unstudied (new) words. The ratio of old to new words differed in each test phase, and was either 25:75, 50:50, or 75:25. In lateral inferior and medial parietal cortex, and the posterior cingulate, greater activity was elicited by correctly classified old than new items independently of old:new ratio. By contrast, in other regions, including anterior, dorsolateral, and ventrolateral prefrontal cortex, differences in the activity elicited by old and new items varied according to old:new ratio, demonstrating in some cases a complete crossover interaction. The results suggest that differential activity elicited by old and new test items is likely to support successful recognition in only a subset of the regions identified in previous studies as exhibiting such differences. In other regions, most notably prefrontal cortex, differences in the activity elicited by old and new items appear to reflect processes that are contingent upon, rather than in support of, successful recognition.

Adolescent↗
PubMed2000

Taking advice, using information and knowing what you are doing.

Subjective descriptions of judgment policies have been found to be imperfect. This could be because subjective weights are obtained on just a single occasion after all judgments have been completed. It could also be because people have tended to state their perception of an ideal way of responding rather than their perception of how they actually responded. Finally, it could be because they experience difficulty in relating variation in stimulus dimensions to variation in quite different response dimensions. In our task, people made sales forecasts on the basis of four pieces of information. They also stated the weight they placed on each one and the weight they should have placed on it. The means of weights stated on each trial were more appropriate than those stated at the end of all trials. Stated actual weights were very similar to stated ideal weights. Weights were more appropriate when forecasts and cues varied along the same dimension than when they did not. Thus, our results are consistent with the view that all three factors affect people's ability to provide subjective descriptions of their judgment policies.

Adult↗
PubMed2000

Probability ratings in claustrophobic patients and normal controls.

Forty-nine DSM-IV diagnosed claustrophobics and 49 sex- and age-matched community controls, without any current or past psychiatric disorder, were asked to estimate the probability that three types if events would occur if they were in the described situations. The events were claustrophobic, generally negative, and positive in nature. The results showed that claustrophobics significantly overestimated the probability of events they specifically feared, i.e. the claustrophobic events, while there was no difference between the groups regarding generally negative events and positive events. This finding remained when the higher scores for claustrophobics on the Claustrophobia scale and the Anxiety Sensitivity Index were covaried out. The conclusion that can be drawn is that claustrophobics' probability ratings are characterized by distortions that are specifically connected to anxiety-arousing events and not negative events in general. The hypothesis is proposed that this may be explained by an exaggerated use of simplified rules-of-thumb for probability estimations that build on availability in memory, simulation, and representativity.

Adult↗
PubMed2001

Solving probabilistic and statistical problems: a matter of information structure and question form.

Is the human mind inherently unable to reason probabilistically, or is it able to do so only when problems tap into a module for reasoning about natural frequencies? We suggest an alternative possibility: naive individuals are able to reason probabilistically when they can rely on a representation of subsets of chances or frequencies. We predicted that naive individuals solve conditional probability problems if they can infer conditional probabilities from the subset relations in their representation of the problems, and if the question put to them makes it easy to consider the appropriate subsets. The results of seven studies corroborated these predictions: when the form of the question and the structure of the problem were framed so as to activate intuitive principles based on subset relations, naive individuals solved problems, whether they were stated in terms of probabilities or frequencies. Otherwise, they failed with both sorts of information. The results contravene the frequentist hypothesis and the evolutionary account of probabilistic reasoning.

Adult↗
PubMed2002

Why are we good at detecting cheaters? A reply to Fodor.

It is argued that the recent criticism by Fodor (Cognition 75 (2000) 29) of "cheater detection" in the Wason selection task is based upon a false presumption about what the task entails. Fodor compares two different ways of presenting the task, rather than two different task domains (social and non-social). Consequently, the conclusion that the selection task can tell us nothing about either the architecture or the history of cognition is invalid. Fodor's explanation of the Wason selection task is examined experimentally and compared to predictions derived from social contract theory (Cognition 31 (1989) 187). It is concluded that, although Fodor's variant of the Wason selection task improves performance, this improvement is independent of the task domain and is insufficient to account for the "cheater detection" effect.

Attention↗
PubMed2002

Representation facilitates reasoning: what natural frequencies are and what they are not.

A good representation can be crucial for finding the solution to a problem. Gigerenzer and Hoffrage (Psychol. Rev. 102 (1995) 684; Psychol. Rev. 106 (1999) 425) have shown that representations in terms of natural frequencies, rather than conditional probabilities, facilitate the computation of a cause's probability (or frequency) given an effect--a problem that is usually referred to as Bayesian reasoning. They also have shown that normalized frequencies--which are not natural frequencies--do not lead to computational facilitation, and consequently, do not enhance people's performance. Here, we correct two misconceptions propagated in recent work (Cognition 77 (2000) 197; Cognition 78 (2001) 247; Psychol. Rev. 106 (1999) 62; Organ. Behav. Hum. Decision Process. 82 (2000) 217): normalized frequencies have been mistaken for natural frequencies and, as a consequence, "nested sets" and the "subset principle" have been proposed as new explanations. These new terms, however, are nothing more than vague labels for the basic properties of natural frequencies.

Bayes Theorem↗
PubMed2002

Chances and frequencies in probabilistic reasoning: rejoinder to Hoffrage, Gigerenzer, Krauss, and Martignon.

Do individuals unfamiliar with probability and statistics need a specific type of data in order to draw correct inferences about uncertain events? Girotto and Gonzalez (Cognition 78 (2001) 247) showed that naive individuals solve frequency as well as probability problems, when they reason extensionally, in particular when probabilities are represented by numbers of chances. Hoffrage, Gigerenzer, Krauss, and Martignon (Cognition 84 (2002) 343) argued that numbers of chances are natural frequencies disguised as probabilities, though lacking the properties of true probabilities. They concluded that we failed to demonstrate that naive individuals can deal with true probabilities as opposed to natural frequencies. In this paper, we demonstrate that numbers of chances do represent probabilities, and that naive individuals do not confuse numbers of chances with frequencies. We conclude that there is no evidence for the claim that natural frequencies have a special cognitive status, and the evolutionary argument that the human mind is unable to deal with probabilities.

Biological Evolution↗
PubMed2002

Children's predictions of consistency in people's actions.

Past research suggests that young children are often reluctant to generalize about people's behavior. Three experiments involving 102 4-5-year-olds, 84 7-8-year-olds, and 107 adults explored the conditions under which inductive inferences about people are made. There was an age-based increase in propensity to predict consistency in psychological/intentional causal relations. Children often predicted change; people would behave differently in the future than they did in the past. Younger children limited predictions of consistency to non-psychological contexts. Older children showed some appreciation of stable motivations (e.g. traits, preferences). The results are consistent with the hypothesis that children's theories of mind emphasize situational influences, with personal influences appearing in middle-childhood.

Awareness↗
PubMed2003

The influence of hierarchy on probability judgment.

Consider the task of predicting which soccer team will win the next World Cup. The bookmakers may judge Brazil to be the team most likely to win, but also judge it most likely that a European rather than a Latin American team will win. This is an example of a non-aligned hierarchy structure: the most probable event at the subordinate level (Brazil wins) appears to be inconsistent with the most probable event at the superordinate level (a European team wins). In this paper we exploit such structures to investigate how people make predictions based on uncertain hierarchical knowledge. We distinguish between aligned and non-aligned environments, and conjecture that people assume alignment. Participants were exposed to a non-aligned training set in which the most probable superordinate category predicted one outcome, whereas the most probable subordinate category predicted a different outcome. In the test phase participants allowed their initial probability judgments about category membership to shift their final ratings of the probability of the outcome, even though all judgments were made on the basis of the same statistical data. In effect people were primed to focus on the most likely path in an inference tree, and neglect alternative paths. These results highlight the importance of the level at which statistical data are represented, and suggest that when faced with hierarchical inference problems people adopt a simplifying heuristic that assumes alignment.

Adult↗
PubMed2000

Gigerenzer's normative critique of Kahneman and Tversky.

Gigerenzer has argued that it may be inappropriate to characterize some of the biases identified by Kahneman and Tversky as "errors" or "fallacies," for three reasons: (a) according to frequentists, no norms are appropriate for single-case judgments because single-case probabilities are meaningless; (b) even if single-case probabilities make sense, they need not be governed by statistical norms because such norms are "content-blind" and can conflict with conversational norms; (c) conflicting statistical norms exist. I try to clear up certain misunderstandings that may have hindered progress in this debate. Gigerenzer's main point turns out to be far less extreme than the position of "normative agnosticism" attributed to him by Kahneman and Tversky: Gigerenzer is not denying that norms appropriate for single-case judgments exist, but is rather complaining that the existence and the nature of such norms have been dogmatically assumed by the heuristics and biases literature. In response to this complaint I argue that single-case probabilities (a) make sense and (b) are governed by probabilistic norms, and that (c) the existence of conflicting statistical norms may be less widespread and less damaging than Gigerenzer thinks.

Bias↗
PubMed2002

On the impact of different number representations in the number bisection task.

The number bisection task--in which the numerical middle of two other numbers has to be determined (e.g., 6 is the numerical middle of 4 and 8)--has recently been used in neuropsychological case studies in addition to the number comparison task to assess quantitative capabilities in number processing. While factors determining difficulty in normal participants have often been systematically investigated in the number comparison task, this has not yet been done in the number bisection task. Based on a pilot study by van Herten (1999), we extracted four factors that we hypothesized to modulate difficulty in a verification version of the number bisection task in normal participants: Multiplicativity (whether or not the three numbers are part of a multiplication table), range (distance between the smallest and the largest number) for bisectable number triplets as well as distance of the middle number to the numerical middle, and bisection possibility for non-bisectable triplets. In the current study, we obtained large effects for all four factors on RT and accuracy data and some interesting interactions in normal participants. In a regression analysis, we additionally observed inhibitory effects of decade crossing and of ten inclusion (whether or not one of the three numbers was a decade number). We discuss the impact of these results for the use of the number bisection task as an assessment tool in neuropsychology. Finally, we examine the consequences of these results for models of number processing.

Adult↗
PubMed2000

Impaired planning but intact decision making in early Huntington's disease: implications for specific fronto-striatal pathology.

Previous neuropsychological data have suggested that deficits in early Huntington's disease (HD) include executive impairments, which often are linked with frontal-lobe dysfunction. This study sought to investigate the profile of cognitive deficits using two computerised tasks whose performance is known to rely on intact functions of separate areas of the prefrontal cortex. Twenty patients with early HD and 20 matched controls were given the one-touch Tower of London, a stringent measure of visuo-spatial planning, and a decision making task, which involved selecting and gambling on outcomes on the basis of their differing probabilities. Patients were significantly less accurate than controls on the planning test, which is sensitive to frontal lobe lesions and is strongly associated with the dorsolateral prefrontal cortex in functional imaging studies. On the decision making task, patients were unimpaired on the quality of their decision making, in contrast to previous reports of impairment on this task in patients with ventromedial prefrontal cortex lesions. This dissociation of performance is discussed in terms of the usual path of progression of HD through the striatum and the resultant pattern of disruption of the functioning of the different cortico-striatal functional loops.

Adult↗