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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↗
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↗
PubMed2000

Drug abusers show impaired performance in a laboratory test of decision making.

A defining feature of drug addiction is persistent drug use despite long-term adverse consequences. This study examined the performance of drug abusers on a neuropsychological test that requires evaluation of long-term outcomes in the presence of a complex set of mixed reward/punishment contingencies (the Gambling Task). In order to control for generalized deficits related to choice and planning, subjects were also administered the Wisconsin Card Sorting Task. Thirty polysubstance abusers were compared to a comparison group of 24 subjects who did not use illicit drugs of abuse. Drug abusers performed much more poorly on the Gambling Task (net score = 10.2 +/- 4.7, mean +/- s.e.m.) than controls (26.0 +/- 5.3), but did not differ from controls on the Wisconsin Card Sorting Task. The results show that drug abusers are more likely to make maladaptive decisions in the Gambling Task that result in long-term losses exceeding short-term gains. These findings indicate that the Gambling Task may be a useful model in laboratory studies of cognitive dysfunctions associated with drug abuse.

Adult↗
PubMed1997

Transynaptic modulation by insulin-like growth factor I of dendritic spines in Purkinje cells.

Purkinje cells synthesize insulin-like growth factor I and express insulin-like growth factor I receptors during their entire life. An additional source of insulin-like growth factor I for these cells is provided by climbing fiber afferents originating in the inferior olive nucleus. Recently we found that insulin-like growth factor I from the inferior olive is necessary for motor learning processes probably involving Purkinje cell synaptic plasticity. We now studied whether inferior olive insulin-like growth factor I influences the synaptic structure of Purkinje cells, because changes in synaptic morphology are related to neuronal plasticity events. We injected an insulin-like growth factor I antisense in the inferior olive of adult rats, a procedure which we previously found to elicit a significant and reversible decrease of insulin-like growth factor I levels in the contralateral cerebellum. Ultrastructural analysis of the cerebellar cortex of these animals showed a significant reduction in the size of dendritic spines on Purkinje cells of antisense-treated rats compared to controls. The decrease in spine size was linked to a diminished numerical density of dendritic spines on Purkinje cells, without affecting the numerical density of synapses in the molecular layer of the cerebellum. This reduction was not due to a change in the thickness of the molecular layer. Climbing or parallel fiber terminals were also unaffected. Taken together with previous findings, these results support a role for insulin-like growth factor I produced in the inferior olive in the maintenance of Purkinje cell synaptic plasticity.

Animals↗
PubMedDate not supplied

A priori expectancy bias in patients with panic disorder.

BACKGROUND: Several studies have indicated that phobic participants tend to overassociate fear-relevant stimuli and aversive outcomes, i.e, they show a covariation bias. Such a bias seems to be a powerful way to confirm danger expectations and enhance fear. Therefore, a covariation bias might be an important factor in the maintenance of fear. METHODS: To investigate a covariation bias in patients with panic disorder, we had 29 patients and 29 healthy control participants rate the a priori probabilities with which they would expect pictures of mushrooms, spiders, erotic scenes, and emergency situations to be paired with a tone, shock, or nothing. RESULTS: This is the first study to show that patients with panic disorder specifically overestimate the association between panic-relevant stimuli and a following negative consequence. This distorted contingency expectancy represents a panic-specific covariation bias, since it was not observable for other stimuli-consequence combinations and only to a significantly lesser degree in control participants. CONCLUSIONS: The underpinning hypothesis is that overestimation of threat plays a casual role in the origins and maintenance of anxiety. Thus anxiety may induce a covariation bias, which in turn may enhance the perceived threat, which in turn may intensify the anxiety etc. This reciprocal relationship between covariation bias and anxiety may have clinical implications for prediction and treatment in patients with panic disorder.

Adult↗
PubMed2000

Learning non-stationary conditional probability distributions.

While sophisticated neural networks and graphical models have been developed for predicting conditional probabilities in a non-stationary environment, major improvements in the training schemes are still required to make these approaches practically viable.

Models, Neurological↗
PubMed1997

Application of autonomous neural network systems to medical pattern classification tasks.

This paper presents a study of the application of autonomously learning multiple neural network systems to medical pattern classification tasks. In our earlier work, a hybrid neural network architecture has been developed for on-line learning and probability estimation tasks. The network has been shown to be capable of asymptotically achieving the Bayes optimal classification rates, on-line, in a number of benchmark classification experiments. In the context of pattern classification, however, the concept of multiple classifier systems has been proposed to improve the performance of a single classifier. Thus, three decision combination algorithms have been implemented to produce a multiple neural network classifier system. Here the applicability of the system is assessed using patient records in two medical domains. The first task is the prognosis of patients admitted to coronary care units; whereas the second is the prediction of survival in trauma patients. The results are compared with those from logistic regression models, and implications of the system as a useful clinical diagnostic tool are discussed.

Artificial Intelligence↗
PubMed1990

Random number generation by normal, alcoholic and schizophrenic subjects.

Controls (N = 45), schizophrenics (N = 20) and alcoholics (N = 23) were asked to choose at random a number between 1 and 10, 100 times. The correlation matrices of five different randomization indices were used to study within group variation; these matrices were similar for the normal and alcoholic groups, but very different for the schizophrenic group. The differences between the three groups were studied by canonical analysis and, in terms of the canonical variables, the mean performance of the normal group is clearly discriminated from that of the alcoholic and schizophrenic subjects.

Adult↗
PubMed1997

Probabilistic reasoning in deluded, depressed and normal subjects: effects of task difficulty and meaningful versus non-meaningful material.

BACKGROUND: Research indicates that deluded patients 'jump to conclusions' on probabilistic reasoning tasks. Two experiments were carried out with patients suffering from persecutory delusions and depressed and normal controls in order to determine whether this response bias is affected by task difficulty and the meaningfulness of the materials. METHODS: Tasks were variants of those employed by Huq et al. (1988) and Garety et al. (1991). In Experiment 1, subjects judged which of two bags a sequence of coloured beads had been taken from. Difficulty was manipulated by varying the ratios of coloured beads in the bags. In experiment 2, a neutral condition required judgements about coloured beads drawn whereas, in meaningful conditions, subjects had to judge whether personality characteristics described one of two individuals. RESULTS: In Experiment 1, estimates of certainty varied with task difficulty, and there was no evidence of 'jumping to conclusions' in the deluded group. In Experiment 2, all groups reached an initial level of certainty and reduced their estimates of certainty following disconfirmatory evidence more quickly in the meaningful conditions. Both clinical groups expressed higher certainty levels in early trials, and a greater magnitude of reduction in certainty following disconfirmatory information. These group differences were more evident in the meaningful conditions than in the neutral conditions. CONCLUSIONS: Probabilistic reasoning is affected by task difficulty and meaningfulness of materials in both deluded and depressed subjects. Observed reasoning abnormalities were not specific to the deluded group.

Adult↗
PubMed1999

The importance of pragmatic aspects in conditional reasoning.

The importance of pragmatic aspects in conditional reasoning was assessed in the performance of 54 subjects (26 female and 28 male; mean age 17.6 years) on 48 conditional inference problems, using a 3 x 2 x 4 design, with repeated measurements. The independent variables were probability of empirical frequency in the real world, type of conditional rule, and scenario availability. Number of correct responses and subjects' certainty about the correctness of their responses were the dependent variables. The results showed: a) the scenario availability is not sufficient in itself to explain differences in performance, but it does affect the subjects' degree of confidence in their conclusions; b) there is an interaction between probability of empirical frequency in the real world and type of conditional rule on correct performance. The results were contrasted with the predictions made by the mental models theory and its revised version proposed by Evans (1993). These findings support the semantic theories of conditional reasoning.

Adolescent↗
PubMed2002

Random number generation in autism.

This study explored the ability of individuals with autism to generate a unique series of digits. Fourteen low-functioning individuals with autism, 14 intellectually disabled individuals, and 14 postgraduate university students generated a series of pseudo-random digits. Individuals with autism were more likely to repeat previous digits than were either of the control groups. The normal control group, however, was less likely to attempt cycling through all digits before repeating. Accordingly, low-functioning individuals with autism may exhibit a short-fall in response inhibition. This finding supports the executive dysfunction theory of autism.

Adolescent↗
PubMed2003

Facilitating normative judgments of conditional probability: frequency or nested sets?

Recent probability judgment research contrasts two opposing views. Some theorists have emphasized the role of frequency representations in facilitating probabilistic correctness; opponents have noted that visualizing the probabilistic structure of the task sufficiently facilitates normative reasoning. In the current experiment, the following conditional probability task, an isomorph of the "Problem of Three Prisoners" was tested. "A factory manufactures artificial gemstones. Each gemstone has a 1/3 chance of being blurred, a 1/3 chance of being cracked, and a 1/3 chance of being clear. An inspection machine removes all cracked gemstones, and retains all clear gemstones. However, the machine removes 1/2 of the blurred gemstones. What is the chance that a gemstone is blurred after the inspection?" A 2 x 2 design was administered. The first variable was the use of frequency instruction. The second manipulation was the use of a roulette-wheel diagram that illustrated a "nested-sets" relationship between the prior and the posterior probabilities. Results from two experiments showed that frequency alone had modest effects, while the nested-sets instruction achieved a superior facilitation of normative reasoning. The third experiment compared the roulette-wheel diagram to tree diagrams that also showed the nested-sets relationship. The roulette-wheel diagram outperformed the tree diagrams in facilitation of probabilistic reasoning. Implications for understanding the nature of intuitive probability judgments are discussed.

Adult↗
PubMed2002

The malleability of anchoring effects.

Anchoring effects--the assimilation of a numeric estimate to a previously considered standard--are typically described as very robust and persistent. Based on the assumption that judgmental anchoring involves a hypothesis-testing process in which judges actively seek and generate judgment-relevant target knowledge, it was assumed that anchoring effects might at the same time be fairly malleable. Specifically, subtle influences that change the nature of the tested hypothesis are likely to affect the magnitude of anchoring. Using a procedural priming task, judges were induced to focus on similarities versus differences during a series of anchoring tasks. The results demonstrate that the magnitude of the obtained effect critically depended on this manipulation. In particular, a more pronounced anchoring assimilation effect resulted for judges with a similarity rather than a difference focus. Implications of these findings for models of anchoring as well as for the nature of the anchoring phenomenon are discussed.

Adult↗