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The science of choosing the right decision threshold in high-stakes diagnostics.

Many diagnostic tasks require that a threshold be set to convert evidence that is a matter of degree into a positive or negative decision. Although techniques of decision analysis used in psychology help one select the particular threshold that is appropriate to a given situation and purpose, just the concept of adjusting the threshold to the situation is not appreciated in many important practical arenas. Testing for the human immunodeficiency virus (HIV) and for dangerous flaws in aircraft structures are used here as illustrations. This article briefly reviews the relevant techniques and develops those two examples with data. It suggests that use of the decision techniques could substantially benefit individuals and society and asks how that use might be facilitated.

Aircraft

Young children's predictions of illness: failure to recognize probabilistic causation.

In this study preschool-age children made predictions for a set of salient probabilistic causes. Of interest was whether the children viewed outcomes of familiar causes of illness as definite or as probabilistic. In Experiment 1, children judged that a common cause would affect all members of a group in the same way. In Experiment 2, children believed they could definitely predict illness outcomes in a single case. These judgments contrasted with adults' variable and uncertain predictions. Children did recognize uncertainty in outcomes dependent on voluntary choices. Experiment 3 presented both high- and low-potency causes of illness. Children treated all causes of illness as nonprobabilistic. These results are discussed in the context of children's understanding of causal relations and the sources of variability.

Adult

Covariation bias in panic-prone individuals.

Covariation estimates between fear-relevant (FR; emergency situations) or fear-irrelevant (FI; mushrooms and nudes) stimuli and an aversive outcome (electrical shock) were examined in 10 high-fear (panic-prone) and 10 low-fear respondents. When the relation between slide category and outcome was random (illusory correlation), only high-fear participants markedly overestimated the contingency between FR slides and shocks. However, when there was a high contingency of shocks following FR stimuli (83%) and a low contingency of shocks following FI stimuli (17%), the group difference vanished. Reversal of contingencies back to random induced a covariation bias for FR slides in high- and low-fear respondents. Results indicate that panic-prone respondents show a covariation bias for FR stimuli and that the experience of a high contingency between FR slides and aversive outcomes may foster such a covariation bias even in low-fear respondents.

Adult

A probabilistic contrast model of causal induction.

Deviations from the predictions of covariational models of causal attribution have often been reported in the literature. These include a bias against using consensus information, a bias toward attributing effects to a person, and a tendency to make a variety of unpredicted conjunctive attributions. It is contended that these deviations, rather than representing irrational biases, could be due to (a) unspecified information over which causal inferences are computed and (b) the questionable normativeness of the models against which these deviations have been measured. A probabilistic extension of Kelley's analysis-of-variance analogy is proposed. An experiment was performed to assess the above biases and evaluate the proposed model against competing ones. The results indicate that the inference process is unbiased.

Adult

The overconfidence effect in social prediction.

In five studies with overlapping designs and intents, subjects predicted a specific peer's responses to a variety of stimulus situations, each of which offered a pair of mutually exclusive and exhaustive response alternatives. Each prediction was accompanied by a subjective probability estimate reflecting the subjects' confidence in its accuracy--a measure validated in Study 5 by having subjects choose whether to "gamble" on the accuracy of their prediction or on the outcome of a simple aleatory event. Our primary finding was that in social prediction, as in other judgmental domains, subjects consistently proved to be highly overconfident. That is, regardless of the type of prediction item (e.g., responses to hypothetical dilemmas, responses to contrived laboratory situations, or self-reports of everyday behaviors) and regardless of the type of information available about the person whose responses they were predicting (e.g., predictions about roommates or predictions based on prior interviews), the levels of accuracy subjects achieved fell considerably below the levels required to justify their confidence levels. Further analysis revealed two specific sources of overconfidence. First, subjects generally were overconfident to the extent they were highly confident. Second, subjects were most likely to be overconfident when they knowingly or unknowingly made predictions that ran counter to the relevant response base rates and, as a consequence, achieved low accuracy rates that their confidence estimates failed to anticipate. Theoretical and normative implications are discussed and proposals for subsequent research offered.

Adult

Does memory affect judgment? Self-generated versus recall memory measures.

Most evidence regarding the independence of memory and judgment comes from studies that used memory measures consisting of Ss' recall of raw input data (recall measures). Such evidence provides the primary support for on-line judgment formation. The results of 2 experiments suggest that self-generated memory measures capture the contents of memory at the time of judgement more effectively than recall measures and, accordingly, are more likely to provide evidence that memory and judgment are related. When directly compared, a self-generated measure provided evidence of a memory-judgment relationship and a recall measure did not. Thus, memory-based judgment formation may be more prevalent than the on-line processing literature suggests.

Adult

Conflict between intuitive and rational processing: when people behave against their better judgment.

When offered an opportunity to win $1 on every "win" trial in which they drew a red jelly bean, subjects frequently elected to draw from a bowl that contained a greater absolute number, but a smaller proportion, of red beans (e.g., 7 in 100) than from a bowl with fewer red beans but better odds (e.g., 1 in 10). Subjects reported that although they knew the probabilities were against them, they felt they had a better chance when there were more red beans. Similar, but less extreme results were obtained on "lose" trials, where drawing a red bean meant losing $1. These results were predicted from the concretive and experiential principles of cognitive-experiential self-theory. Nonoptimal choices in the laboratory were significantly correlated with heuristic responses to relevant vignettes and with self-reported gambling in real life.

Adult

Probability and category redefinition in the fault tree paradigm.

Fault trees have been advocated as aids for problem solvers. However, research has suggested limitations in their usefulness. Fischhoff, Slovic, and Lichtenstein (1978) found that subjects given incomplete (pruned) trees were insensitive to omissions; these authors hypothesized that Tversky and Kahneman's (1974) availability heuristic was the mediating factor. Using a within-subjects design, subjects in Experiment 1 received both full and pruned trees and estimated probabilities for various reasons why a car would fail to start. To increase the availability of omissions, some Experiment 1 subjects first generated possible causes of starting failure. The basic Fischhoff et al. findings were replicated, but several aspects of the results argued against the availability hypothesis as the mechanism for judgment. Instead, subjects appeared to idiosyncratically redefine category membership when making judgments based upon pruned trees. By employing a sorting task in Experiment 2 we corroborated the results of Experiment 1: Subjects do redefine the actual contents of the categories when faced with an omission from the fault tree. The implications of these results for the use of fault trees as a problem solving aid are discussed.

Decision Trees

Components of the location probability effect in visual search tasks.

In visual search tasks, targets are detected more rapidly when they appear in locations that commonly contain a target than when they appear in locations that rarely contain a target. Five experiments were conducted to investigate two specific properties of this location probability effect: its dependence on spatial location versus relative position and its dependence on or independence of target identity. In Experiment 1 spatial location of a stimulus row was varied to determine whether high location probability facilitates target detection in a particular location in visual space or a particular relative position within the row. Both were facilitated to approximately the same extent. In Experiment 2 an inducing target occurred with high probability in one of four display locations, and a test target occurred with equal probability in all four locations. Both targets were found more quickly in the high-probability location than in the other locations, but the advantage associated with targets in the high-probability location was larger for the inducing target than for the test target. In Experiments 3-5 the correspondence between the components observed in Experiments 1 and 2 was examined. The overall pattern of results was compatible with a model in which the location probability effect is produced partly by an attentional spotlight, which facilitates processing of any stimulus appearing in a particular location in visual space, and partly by a network of position-specific letter detectors, which facilitates detection of a particular letter in a particular relative position within a display. Models with flexible scanning strategies were also considered.

Attention

Information transfer in iconic memory experiments.

To report letters from briefly exposed letter arrays, subjects must transfer information from a rapidly decaying trace (iconic memory) to more durable storage. In a partial-report paradigm, we systematically varied the proportion (P) of trials with a long cue delay relative to a short cue delay. Practiced subjects used the same transfer strategy independent of P. Data from a partial-report-plus-masking experiment were used to construct a computational model that accurately predicted partial- and whole-report performance with and without masks. Assumptions: Prior to a cue, subjects attend primarily to the middle row of a three-row display, resulting in nonselective transfer. After the cue, they attend only to the cued row. Transfer rate is the product of iconic legibility (which depends on time and retinal location) and attention allocation (which shifts after a cue). Cumulative transfer is limited by the capacity of durable storage.

Adult

More thoughts on the unconscious: reply to Brody and to Lewicki and Hill.

Brody (1989) and Lewicki and Hill (1989) present commentaries on my central thesis (Reber, 1989) that there exist powerful induction routines that operate largely independently of awareness and yield rich and complex tacit knowledge that resists attempts to make it conscious, although these commentaries are of dramatically different kinds. Because there is a fairly clear basis of agreement between Lewicki and Hill and the points that I made, this reply deals almost entirely with the issues raised by Brody. The focus is on two classes of issues: (a) those of a methodological nature that surround the general problem of doing experiments on unconscious cognition and (b) those that derive from considerations of evolutionary biology that provide a basis for arguing that implicit operations are primary and form the foundation for conscious processes.

Concept Formation

Choice behavior in transition: development of preference with ratio and interval schedules.

In Experiment 1, the choice responses of 8 pigeons were observed during 50 periods of transition. Each condition began with equal probabilities of reinforcement on 2 response keys and switched to unequal probabilities. With the ratio of the 2 probabilities held constant, preference for the higher probability developed more rapidly when the 2 probabilities were high than when they were low. In Experiment 2, each condition began with 2 equal variable-interval schedules, but later 1 key delivered 60%, 75%, or 90% of the reinforcers. The rate of approach to asymptotic performance was roughly the same with all 3 reinforcement percentages. These and previous results pose difficulties for some well-known models of acquisition, but the results are well described by a simple model that states that the strength of each response is independently increased by reinforcement and decreased by nonreinforcement.

Animals

Bayesian analysis of foraging by pigeons (Columba livia).

In this article, the authors combine models of timing and Bayesian revision of information concerning patch quality to predict foraging behavior. Pigeons earned food by pecking on 2 keys (patches) in an experimental chamber. Food was primed for only 1 of the patches on each trial. There was a constant probability of finding food in a primed patch, but it accumulated only while the animals searched there. The optimal strategy was to choose the better patch first and remain for a fixed duration, thereafter alternating evenly between the patches. Pigeons were nonoptimal in 3 ways: (a) they departed too early, (b) their departure times were variable, and (c) they were biased in their choices after initial departure. The authors review various explanations of these data.

Animals

Contributions of specific cell information to judgments of interevent contingency.

College students considered the possible effect of an experimental drug on a skin rash. The information came from a 2 x 2 contingency table involving receipt or nonreceipt of the drug and improvement or nonimprovement of the rash: Cell A = receipt-improvement; Cell B = receipt-nonimprovement; Cell C = nonreceipt-improvement; Cell D = nonreceipt-nonimprovement. Without numerical information. Ss judged cells to be ordered A greater than B greater than C greater than D. The same order held when the contribution of each cell was derived from the contingency judgments of other subjects given numerical information. No such consistency was seen when one group of Ss made both judgments: whether individual Ss equally or unequally assessed the importance of the four cells, their contingency estimates showed cell use to be ordered A greater than B greater than C greater than D. These findings may result from strong biases that Ss harbor in processing contingency information.

Adult

Reasoning with conditionals containing negated constituents.

Three experiments investigated matching bias in conditional reasoning tasks. Matching bias occurs when Ss ignore negations and match named items. Experiment 1 used an abstract and a thematic version of Evans's (1972) construction task. Results showed that matching may be due to an interaction between task demands and constructing contrast classes when interpreting negations. Experiment 2, which used Wason's (1968) selection task, introduced a manipulation to ease contrast-class construction. Confirmation plus falsification dominated over matching. Experiment 3 introduced two other manipulations to aid contrast-class construction with abstract material. Confirmation was facilitated, matching was suppressed, and falsification remained unchanged. These results suggest that matching occurs only when insufficient or ambiguous information prevents the intended interpretation of negations.

Adult

Effects of probability mode on preference reversal.

Six analysts estimated verbally and numerically the chances that specific events will occur. Sixty decision makers used each type of estimate to make binary-choice decisions and to bid for lotteries based on the events. The usual reversal of preference between choice and bidding procedures was found in the numerical condition, but the frequency of preference reversals was significantly reduced in the verbal condition. This reduction occurred because risk aversion was reduced in choice when verbal estimates were given, whereas bidding was unaffected by presentation mode. The pattern of results was predicted by and supports the hypothesis that the relative importance given to the dimensions of a prospect depends on the form in which the information is displayed.

Decision Theory