Judging response-outcome relations: the role of response-outcome contingency, outcome probability, and method of information presentation.
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Concept Formation↗
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Prediction and judgment as indicators of sensitivity to covariation of continuous variables.
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Adolescent↗
A pattern recognition account of decision making.
In the domain of pattern recognition, experiments have shown that perceivers integrate multiple sources of information in an optimal manner. In contrast, other research has been interpreted to mean that decision making is nonoptimal. As an example, Tversky and Kahneman (1983) have shown that subjects commit a conjunction fallacy because they judge it more likely that a fictitious person named Linda is a bank teller and a feminist than just a bank teller. This judgment supposedly violates probability theory, because the probability of two events can never be greater than the probability of either event alone. The present research tests the hypothesis that subjects interpret this judgment task as a pattern recognition task. If this hypothesis is correct, subjects' judgments should be described accurately by the fuzzy logical model of perception (FLMP)--a successful model of pattern recognition. In the first experiment, the Linda task was extended to an expanded factorial design with five vocations and five avocations. The probability ratings were described well by the FLMP and described poorly by a simple probability model. The second experiment included (1) two fictitious people, Linda and Joan, as response alternatives and (2) both ratings and categorization judgments. Although the ratings were accurately described by both the FLMP and an averaging of the sources of information, the categorization judgments were described better by the FLMP. These results reveal important similarities in recognizing patterns and in decision making. Given that the FLMP is an optimal method for combining multiple sources of information, the probability judgments appear to be optimal in the same manner as pattern-recognition judgments.
Adult↗
The base-rate fallacy in the context of sequential categories.
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Attention↗
Asymptotic judgment of cause in a relative validity paradigm.
We report three experiments in which we tested asymptotic and dynamic predictions of the Rescorla-Wagner (R-W) model and the asymptotic predictions of Cheng's probabilistic contrast model (PCM) concerning judgments of causality when there are two possible causal candidates. We used a paradigm in which the presence of a causal candidate that is highly correlated with an effect influences judgments of a second, moderately correlated or uncorrelated cause. In Experiment 1, which involved a moderate outcome density, judgments of a moderately positive cause were attenuated when it was paired with either a perfect positive or perfect negative cause. This attenuation was robust over a large set of trials but was greater when the strong predictor was positive. In Experiment 2, in which there was a low overall density of outcomes, judgments of a moderately correlated positive cause were elevated when this cause was paired with a perfect negative causal candidate. This elevation was also quite robust over a large set of trials. In Experiment 3, estimates of the strength of a causal candidate that was uncorrelated with the outcome were reduced when it was paired with a perfect cause. The predictions of three theoretical models of causal judgments are considered. Both the R-W model and Cheng's PCM accounted for some but not all aspects of the data. Pearce's model of stimulus generalization accounts for a greater proportion of the data.
Adult↗
The use of schematic knowledge about sources in source monitoring.
Source monitoring refers to mental processes leading to attributions regarding the origin of information. We tested Johnson, Hashtroudi, and Lindsay's (1993) assumption that prior source-relevant knowledge is used in some source-monitoring tasks. In two experiments using different domains of schematic knowledge, two sources presented information that was expected for one source and somewhat unexpected for the other. In a later source-monitoring test, participants decided whether items had been presented by Source A, by Source B, or were new. The results of both experiments show that source identification is better for expected items than for somewhat unexpected items. Multinomial modeling analyses revealed that when participants do not remember the source of information, they guess that it was presented by the expected source. These results provide evidence for the claim that source monitoring can be based on prior knowledge and support a guessing hypothesis.
Adolescent↗
Suppression of valid inferences and knowledge structures: the curious effect of producing alternative antecedents on reasoning with causal conditionals.
These studies looked at the difficulty that reasoners have in accepting conditional ("If P then Q") major premises that are not necessarily true empirically, as a basis for deductive reasoning. Preliminary results have shown that when reasoners are asked to produce possible alternate antecedents to the major premise ("If A then Q"), they paradoxically tend to deny the modus ponens (MP) inference ("If P is true, then Q is true"). Three studies further explored these results. The first study gave university students paper-and-pencil tests in which instructions to "suppose that the major premise is true" was followed by a request to determine the next number in a sequence, to retrieve information unrelated to the premises, or to retrieve a possible case of "If A then Q." Relative to a control group, reasoners asked to produce an alternative antecedent showed a significant tendency to deny the MP inference, whereas no such tendency was observed for the two other tasks used. A second study compared performance on a condition in which reasoners were asked to produce an alternative antecedent with that when they were given an explicit alternative. Premises used in this study were such that the latter alternative antecedent was also spontaneously produced by over 70% of reasoners. Results showed that the tendency to refuse the MP premise could not be accounted for by the specific nature of the alternative produced. A third study found that the tendency to refuse the MP inference after producing an alternative antecedent was affected by the number of "disabling conditions" (i.e., conditions that allow "P to be true" and "Q to be false") available for the major premise. These results are interpreted as being consistent with a model that supposes that logical reasoning requires selective inhibition of real-world knowledge.
Adult↗
On people's understanding of the diagnostic implications of probabilistic data.
Two lines of prior research into the conditions under which people seek information are examined in light of two statistical definitions of diagnosticity. Five experiments are reported. In two, subjects selected information in order to test a hypothesis. In the remaining three, they selected information in order to convince someone else of the truth of a known hypothesis. A total of 567 university students served as subjects. The two primary conclusions were as follows: (1) When the task is highly structured by the environment, subjects select information diagnostically, and (2) when the task is less structured, so that subjects must seek relevant information not manifest, they select information pseudodiagnostically. Possible relations to other laboratory inference tasks and to clinical judgment are discussed.
Concept Formation↗
When to trust the data: further investigations of system error in a scientific reasoning task.
When evaluating experimental evidence, how do people deal with the possibility that some of the feedback is erroneous? The potential for error means that evidence evaluation must include decisions about when to "trust the data." In this paper we present two studies that focus on subjects' responses to erroneous feedback in a hypothesis testing situation-a variant of Wason's (1960) 2-4-6 rule discovery task in which some feedback was subject to system error: "hits" were reported as "misses" and vice versa. Our results show that, in contrast to previous research, people are equally adept at identifying false negatives and false positives; further, successful subjects were less likely to use a positive test strategy (Klayman & Ha, 1987) than were unsuccessful subjects. Finally, although others have found that generating possible hypotheses prior to experimentation increases success and task efficiency, such a manipulation did little to mitigate the effects of system error.
Adult↗
The effect of prediction accuracy on choice reaction time.
In this study, we examined the effect of prediction accuracy on reaction time (RT). Subjects performed on three blocks of choice RT trials, all of which involved the mapping of four stimuli (red, green, 1, or 0) onto two response keys. The subjects were told that the four stimuli were equally probable and that their task was to respond to each stimulus onset by pressing the correct key. In one block (stimulus-prediction), the subjects predicted, prior to each trial, the precise stimulus that would appear. In a second block (category-prediction), the subjects predicted the category of the stimulus (i.e., color or digit) that would appear. In a third block (no-prediction), the subjects simply responded to each stimulus without making a prior prediction. In the stimulus-prediction block, RT was faster for correct predictions than for incorrect predictions. In addition, RT was faster on trials in which an incorrect prediction involved the correct category than on trials in which it involved the incorrect category: that is, a "half-wrong" prediction was better than an "all-wrong" prediction. In the category-prediction block, RT was faster when the stimulus category was predicted correctly than when it was not. There was little evidence of a response-facilitation contribution to the correct-prediction effect. These results permit inferences concerning the encoding and organization of information in memory.
Adult↗
The conjunction fallacy?
Tversky and Kahneman (1983) showed that when subjects are asked to rate the likelihood of several alternatives, including single and joint events, they often make a "conjunction fallacy." That is, they rate the conjunction of two events as being more likely than one of the constituent events. This, they claim, is a fallacy, since the conjunction of two events can never be more probable than either of the component events. In addition, they found that prior training in probability theory does not decrease the likelihood of making this fallacy. We argue that in some contexts, an alternative that contains the conjunction of two events can be more probable than an alternative that contains only one of the conjunction's constituent events. We carried out four experiments in which we manipulated this context. The frequency of making a conjunction fallacy was affected by the manipulation of context. Furthermore, when the context was clearly specified, prior training in statistics influenced the ratings.
Decision Making↗
Role of predictability of sequence in auditory stream segregation.
This study evaluates the role of item predictability in auditory temporal coherence. Thirteen normal-hearing subjects were required to hold together long tonal sequences as single strings of notes. Temporal and spectral predictability of successive notes in a sequence varied as a function of experimental condition. As the frequency separation of the notes in the sequence increased, the subjects found it more difficult to hold the sequence together as a single stream. There was no significant difference in subjects' abilities in performing this task as a function of experimental condition. That is, the predictability of successive notes appeared not to have a role in temporal coherence.
Attention↗
Judged displacement in apparent vertical and horizontal motion.
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Attention↗
Two response processes in a guessing task.
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Feedback↗
How to eliminate illusions in quantified reasoning.
The mental model theory postulates that reasoners build models of situations described in premises. These models normally make explicit only what is true according to the premises. The theory has an unexpected consequence. It predicts the existence of illusions in inferences: Certain inferences should have compelling but erroneous conclusions. Previous studies have corroborated the existence of such illusions. The present study reports the first effective antidote to them. For example, most people incorrectly answer "yes" to the following problem: Only one of the following statements is true ... /At least some of the plastic beads are not red./None of the plastic beads are red./Is it possible that none of the red beads are plastic? In two experiments, we progressively eliminated this fallacy and others by using instructions designed to overcome the bias toward truth. The difference between the illusory and the control problems disappeared when the participants were instructed to work out both the case in which the first premise was true and second premise was false and the case in which the second premise was true and the first premise was false.
Attention↗
Estimating psychometric functions in forced-choice situations: significant biases found in threshold and slope estimations when small samples are used.
When a theoretical psychometric function is fitted to experimental data (as in the obtaining of a psychophysical threshold), maximum-likelihood or probit methods are generally used. In the present paper, the behavior of these curve-fitting methods is studied for the special case of forced-choice experiments, in which the probability of a subject's making a correct response by chance is not zero. A mathematical investigation of the variance of the threshold and slope estimators shows that, in this case, the accuracy of the methods is much worse, and their sensitivity to the way data are sampled is greater, than in the case in which chance level is zero. Further, Monte Carlo simulations show that, in practical situations in which only a finite number of observations are made, the mean threshold and slope estimates are significantly biased. The amount of bias depends on the curve-fitting method and on the range of intensity values, but it is always greater in forced-choice situations than when chance level is zero.
Choice Behavior↗
Information selection and use in hypothesis testing: what is a good question, and what is a good answer?
The process of hypothesis testing entails both information selection (asking questions) and information use (drawing inferences from the answers to those questions). We demonstrate that although subjects may be sensitive to diagnosticity in choosing which questions to ask, they are insufficiently sensitive to the fact that different answers to the same question can have very different diagnosticities. This can lead subjects to overestimate or underestimate the information in the answers they receive. This phenomenon is demonstrated in two experiments using different kinds of inferences (category membership of individuals and composition of sampled populations). In combination with certain information-gathering tendencies, demonstrated in a third experiment, insensitivity to answer diagnosticity can contribute to a tendency toward preservation of the initial hypothesis. Results such as these illustrate the importance of viewing hypothesis-testing behavior as an interactive, multistage process that includes selecting questions, interpreting data, and drawing inferences.
Adult↗
Not only base rates are neglected in the Engineer-Lawyer problem: an investigation of reasoners' underutilization of complementarity.
The standard Engineer-Lawyer problem (Kahneman & Tversky, 1973) points to the failure of reasoners to integrate mentioned base-rate information in arriving at likelihood estimates. Research in this area nevertheless has presupposed that participants respect complementarity (i.e., participants ensure that competing estimates add up to 100%). A survey of the literature leads us to doubt this pre-supposition. We propose that the participants' non-normative performance on the standard Engineer-Lawyer problem reflects a reluctance to view the task probabilistically and that normative responses become more prominent as probabilistic aspects of the task do. In the present experiments, we manipulated two kinds of probabilistic cues and determined the extent to which (1) base rates were integrated and (2) the complementarity constraint was respected. In Experiment 1, six versions of an Engineer-Lawyer-type problem (that varied three levels of cue to complementarity and two base rates) were presented. The results showed that base-rate integration increased as cues to complementary did. Experiment 2 confirmed that Gigerenzer, Hell, and Blank's (1988) random-draw paradigm facilitates base-rate integration; a second measure revealed that it also prompts respect for complementarity. In Experiment 3, we replicated two of our main findings in one procedure while controlling for the potential influence of extraneous task features. We discuss approaches that describe how probabilistic cues might prompt normative responding.
Adult↗