Within‐Pair Consistency in Child Witnesses: The Diagnostic Value of Telling the Same Story

Judges and jurors often rely on consistency for assessing veracity. The present study examined the diagnostic value of within‐pair consistency to predict truth‐telling in pairs of children aged 8 to 10 years. Twenty‐three pairs were questioned about one experienced event and one imagined event (which they had discussed before questioning). Within‐pair consistency was significantly higher for experienced events than for imagined events. The diagnostic value of within‐pair consistency to predict truth‐telling was, however, modest: approximately one out of three judgments based on this cue would have been mistaken. Analyses of children's discussions of the imagined events revealed that interview questions about topics that had been discussed before questioning did not effectively discriminate experienced and imagined events, providing support for theoretical assumptions underlying the unanticipated‐question approach. Practical recommendations for police interviewers are provided. Copyright © 2013 John Wiley & Sons, Ltd.     

Naive Probability: Model‐Based Estimates of Unique Events

We describe a dual‐process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non‐numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non‐numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P(A), P(B), P(A and B), disjunctions: P(A), P(B), P(A or B or both), and conditional probabilities P(A), P(B), P(B|A). They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning.     

More than 50% or Less than 70% Chance: Pragmatic Implications of Single‐Bound Probability Estimates

Probability estimates can be given as ranges or uncertainty intervals, where often only one of the interval bounds (lower or upper) is specified. For instance, a climate forecast can describe La Niña as having “more than 70% chance” or “less than 90% chance” of occurring. In three experiments, we studied how research participants perceived climate‐related forecasts expressed with lower‐bound (“over X% chance”) or upper‐bound (“under Y% chance”) probability statements. Results indicate that such single‐bound statements give pragmatic information in addition to the numeric probabilities they convey. First, the studies show that these statements are directional, leading the listeners' attention in opposite directions. “Over” statements guide attention towards the possible occurrence of the event and are explained by reasons for why it might happen, while “under” statements direct attention to its possible non‐occurrence and are more often explained by reasons for why the target event might not appear, corresponding to positive (it is possible) versus negative (it is uncertain) verbal probabilities. Second, boundaries were found to reveal the forecaster's beliefs and could be perceived as indicative of an increasing or a decreasing trend. Single‐bound probability estimates are therefore not neutral communications of probability level but might “leak” information about the speaker's expectations and about past and future developments of the forecast. Copyright © 2017 John Wiley & Sons, Ltd.     

Engaging in self‐regulation results in low‐level construals

Previous research has suggested that self‐regulation results in low‐level construals but has inferred construal levels after self‐regulation only indirectly, through construal‐dependent judgments and choices. In the present paper, we demonstrate a direct link between engaging in self‐regulation and low‐level construals, by manipulating self‐regulation and subsequently assessing construal levels using well‐established and straightforward measures of construal level in three studies. Participants who engaged in self‐regulation subsequently provided lower egocentric spatial distance estimates (Studies 1A and 1B), formed more groups when categorizing objects (Study 2), and used more concrete language when describing cartoon main characters' behavior (Study 3) than participants who did not engage in self‐regulation. These findings provide direct evidence that low‐level construals result from engaging in self‐regulation. Copyright © 2012 John Wiley & Sons, Ltd.     

Ratio scale measurement of the perceived lengths of lines.

In Experiments 1 and 2, magnitude and category estimates of perceived line length difference were used to rank order 36 pairs of lines with respect to the psychological length difference between the lines forming a pair. In Experiment 3 magnitude estimates of line length ratios were used to order the same 36 pairs with respect to the psychological length ratio between the lines comprising a pair. A nonmetric analysis of the rank-order of the difference and ratio judgments was used to construct a ratio scale of perceived line length. Perceived line length was found to be a power function of physical line length with an exponent of .46. In Experiments 4 and 5, magnitude and category estimates of line length similarity were obtained. A nonmetric analysis of these data indicated that similarity judgments were monotonic inverses of judgments of psychological ratios.     

Revisiting Thurstone's and Coombs' scales on the seriousness of crimes and offences

The classical studies by Thurstone (1927b) and Coombs (1967) on the seriousness of crimes and offences are replicated here for a sample of male and female students. Eighty subjects used both forced choice and graded dominance ratios to assess all pairs of 10 crimes/offences. The direct ratio estimates correlate very highly with pair-comparison probabilities, thus making it possible to interpret the former as direct estimates of dominance probabilities. These data can be scaled with excellent fit in Thurstone's sense. The resulting scales are quite similar to those obtained by Thurstone and Coombs. An analysis of the individual data shows, however, that 69 per cent of the average data are aggregated over a variety of distinct subgroups of individuals who partition the crimes/offences into subsets that are incomparable in their seriousness. Thurstone's and Coombs' seriousness scales must therefore be considered a population lawfulness.     

Using Ordinal Data to Estimate Cardinal Values

We investigate methods developed in multiple criteria decision‐making that use ordinal information to estimate numerical values. Such methods can be used to estimate attribute weights, attribute values, or event probabilities given ranks or partial ranks. We first review related studies and then develop a generalized rank‐sum (GRS) approach in which we provide a derivation of the rank‐sum approach that had been previously proposed. The GRS approach allows for incorporating the concept of degree of importance (or, difference in likelihood with respect to probabilities and difference in value for attribute values), information that most other rank‐based formulas do not utilize. We then present simulation results comparing the GRS method with other rank‐based formulas such as the rank order centroid method and comparing the GRS methods using as many as three levels of importance (i.e., GRS‐3) with Simos' procedure (which can also incorporate degree of importance). To our surprise, our results show that the incorporation of additional information (i.e., the degree of the importance), both GRS‐3 and Simos' procedure, did not result in better performance than rank order centroid or GRS. Further research is needed to investigate the modelling of such extra information. We also explore the scenario when a decision‐maker has indifference judgments and cannot provide a complete rank order. Copyright © 2014 John Wiley & Sons, Ltd.     

Semantic coherence and fallacies in estimating joint probabilities

In three experiments on joint probability estimation, gist representations were manipulated with analogies, and the suboptimal strategy of ignoring relevant denominators was counteracted with training in using 2 × 2 tables to clarify joint probability estimates. The estimated probabilities of two events, as well as their conjunctive and disjunctive probabilities, were assessed against two benchmarks, logical fallacies and semantic coherence—a constellation of estimates consistent with the relationship among sets. Fuzzy‐trace theory (FTT) predicts that analogies will increase semantic coherence, and a table intervention affecting denominator neglect will both increase semantic coherence and reduce fallacies. In all three experiments, analogies increased semantic coherence. In both experiments training participants to use 2 × 2 tables, such tables reduced fallacies and increased semantic coherence. As the relations among sets in the problem materials progressed in cognitive complexity from identical sets, mutually exclusive sets, and subsets to overlapping sets, fallacies generally increased, and semantic coherence generally decreased. These findings indicate that denominator neglect is pervasive, but that it can be remedied with a straightforward intervention that clarifies relations among sets. Further, intuitive gist‐based probability estimation can be improved through the use of simple analogies. Copyright © 2009 John Wiley & Sons, Ltd.     

Acquisition functions in contingency judgment

Two experiments investigated the way in which judgments of the extent to which an action caused an outcome changed as more experience of the actionoutcome contingency was presented. In the first experiment judgments increased across trials when there was a positive contingency and decreased when there was a negative contingency. In noncontingent situations judgments were biased by the overall probability of the outcome. In the second experiment the changes across trials under positive and negative contingencies persisted even when the subjects were given the opportunity to dissociate their causality judgments from their degree of confidence in those judgments. The results are at variance with the dP and dD theories which attempt to account for causality judgments in terms of statistical rules based on the probabilities or frequencies of the relevant events. If such theories were modified, however, to take account of the regression of the subjects' estimates onto the actual probabilities or frequencies, then the data could be accommodated. On the other hand, a simple associative view is also able to account for the data.     

Power of pairwise comparisons in the equal variance and unequal sample size case

A Monte Carlo simulation was conducted to compare five, pairwise multiple comparison procedures. The number of means varied from 4 to 6 and the sample size ratio varied from 1 to 60. Procedures were evaluated on the basis of Type I errors, any‐pair power and all‐pairs power. Four procedures were shown to be conservative, while the fifth provided adequate control of Type I errors only for restricted values of sample size ratios. No procedure was found to be uniformly most powerful. The Tukey‐Kramer procedure was found to provide the best any‐pair power provided it is applied without requiring a significant overall F test. In most cases, the Hayter‐Fisher modification of the Tukey‐Kramer was found to provide very good any‐pair power and to be uniformly more powerful than the Tukey‐Kramer when a significant overall F test is required. A partition‐based version of Peritz's method usually provided the greatest all‐pairs power. A modification of the Shaffer‐Welsch was found to be useful in certain conditions.     

Children's memory for the times of events from the past years

This study tested 8–12‐year‐olds' ability to localize in time parent‐reported events from four time intervals ranging from 6 months to 4 years ago. Memory for content was very accurate, and children's time estimates showed substantial agreement with the times provided by their parents. Accuracy of year judgments declined with retention interval, with the greatest change occurring between the 1–2‐year and 2–3‐year intervals. Season, month and time of day accuracy were much more stable over time. There were significant improvements with age in performance on measures of conventional time knowledge, and this performance was correlated with the accuracy of time estimates on the long time scales, controlling for age and general cognitive ability. Copyright © 2010 John Wiley & Sons, Ltd.     

The effect of feedback training on distance estimation in virtual environments

It is often noted that distances are significantly underestimated in computer‐simulated (virtual) environments. Two experiments examine observers' ability to use error corrective feedback to improve the accuracy of judgments of egocentric and exocentric distances. In Experiment 1, observers viewed objects in an immersive virtual environment and estimated their distance through a blindfolded walking task. Different groups received feedback on either egocentric, exocentric or none of these judgments. Receiving feedback improved observers' ability to estimate only those distances for which feedback was provided. These effects persisted for at least 1 week. In Experiment 2, observers estimated egocentric distance by means of both a direct and indirect walking task. Receiving feedback on the direct walking task predominantly improved direct estimates and not indirect estimates. These findings suggest that although feedback training offers a relatively straightforward and immediate way of overcoming problems of distance estimation, its effects are specific to both the type of judgment and the type of response. Copyright © 2005 John Wiley & Sons, Ltd.     

Post‐identification feedback effects: Investigators and evaluators

We investigated the effects of post‐identification feedback and viewing conditions on beliefs and interviewing tactics of participant‐investigators, crime reports of participant‐witnesses and participant‐evaluators' credibility judgments of the witnesses. Study 1 participants assumed the roles of witness and investigator (N = 167 pairs). Witnesses' view of a simulated crime video was manipulated by distance from viewing monitor: 2 or 9 ft. Participants made a line‐up identification and received either positive feedback or no feedback. Significant effects for witnesses and investigators were associated with viewing condition and post‐identification feedback. Interviews between investigator‐witness pairs were videotaped. Investigators asked more positive, leading questions when they were led to believe that the witness had identified the suspect. In Study 2 evaluators (N = 302) viewed the witness‐investigator interviews. Viewing condition had no effect on judgments of witness credibility but positive post‐identification feedback led evaluators to judge witnesses as more credible than witnesses who received no feedback. Copyright © 2010 John Wiley & Sons, Ltd.     

What is preexisting strength? Predicting free association probabilities,similarity ratings,and cued recall probabilities

Measuring lexical knowledge poses a challenge to the study of the influence of preexisting knowledge on the retrieval of new memories. Many tasks focus on word pairs, but words are embedded in associative networks, so how should preexisting pair strength be measured? It has been measured by free association, similarity ratings, and co-occurrence statistics. Researchers interpret free association response probabilities as unbiased estimates of forward cue-to-target strength. In Study 1, analyses of large free association and extralist cued recall databases indicate that this interpretation is incorrect. Competitor and backward strengths bias free association probabilities, and as with other recall tasks, preexisting strength is described by a ratio rule. In Study 2, associative similarity ratings are predicted by forward and backward, but not by competitor, strength. Preexisting strength is not a unitary construct, because its measurement varies with method. Furthermore, free association probabilities predict extralist cued recall better than do ratings and co-occurrence statistics. The measure that most closely matches the criterion task may provide the best estimate of the identity of preexisting strength.     

Mainstreaming,resonance, and impersonal impact.

People may use information from a variety of sources in constructing their judgments of crime risk, including direct experience, word‐of‐mouth, and the mass media. One hundred fifty‐eight general population respondents provided 3 estimates of risk of violent crime: societal crime risk, personal crime risk to themselves in their own neighborhood, and personal crime risk to themselves in New York City. Respondents' level of television viewing was related to their estimates of societal crime risk and to their estimates of personal crime risk in New York City (p < .05) but not to their estimates of personal crime risk in their own neighbourhood (p < .05): all 3 risk estimates were related to respondents' level of television viewing only for those with high direct experience with crime, results that are consistent with Gerbner's concept of resonance (Gerbner et al., 1980). The implications for the concept of impersonal impact (Tyler, 1980) and Gerbner et al.'s concepts of cultivation and mainstreaming are also discussed.     

The perceptual basis of loudness ratio judgments

In Experiment 1, subjects were required to estimateloudness ratios for 45 pairs of tones. Ten 1,200-Hz tones, differing only in intensity, were used to generate the 45 distinct tone pairs. In Experiment 2, subjects were required to directly compare two pairs of tones (chosen from among the set of 45) and indicate which pair of tones had the greaterloudness ratio. In both Experiments 1 and 2, the subjects’ judgments were used to rank order the tone pairs with respect to their judged loudness ratios. Nonmetric analyses of these rank orders indicated that both magnitude estimates of loudness ratios and direct comparisons of loudness ratios were based on loudnessintervals ordifferences where loudness was a power function of sound pressure. These experiments, along with those on loudness difference judgments (Parker & Schneider, 1974; Schneider, Parker, & Stein, 1974), support Torgerson’s (1961) conjecture that there is but one comparative perceptual relationship for ioudnesses, and that differences in numerical estimates for loudness ratios as opposed to loudness intervals simply reflect different reporting strategies generated by the two sets of instructions.     

Contrasting stochastic and support theory accounts of subadditivity

Numerous studies have found that likelihood judgment typically exhibits subadditivity in which judged probabilities of events are less than the sum of judged probabilities of constituent events. Whereas traditional accounts of subadditivity attribute this phenomenon to deterministic sources, this paper demonstrates both formally and empirically that subadditivity is systematically influenced by the stochastic variability of judged probabilities. First, making rather weak assumptions, we prove that regressive error (or variability) in mapping covert probability judgments to overt responses is sufficient to produce subadditive judgments. Experiments follow in which participants provided repeated probability estimates. The results support our model assumption that stochastic variability is regressive in probability estimation tasks and show the contribution of such variability to subadditivity. The theorems and the experiments focus on within-respondent variability, but most studies use between-respondent designs. Numerical simulations extend the work to contrast within- and between-respondent measures of subadditivity. Methodological implications of all the results are discussed, emphasizing the importance of taking stochastic variability into account when estimating the role of other factors (such as the availability bias) in producing subadditive judgments.     

An account of subjective probability judgment for joint events: Conjunctive and disjunctive

Probability judgment is a vital part of many aspects of everyday life. In the present paper, we present a new theory of the way in which individuals produce probability estimates for joint events: conjunctive and disjunctive. We propose that a majority of individuals produce conjunctive (disjunctive) estimates by making a quasi‐random adjustment, positive or negative, from the less (more) likely component probability with the other component playing no obvious role. In two studies, we produce evidence supporting propositions that follow from our theory. First, the component probabilities do appear to play the distinct roles we propose in determining the joint event probabilities. Second, contrary to probability theory and other accounts of probability judgment, we show that the conjunctive‐less likely probability difference is unrelated to the more likely disjunctive probability difference (in normative theory these quantities are identical). In conclusion, while violating the norms of probability judgment, we argue that estimates produced in the manner we propose will be close enough to the normative values especially given the changing nature of the external environment and the incomplete nature of available information.     

Comparative Optimism and Event Skewness

Comparative judgment biases—wherein a majority of people report being above‐ or below‐average in their abilities, traits, or future events—are a robust phenomenon in psychology. A recent explanation for these biases has focused on people's awareness that many comparative judgment domains form skewed distributions, and, hence, a majority of people can feasibly be above or below average. Indeed, this prior research found that comparative biases for abilities emerged more for skewed (vs. normal) distributions. In the current research, we attempted to (i) conceptually replicate this finding in a comparative likelihood context and (ii) provide evidence of an alternative explanation for the prior results. Replicating prior research, three correlational studies and one experimental study found that event skewness was related to direct comparative likelihood judgments for health events, such that comparative optimism emerged more for events judged or manipulated to come from positively skewed distributions than from negatively skewed distributions. However, event skewness was unrelated to indirect comparisons (absolute self minus absolute other). Moreover, consistent with an egocentric‐processes account, absolute self‐judgments were more predictive of direct comparisons than were absolute other judgments and showed the same association with event skewness as direct comparisons. Implications for explaining and interpreting comparative judgment biases are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

The effects of source and type of feedback on child witnesses' metamemory accuracy

This study investigated the effect of feedback on the accuracy (realism) of 12‐year‐old children's metacognitive judgments of their answers to questions about a film clip. Two types of judgments were investigated: confidence judgments (on each question) and frequency judgments (i.e. estimates of overall accuracy). The source of feedback, whether it was presented as provided by a teacher or a peer child, did not influence metacognitive accuracy. Four types of feedback were given depending on whether the participant's answer was correct and depending on whether the feedback confirmed or disconfirmed the child's answer. The children showed large overconfidence when they received confirmatory feedback but much less so when they received disconfirmatory feedback. The children gave frequency judgments implying that they had more correct answers than they actually had. No main gender differences were found for any of the measures. The results indicate a high degree of malleability in children's metacognitive judgments. Copyright © 2004 John Wiley & Sons, Ltd.