A review of human linguistic probability processing: General principles and empirical evidence

Recruitment of magnitude representations to understand graded words

Language understanding and mathematics understanding are two fundamental forms of human thinking. Prior research has largely focused on the question of how language shapes mathematical thinking. The current study considers the converse question. Specifically, it investigates whether the magnitude representations that are thought to anchor understanding of number are also recruited to understand the meanings of graded words. These are words that come in scales (e.g., Anger) whose members can be ordered by the degree to which they possess the defining property (e.g., calm, annoyed, angry, furious). Experiment 1 uses the comparison paradigm to find evidence that the distance, ratio, and boundary effects that are taken as evidence of the recruitment of magnitude representations extend from numbers to words. Experiment 2 uses a similarity rating paradigm and multi-dimensional scaling to find converging evidence for these effects in graded word understanding. Experiment 3 evaluates an alternative hypothesis - that these effects for graded words simply reflect the statistical structure of the linguistic environment - by using machine learning models of distributional word semantics: LSA, word2vec, GloVe, counterfitted word vectors, BERT, RoBERTa, and GPT-2. These models fail to show the full pattern of effects observed of humans in Experiment 2, suggesting that more is needed than mere statistics. This research paves the way for further investigations of the role of magnitude representations in sentence and text comprehension, and of the question of whether language understanding and number understanding draw on shared or independent magnitude representations. It also informs the role of machine learning models in cognitive psychology research.

A data-driven and cost-oriented FMEA-MCDM approach to risk assessment and ranking in a fuzzy environment: A hydraulic pump factory case study

In today's highly competitive business environment, firms strive to maximize profitability by minimizing or eliminating disruptions and failures to maintain a competitive edge. This study focuses on evaluating risks in a hydraulic pump factory as a means to achieve sustainable growth. To accomplish this, a team of experts was formed to identify potential errors, utilizing a combination of risk priority number criteria weighted by Fuzzy Shannon's entropy and a fusion of multi-criteria decision-making and failure mode and effects analysis for evaluating and ranking failures. Moreover, the study emphasizes the importance of considering the interaction among risk assessment indicators, the inclusion of cost of failure, and modeling under fuzzy uncertainty circumstances, as they have a notable impact on the final ranking of failures to be processed for risk mitigation action planning. This research brings a new dimension to enhance the overall effectiveness of risk assessment by aggregation, as evidenced by a novel use of data classification in machine learning and correlation in statistics. The findings indicate that the aggregated ranking data series is best matched and most influenced by the weighted aggregated sum product assessment method, with the highest rate of recall and precision accomplished.

Developmental Trajectories in the Understanding of Everyday Uncertainty Terms

Dealing with uncertainty and different degrees of frequency and probability is critical in many everyday activities. However, relevant information does not always come in the form of numerical estimates or direct experiences, but is instead obtained through qualitative, rather vague verbal terms (e.g., "the virus often causes coughing" or "the train is likely to be delayed"). Investigating how people interpret and utilize different natural language expressions of frequency and probability is therefore crucial to understand reasoning and behavior in real-world situations. While there is considerable work exploring how adults understand everyday uncertainty phrases, very little is known about how children interpret them and how their understanding develops with age. We take a developmental and computational perspective to address this issue and examine how 4- to 14-year-old children and adults interpret different terms. Each participant provided numerical estimates for 14 expressions, comprising both frequency and probability phrases. In total we obtained 2856 quantitative judgments, including 2240 judgments from children. Our findings demonstrate that adult-like intuitions about the interpretation of everyday uncertainty terms emerge fairly early in development, with the quantitative estimates of children converging to those of adults from around 9 years on. We also demonstrate how the vagueness of verbal terms can be represented through probability distributions, which provides additional leverage for tracking developmental shifts through cognitive modeling techniques. Taken together, our findings provide key insights into the developmental trajectories underlying the understanding of everyday uncertainty terms, and open up novel methodological pathways to formally model the vagueness of probability and frequency phrases, which are abundant in our everyday life and activities.

Firearm examination: Examiner judgments and computer-based comparisons

Forensic firearm examination provides the court of law with information about the source of fired cartridge cases. We assessed the validity of source decisions of a computer-based method and of 73 firearm examiners who compared breechface and firing pin impressions of 48 comparison sets. We also compared the computer-based method's comparison scores with the examiners' degree-of-support judgments and assessed the validity of the latter. The true-positive rate (sensitivity) and true-negative rate (specificity) of the computer-based method (for the comparison of both the breechface and firing pin impressions) were 94.4% and at least 91.7%, respectively. For the examiners, the true-positive rate was at least 95.3% and the true-negative rate was at least 86.2%. The validity of the source decisions improved when the evaluations of breechface and firing pin impressions were combined and for the examiners also when the perceived difficulty of the comparison decreased. The examiners were reluctant to provide source decisions for "difficult" comparisons even though their source decisions were mostly correct. The correlation between the computer-based method's comparison scores and the examiners' degree-of-support judgments was low for the same-source comparisons to negligible for the different-source comparisons. Combining the outcomes of computer-based methods with the judgments of examiners could increase the validity of firearm examinations. The examiners' numerical degree-of-support judgments for their source decisions were not well-calibrated and showed clear signs of overconfidence. We suggest studying the merits of performance feedback to calibrate these judgments.

Impact of uncertainty and ambiguous outcome phrasing on moral decision-making

The literature has shown that different types of moral dilemmas elicit discrepant decision patterns. The present research investigated the role of uncertainty in contributing to these decision patterns. Two studies were conducted to examine participants' choices in commonly used dilemmas. Study 1 showed that participants' perceived outcome probabilities were significantly associated with their moral choices, and that these associations were independent from the dilemma type. Study 2 revealed that participants had significantly less preference for killing the individual when the outcome probabilities were stated using the modal verb 'will' than when they were stated using the numerical phrasing of '100%'. Our findings illustrate a discord between experimenter and participant in the interpretation of task instructions.

Knowing Ourselves Together: The Cultural Origins of Metacognition

Metacognition - the ability to represent, monitor and control ongoing cognitive processes - helps us perform many tasks, both when acting alone and when working with others. While metacognition is adaptive, and found in other animals, we should not assume that all human forms of metacognition are gene-based adaptations. Instead, some forms may have a social origin, including the discrimination, interpretation, and broadcasting of metacognitive representations. There is evidence that each of these abilities depends on cultural learning and therefore that cultural selection might shape human metacognition. The cultural origins hypothesis is a plausible and testable alternative that directs us towards a substantial new programme of research.

Do people really prefer verbal probabilities?

When people communicate uncertainty, do they prefer to use words (e.g., "a chance", "possible") or numbers (e.g., "20%", "a 1 in 2 chance")? To answer this question, past research drew from a range of methodologies, yet failed to provide a clear-cut answer. Building on a review of existing methodologies, theoretical accounts and empirical findings, we tested the hypothesis that the preference for a particular format is driven by the variant of uncertainty that people experience. We expected that epistemic uncertainty would be more often communicated in words, whereas distributional uncertainty would be more often communicated in numbers; for the dispositional uncertainty, we expected that an individual's disposition would be more often communicated in words, whereas dispositions from the world would be more often communicated numerically. In three experiments (one oral, two written), participants communicated their uncertainty regarding two outcomes per variants of uncertainty: epistemic, dispositional and distributional. Overall, participants communicated their uncertainty more often in words, but this preference depended on the variants of uncertainty. Participants conveyed their epistemic and dispositional uncertainties more often in words and their distributional uncertainty in numbers (Experiments 1 and 2) but this effect was greatly reduced when the precision of uncertainty was held constant (Experiment 3), pointing out the key role of uncertainty vagueness. We have reviewed the implications of our findings for the existing accounts of format preferences.

Verbal probabilities: Very likely to be somewhat more confusing than numbers

People interpret verbal expressions of probabilities (e.g. 'very likely') in different ways, yet words are commonly preferred to numbers when communicating uncertainty. Simply providing numerical translations alongside reports or text containing verbal probabilities should encourage consistency, but these guidelines are often ignored. In an online experiment with 924 participants, we compared four different formats for presenting verbal probabilities with the numerical guidelines used in the US Intelligence Community Directive (ICD) 203 to see whether any could improve the correspondence between the intended meaning and participants' interpretation ('in-context'). This extends previous work in the domain of climate science. The four experimental conditions we tested were: 1. numerical guidelines bracketed in text, e.g. X is very unlikely (05-20%), 2. click to see the full guidelines table in a new window, 3. numerical guidelines appear in a mouse over tool tip, and 4. no guidelines provided (control). Results indicate that correspondence with the ICD 203 standard is substantially improved only when numerical guidelines are bracketed in text. For this condition, average correspondence was 66%, compared with 32% in the control. We also elicited 'context-free' numerical judgements from participants for each of the seven verbal probability expressions contained in ICD 203 (i.e., we asked participants what range of numbers they, personally, would assign to those expressions), and constructed 'evidence-based lexicons' based on two methods from similar research, 'membership functions' and 'peak values', that reflect our large sample's intuitive translations of the terms. Better aligning the intended and assumed meaning of fuzzy words like 'unlikely' can reduce communication problems between the reporter and receiver of probabilistic information. In turn, this can improve decision making under uncertainty.

Guidance on Communication of Uncertainty in Scientific Assessments

This document provides guidance for communicators on how to communicate the various expressions of uncertainty described in EFSA's document: 'Guidance on uncertainty analysis in scientific assessments'. It also contains specific guidance for assessors on how best to report the various expressions of uncertainty. The document provides a template for identifying expressions of uncertainty in scientific assessments and locating the specific guidance for each expression. The guidance is structured according to EFSA's three broadly defined categories of target audience: 'entry', 'informed' and 'technical' levels. Communicators should use the guidance for entry and informed audiences, while assessors should use the guidance for the technical level. The guidance was formulated using evidence from the scientific literature, grey literature and two EFSA research studies, or based on judgement and reasoning where evidence was incomplete or missing. The limitations of the evidence sources inform the recommendations for further research on uncertainty communication.

The Role of Type and Source of Uncertainty on the Processing of Climate Models Projections

Scientists agree that the climate is changing due to human activities, but there is less agreement about the specific consequences and their timeline. Disagreement among climate projections is attributable to the complexity of climate models that differ in their structure, parameters, initial conditions, etc. We examine how different sources of uncertainty affect people's interpretation of, and reaction to, information about climate change by presenting participants forecasts from multiple experts. Participants viewed three types of sets of sea-level rise projections: (1) precise, but conflicting; (2) imprecise, but agreeing, and (3) hybrid that were both conflicting and imprecise. They estimated the most likely sea-level rise, provided a range of possible values and rated the sets on several features - ambiguity, credibility, completeness, etc. In Study 1, everyone saw the same hybrid set. We found that participants were sensitive to uncertainty between sources, but not to uncertainty about which model was used. The impacts of conflict and imprecision were combined for estimation tasks and compromised for feature ratings. Estimates were closer to the experts' original projections, and sets were rated more favorably under imprecision. Estimates were least consistent with (narrower than) the experts in the hybrid condition, but participants rated the conflicting set least favorably. In Study 2, we investigated the hybrid case in more detail by creating several distinct interval sets that combine conflict and imprecision. Two factors drive perceptual differences: overlap - the structure of the forecast set (whether intersecting, nested, tangent, or disjoint) - and asymmetry - the balance of the set. Estimates were primarily driven by asymmetry, and preferences were primarily driven by overlap. Asymmetric sets were least consistent with the experts: estimated ranges were narrower, and estimates of the most likely value were shifted further below the set mean. Intersecting and nested sets were rated similarly to imprecision, and ratings of disjoint and tangent sets were rated like conflict. Our goal was to determine which underlying factors of information sets drive perceptions of uncertainty in consistent, predictable ways. The two studies lead us to conclude that perceptions of agreement require intersection and balance, and overly precise forecasts lead to greater perceptions of disagreement and a greater likelihood of the public discrediting and misinterpreting information.

Seeing What You Want to See: How Imprecise Uncertainty Ranges Enhance Motivated Reasoning

In this article, we consider a novel criterion for evaluating representations of uncertainty ranges, namely, the extent to which a representation enhances motivated reasoning. In two studies, we show that perceptions of the distribution underlying ambiguous numerical ranges are affected by the motivations and worldviews of end users. This motivated reasoning effect remained after controlling for objective numeracy and fluid intelligence but was attenuated when the correct interpretation was made clear. We suggest that analysts and communicators explicitly consider the potential for motivated evaluation when evaluating uncertainty displays.

Improving Intelligence Analysis With Decision Science

Intelligence analysis plays a vital role in policy decision making. Key functions of intelligence analysis include accurately forecasting significant events, appropriately characterizing the uncertainties inherent in such forecasts, and effectively communicating those probabilistic forecasts to stakeholders. We review decision research on probabilistic forecasting and uncertainty communication, drawing attention to findings that could be used to reform intelligence processes and contribute to more effective intelligence oversight. We recommend that the intelligence community (IC) regularly and quantitatively monitor its forecasting accuracy to better understand how well it is achieving its functions. We also recommend that the IC use decision science to improve these functions (namely, forecasting and communication of intelligence estimates made under conditions of uncertainty). In the case of forecasting, decision research offers suggestions for improvement that involve interventions on data (e.g., transforming forecasts to debias them) and behavior (e.g., via selection, training, and effective team structuring). In the case of uncertainty communication, the literature suggests that current intelligence procedures, which emphasize the use of verbal probabilities, are ineffective. The IC should, therefore, leverage research that points to ways in which verbal probability use may be improved as well as exploring the use of numerical probabilities wherever feasible.

Individual consistency in the accuracy and distribution of confidence judgments

We examine which aspects of the confidence distributions - its shape, its bias toward higher or lower values, and its ability to distinguish correct from erred trials - are idiosyncratic of the who (individual specificity), the when (variability across days) and the what (task specificity). Measuring confidence across different sessions of four different perceptual tasks we show that: (1) Confidence distributions are virtually identical when measured in different days for the same subject and the same task, constituting a subjective fingerprint, (2) The capacity of confidence reports to distinguish correct from incorrect responses is only modestly (but significantly) correlated when compared across tasks, (3) Confidence distributions are very similar for tasks that involve different sensory modalities but have similar structure, (4) Confidence accuracy is independent of the mean and width of the confidence distribution, (5) The mean of the confidence distribution (an individual's confidence bias) constitutes the most efficient indicator to infer a subject's identity from confidence reports and (6) Confidence bias measured in simple perceptual decisions correlates with an individual's optimism bias measured with standard questionnaire.

Presenting Numeric Information with Percentages and Descriptive Risk Labels: A Randomized Trial

BACKGROUND

Previous research demonstrated that providing (v. not providing) numeric information about the adverse effects (AEs) of medications increased comprehension and willingness to use medication but left open the question about which numeric format is best. The objective was to determine which of 4 tested formats (percentage, frequency, percentage + risk label, frequency + risk label) maximizes comprehension and willingness to use medication across age and numeracy levels.

METHODS

In a cross-sectional internet survey (N = 368; American Life Panel, 15 May 2008 to 18 June 2008), respondents were presented with a hypothetical prescription medication for high cholesterol. AE likelihoods were described using 1 of 4 tested formats. Main outcome measures were risk comprehension (ability to identify AE likelihood from a table) and willingness to use the medication (7-point scale; not likely = 0, very likely = 6).

RESULTS

The percentage + risk label format resulted in the highest comprehension and willingness to use the medication compared with the other 3 formats (mean comprehension in percentage + risk label format = 95% v. mean across the other 3 formats = 81%; mean willingness = 3.3 v. 2.95, respectively). Comprehension differences between percentage and frequency formats were smaller among the less numerate. Willingness to use medication depended less on age and numeracy when labels were used. Generalizability is limited by the use of a sample that was older, more educated, and better off financially than national averages.

CONCLUSIONS

Providing numeric AE-likelihood information in a percentage format with risk labels is likely to increase risk comprehension and willingness to use a medication compared with other numeric formats.

A generic method for the evaluation of interval type-2 fuzzy linguistic summaries

Linguistic summarization has turned out to be an important knowledge discovery technique by providing the most relevant natural language-based sentences in a human consistent manner. While many studies on linguistic summarization have handled ordinary fuzzy sets [type-1 fuzzy set (T1FS)] for modeling words, only few of them have dealt with interval type-2 fuzzy sets (IT2FS) even though IT2FS is better capable of handling uncertainties associated with words. Furthermore, the existent studies work with the scalar cardinality based degree of truth which might lead to inconsistency in the evaluation of interval type-2 fuzzy (IT2F) linguistic summaries. In this paper, to overcome this shortcoming, we propose a novel probabilistic degree of truth for evaluating IT2F linguistic summaries in the forms of type-I and type-II quantified sentences. We also extend the properties that should be fulfilled by any degree of truth on linguistic summarization with T1FS to IT2F environment. We not only prove that our probabilistic degree of truth satisfies the given properties, but also illustrate by examples that it provides more consistent results when compared to the existing degree of truth in the literature. Furthermore, we carry out an application on linguistic summarization of time series data of Europe Brent Spot Price, along with a comparison of the results achieved with our approach and that of the existing degree of truth in the literature.

The measurement of subjective probability: evaluating the sensitivity and accuracy of various scales

The RISK of an event generally relates to its expected severity and the perceived probability of its occurrence. In RISK research, however, there is no standard measure for subjective probability estimates. In this study, we compared five commonly used measurement formats--two rating scales, a visual analog scale, and two numeric measures--in terms of their ability to assess subjective probability judgments when objective probabilities are available. We varied the probabilities (low vs. moderate) and severity (low vs. high) of the events to be judged as well as the presentation mode of objective probabilities (sequential presentation of singular events vs. graphical presentation of aggregated information). We employed two complementary goodness-of-fit criteria: the correlation between objective and subjective probabilities (sensitivity), and the root mean square deviations of subjective probabilities from objective values (accuracy). The numeric formats generally outperformed all other measures. The severity of events had no effect on the performance. Generally, a rise in probability led to decreases in performance. This effect, however, depended on how the objective probabilities were encoded: pictographs ensured perfect information, which improved goodness of fit for all formats and diminished this negative effect on the performance. Differences in performance between scales are thus caused only in part by characteristics of the scales themselves-they also depend on the process of encoding. Consequently, researchers should take the source of probability information into account before selecting a measure.

CLOUD DELPHI METHOD

Group decision making is an important category of problem solving techniques for complicated problems, among which the Delphi method has been widely applied. In this paper an improved Delphi method based on Cloud model is proposed in order to deal with the fuzziness and uncertainty in experts' subjective judgments. The proposed Cloud Delphi Method (CDM) describes experts' opinions by Cloud model and we aggregate the experts' Cloud opinions by synthetic algorithm and weighted average algorithm. Another key point of CDM is to stabilize and accommodate the individual fuzzy estimates by the defined stability rules rather than having to force them to converge, or reduce. The Cloud opinions and aggregation results can be exhibited in a graphically way leading experts to judge intuitively and it can decrease the number of repetitive surveys and/or interviews. Moreover, it is more scientific and easier to represent experts' opinion base on Cloud model which can combine fuzziness and uncertainty well. A numerical example is examined to demonstrate applicability and implementation process of CDM.

Comparative judgments as an alternative to ratings: identifying the scale origin

Although comparative judgment methods have a number of distinct advantages over ratings, they share one common problem: On the basis of comparative judgments, it is not possible to recover the origin of item evaluations. One item may be judged more positively than another, but this result does not allow any conclusions about whether either of the items are attractive or unattractive. This article discusses the implications of this limitation for the interpretation of individual differences in comparative judgments. It also presents 3 different methods that may allow determination of the scale origin using a nested model comparison approach. An application illustrates the proposed approach as well as the benefits of determining the scale origin in understanding value judgments.

Displaying uncertainty: investigating the effects of display format and specificity

We conducted four studies regarding the representation of probabilistic information. Experiments 1 through 3 compared performance on a simulated stock purchase task, in which information regarding stock profitability was probabilistic. Two variables were manipulated: display format for probabilistic information (blurred and colored icons, linguistic phrases, numeric expressions, and combinations) and specificity level (in which the number and size of discrete steps into which the probabilistic information was mapped differed). Results indicated few performance differences attributable to display format; however, performance did improve with greater specificity. Experiment 4, in which participants generated membership functions corresponding to three display formats, found a high degree of similarity in functions across formats and participants and a strong relationship between the shape of the membership function and the intended meaning of the representation. These results indicate that participants can successfully interpret nonnumeric representations of uncertainty and can use such representations in a manner similar to the way numeric expressions are used in a decision-making task. Actual or potential applications of this research include the use of graphical representations of uncertainty in systems such as command and control and situation displays.

Cytologic diagnosis: expression of probability by clinical pathologists

BACKGROUND

Clinical pathologists use descriptive terms or modifiers to express the probability or likelihood of a cytologic diagnosis. Words are imprecise in meaning, however, and may be used and interpreted differently by pathologists and clinicians.

OBJECTIVES

The goals of this study were to 1) assess the frequency of use of 18 modifiers, 2) determine the probability of a positive diagnosis implied by the modifiers, 3) identify preferred modifiers for different levels of probability, 4) ascertain the importance of factors that affect expression of diagnostic certainty, and 5) evaluate differences based on gender, employment, and experience.

METHODS

We surveyed 202 clinical pathologists who were board-certified by the American College of Veterinary Pathologists (Clinical Pathology). Surveys were distributed in October 2001 and returned by e-mail, fax, or surface mail over a 2-month period. Results were analyzed by parametric and nonparametric tests.

RESULTS

Survey response rate was 47.5% (n = 96) and primarily included clinical pathologists at veterinary schools (n = 58) and diagnostic laboratories (n = 31). Eleven of 18 terms were used "often" or "sometimes" by >/= 50% of respondents. Broad variability was found in the probability assigned to each term, especially those with median values of 75 to 90%. Preferred modifiers for 7 numerical probabilities ranging from 0 to 100% included 68 unique terms; however, a set of 10 terms was used by >/= 50% of respondents. Cellularity and quality of the sample, experience of the pathologist, and implications of the diagnosis were the most important factors affecting the expression of probability.

CONCLUSION

Because of wide discrepancy in the implied likelihood of a diagnosis using words, defined terminology and controlled vocabulary may be useful in improving communication and the quality of data in cytology reporting.

What number is "fifty-fifty"?: redistributing excessive 50% responses in elicited probabilities

Studies using open-ended response modes to elicit probabilistic beliefs have sometimes found an elevated frequency (or blip) at 50 in their response distributions. Our previous research suggests that this is caused by intrusion of the phrase "fifty-fifty," which represents epistemic uncertainty, rather than a true numeric probability of 50%. Such inappropriate responses pose a problem for decision analysts and others relying on probabilistic judgments. Using an explicit numeric probability scale (ranging from 0-100%) reduces thinking about uncertain events in verbal terms like "fifty-fifty," and, with it, exaggerated use of the 50 response. Here, we present two procedures for adjusting response distributions for data already collected with open-ended response modes and hence vulnerable to an exaggerated presence of 50%. Each procedure infers the prevalence of 50s had a numeric probability scale been used, then redistributes the excess. The two procedures are validated on some of our own existing data and then applied to judgments elicited from experts in groundwater pollution and bioremediation.

General performance on a numeracy scale among highly educated samples

BACKGROUND

Numeracy, how facile people are with basic probability and mathematical concepts, is associated with how people perceive health risks. Performance on simple numeracy problems has been poor among populations with little as well as more formal education. Here, we examine how highly educated participants performed on a general and an expanded numeracy scale. The latter was designed within the context of health risks.

METHOD

A total of 463 men and women aged 40 and older completed a 3-item general and an expanded 7-item numeracy scale. The expanded scale assessed how well people 1) differentiate and perform simple mathematical operations on risk magnitudes using percentages and proportions, 2) convert percentages to proportions, 3) convert proportions to percentages, and 4) convert probabilities to proportions.

RESULTS

On average, 18% and 32% of participants correctly answered all of the general and expanded numeracy scale items, respectively. Approximately 16% to 20% incorrectly answered the most straightforward questions pertaining to risk magnitudes (e.g., Which represents the larger risk: 1%, 5%, or 10%?). A factor analysis revealed that the general and expanded risk numeracy items tapped the construct of global numeracy.

CONCLUSIONS

These results suggest that even highly educated participants have difficulty with relatively simple numeracy questions, thus replicating in part earlier studies. The implication is that usual strategies for communicating numerical risk may be flawed. Methods and consequences of communicating health risk information tailored to a person's level of numeracy should be explored further.

Informing women about their breast cancer risks: truth and consequences

We assessed the extent to which informing women about their risk for breast cancer affected their perceived 10-year and lifetime risks for getting breast cancer, their emotional reactions toward getting breast cancer, and their intentions to get mammograms. In a pre- to posttest design, 121 women were given their 10-year risk of getting breast cancer with or without being compared with women their age and race at lowest risk. Women's perceptions of their 10-year risks became more congruent (i.e., more accurate) with their actual risk. Participants were more accurate when they received their own risk without being compared with women at lowest risk. Women who received only their own risk estimate reported being at lower risk than other women. Overall, women reported that obtaining their 10-year risk estimate either did not affect or increased their intentions to get mammograms. These results suggest that giving women their individual risk of getting breast cancer improves accuracy while also enhancing their feelings that they are at lower risk than other women. Counter to many theories of health behavior, reducing women's perceived risk of breast cancer did not lower their intentions to get mammograms. Implications for the communication of breast cancer risk are discussed.

Physicians' diagnostic judgments and treatment decisions for acute otitis media in children

Physicians' diagnoses of acute otitis media (AOM) and their treatment choices were investigated using judgment and decision-making analyses. Thirty-two pediatricians in the Albany, New York, area provided probability judgments of the presence of AOM and made treatment decisions for 32 patient vignettes, each described in terms of historical and examination variables. Their probability judgments were well predicted by linear combinations of the patient variables (R2s ranged from 0.76 to 0.97). Information about the observed condition of the eardrum proved to be most critical to the physicians' diagnoses. They demonstrated good levels of agreement on diagnoses. They varied, however, in their tendencies to treat with amoxicillin rather than another antibiotic. Case vagueness was related to the rate of antibiotic treatment. The rate of antibiotic treatment was higher for vague than for non-vague cases when the mean judged probability of AOM was low. In combination, the findings highlight the importance of performing and interpreting ear examinations and the role that consistent training may have in improving management of AOM.