Directional verbal probabilities: inconsistencies between preferential judgments and numerical meanings

Verbal probability expressions (e.g., it is possible or doubtful) convey not only vague numerical meanings (i.e., probability) but also semantic functions, called directionality. We performed two experiments to examine whether preferential judgments are consistent with numerical meanings of verbal probabilities regardless of directionality. The results showed that because of the effects of directionality, perceived degrees of certainty for verbal probabilities differed between a binary choice and a numerical translation (Experiment 1), and decisions based on a verbal probability do not correspond to those based on a numerical translation for verbal probabilities (Experiment 2). These findings suggest that directionality of verbal probabilities is an independent feature from numerical meanings; hence numerical meanings of verbal probability alone remain insufficient to explain the effects of directionality on preferential judgments.     

Verbal probabilities: An alternative approach

Previous studies of verbal probabilities have tried to place expressions like a chance, possible, and certain on 0–1 numerical probability scales. We ask instead, out of a range of outcomes, which outcome a verbal probability suggests. When, for instance, a sample of laptop batteries lasts from 1.5 to 3.5 hours, what is a certain and what is a possible duration? Experiment 1 showed that speakers associate certain with low values and possible with (unlikely) high or maximal values. In Experiment 2, this methodology was applied to several positive and negative verbal probability phrases, showing a preference for high rather than low or middle values in a distribution. Experiment 3 showed that such maxima are not universally described by large numbers. For instance, maximum speed is often described in terms of a small number of time units. What can (possibly) happen is accordingly sometimes described with very low and sometimes with very high values, depending upon focus of interest. Finally, participants in Experiment 4 were given the role of hearers rather than speakers and were asked to infer outcome ranges from verbal probabilities. Hearers appeared to be partly aware of speakers' tendencies to describe outcomes at the top of the range.     

Ratings of Orally Presented Verbal Expressions of Probability by a Heterogeneous Sample

Verbal expressions of probability are used in daily conversations, physician-physician and physician-patient communications, and questionnaire and interview responses. To assess the degree of agreement among English-speaking Australian adults in allocating numerical probabilities to these verbal expressions of probability, 966 interviewees provided estimates for 60 isolated expressions of probability and a sequence of seven items placed in a sequence. Means and median scores appeared to be consistent with common sense and with findings from other countries. Mirror-imaged terms were neither symmetrical nor equidistant, with the means and medians for the positive terms being closer to the mid-points of the scale than the means and medians of the negative terms. Items in a sequence of probability terms showed greater symmetry and less variability than isolated expressions. For most items, there was an unacceptably high level of within-subject and between-subject variability. Although subjects with higher levels of education and/ or mathematics education showed less variability, these factors accounted for very little of the variance. The greater variability in Australian results relative to those reported elsewhere was partly attributed to the use of interviews rather than questionnaires. There were no particular stems that yielded greater consistency. It was concluded that the use of these expressions leads to very imprecise communication.     

Selection of verbal probabilities: A solution for some problems of verbal probability expression

A method for verbal expression of degree of uncertainty is described. It requires the subject to select a phrase from a list that spans the full range of probabilities. In a second, optional, step, the subject indicates the numerical meaning of each phrase. The method avoids two problems of verbal probabilities—the indefinitely large lexicon and the individual differences in the interpretation of words. To test whether context and ordinal position might bias subjects' selection or interpretation of the verbal expressions in the list, the list order was varied. When the verbal expressions were arranged in random order, ordinal position had a significant effect on the selection of expressions. However, these effects did not occur when the phrases were listed in ascending or descending order. Considerations of accuracy and interpersonal agreement also support the use of ordered phrase lists.     

Diagnostic causal reasoning with verbal information

In diagnostic causal reasoning, the goal is to infer the probability of causes from one or multiple observed effects. Typically, studies investigating such tasks provide subjects with precise quantitative information regarding the strength of the relations between causes and effects or sample data from which the relevant quantities can be learned. By contrast, we sought to examine people’s inferences when causal information is communicated through qualitative, rather vague verbal expressions (e.g., “X occasionally causes A”). We conducted three experiments using a sequential diagnostic inference task, where multiple pieces of evidence were obtained one after the other. Quantitative predictions of different probabilistic models were derived using the numerical equivalents of the verbal terms, taken from an unrelated study with different subjects. We present a novel Bayesian model that allows for incorporating the temporal weighting of information in sequential diagnostic reasoning, which can be used to model both primacy and recency effects. On the basis of 19,848 judgments from 292 subjects, we found a remarkably close correspondence between the diagnostic inferences made by subjects who received only verbal information and those of a matched control group to whom information was presented numerically. Whether information was conveyed through verbal terms or numerical estimates, diagnostic judgments closely resembled the posterior probabilities entailed by the causes’ prior probabilities and the effects’ likelihoods. We observed interindividual differences regarding the temporal weighting of evidence in sequential diagnostic reasoning. Our work provides pathways for investigating judgment and decision making with verbal information within a computational modeling framework.     

Laterality effects in visual information processing: Hemispheric specialisation or the orienting of attention?

The notion that visual laterality patterns may be attributable to attentional allocation rather than hemispheric specialisation was examined in three experiments. In Experiment I, high verbal ability subjects were found to be less lateralised on a letter name match task than low verbals. In Experiment II, stimulus probability was shown to affect laterality patterns for name but not for physical matches. Again, low verbals were affected more than highs. Experiment III produced results identical to those of Experiment II although, in the latter experiment, visual fields were defined vertically rather than horizontally from the midline. Together, these results support the following generalisations: (1) visual asymmetries have their locus in a post-perceptual information processing stage; (2) visual asymmetries may be altered by manipulating stimulus probability; (3) verbal ability differences in laterality may not reflect neuroanatomical differences but merely cognitive capacity and (4) it may be unnecessary to invoke differential hemispheric specialisation in order to account for visual lateral asymmetries.     

Context affects the interpretation of low but not high numerical probabilities: A hypothesis testing account of subjective probability

Low numerical probabilities tend to be directionally ambiguous, meaning they can be interpreted either positively, suggesting the occurrence of the target event, or negatively, suggesting its non-occurrence. High numerical probabilities, however, are typically interpreted positively. We argue that the greater directional ambiguity of low numerical probabilities may make them more susceptible than high probabilities to contextual influences. Results from five experiments supported this premise, with perceived base rate affecting the interpretation of an event’s numerical posterior probability more when it was low than high. The effect is consistent with a confirmatory hypothesis testing process, with the relevant perceived base rate suggesting the directional hypothesis which people then test in a confirmatory manner.     

The Effect of Inference Order and Experience-Related Knowledge on Diagnostic Conjunction Probabilities

Ideally, a decision maker′s diagnostic probability judgments should not be affected by making predictive judgments before making diagnostic inferences. The purpose of this study is to investigate how experience-related knowledge and the inference presentation order affect a decision maker′s diagnostic conjunction probability judgments. Specifically, when decision makers are asked to make diagnoses in different judgment domains with which they have different levels of experience, we examine how making predictions first affects their subsequent diagnostic judgments in a standard conjunction paradigm. Professional auditors with experience in the auditing domain and MBA students with little or no auditing experience participated in the experiment. The results indicate that when the task involves a domain with which people have experience, making predictions prior to diagnoses has a significant influence on their subsequent diagnostic conjunction probabilities. When auditors made diagnoses in a familiar audit task situation, they were strongly influenced by whether or not they were asked to make predictions in advance. However, there was no influence of inference order on auditors′ diagnoses in a medical task, with which they do not have experience-related knowledge. Similarly, MBA students, having no experience-related knowledge in either audit or medical domains, were not affected by the inference order in making diagnoses. In the discussion of these exploratory results, we suggest that this inference order effect may be due to subjects′ anchoring on the predictive probability and insufficiently adjusting it to yield the diagnostic probability judgment.     

A possible basis for conservatism in signal detection and probabilistic categorization tasks

It is commonly claimed that conservative placement of the criterion in signal detection is due to the form of the utility function of money, to conservatism in the estimation of prior probabilities, or to probability matching tendencies. This article shows how conservatism could be caused by a systematic misconception of the shape of the underlying distributions. An experiment is described in which subjects were asked to make posterior probability judgments after performing numerical analogues of signal detection. The posterior probability judgments were radical, i.e., high posterior probabilities were overestimated and low posterior probabilities were underestimated; if this pattern of radical probability estimation reflects the subjects’ understanding of the underlying distributions, it would account for conservative criterion placement.     

The Effect of Catastrophe Potential on the Interpretation of Numerical Probabilities of the Occurrence of Hazards1

Two studies demonstrated that identical numerical probabilities of the occurrence of hazards are judged as higher when these involve potential catastrophes compared to noncatastrophic hazards. Fifteen hazards were presented that involve a potential catastrophe and 15 noncatastrophic hazards. Each hazard was given a numerical probability, which was either 1:10, 1:1,000, or 1:100,000. Numerical probabilities were rated as larger when these concerned hazards that have catastrophe potential compared to the noncatastrophic hazards, also when this effect was controlled for perceived benefits. Similar results were obtained in a second study, which controlled for possible confounds (e.g., base rate). The results suggest that verbal interpretations of numerical probabilities of the occurrence of hazards include more than only probability, for instance one's attitude toward the hazardous activity. Implications for risk communication are discussed.     

Saying and doing: A contingency-space analysis

Correspondences between verbal responding (saying) and nonverbal responding (doing) may be organized in terms of the classes of verbal/nonverbal relations into which particular instances of verbal/nonverbal response sequences can enter. Contingency spaces, which display relations among events in terms of the probability of one event given or not given another, have been useful in analyses of nonverbal behavior. We derive a taxonomy of verbal/nonverbal behavior relations from a contingency space that takes into account two conditional probabilities: the probability of a nonverbal response given a verbal response and that probability given the absence of the verbal response. For example, positive correspondence may be said to exist as a response class when the probability of doing is high given saying but is otherwise low. Criteria for other generalized classes, including negative correspondence, follow from this analysis.     

不确定性容忍度、损益概率及延迟风险对延迟选择的影响

研究通过两个实验考查了不确定性容忍度及相关变量对延迟选择的影响,其中实验1采用2（不确定性容忍度：高/低）×2（概率水平：高/中）被试间实验设计;研究2将实验任务设定在有延迟风险情景下中等概率水平,采用单因素（不确定性容忍度：高/低）被试间实验设计.实验1结果表明：不确定性容忍度与概率水平存在交互作用：中等概率时,低容忍度个体比高容忍度个体更偏好延迟选择,高概率时,两者的延迟选择无显著差异,都偏好于选择决策.实验2结果表明：在有延迟风险中等概率时,高、低容忍度个体的决策偏好无显著差异,都偏好选择决策.结论：不确定性容忍度对延迟选择存在影响且受概率水平和延迟风险的调节.     

An evaluation of the reliability of probability judgments across response modes and over time

Despite the importance of probability assessment methods in behavioral decision theory and decision analysis, little attention has been directed at evaluating their reliability and validity. In fact, no comprehensive study of reliability has been undertaken. Since reliability is a necessary condition for validity, this oversight is significant. The present study was motivated by that oversight. We investigated the reliability of probability measures derived from three response modes: numerical probabilities, pie diagrams, and odds. Unlike previous studies, the experiment was designed to distinguish systematic deviations in probability judgments, such as those due to experience or practice, from random deviations. It was found that subjects assessed probabilities reliably for all three assessment methods regardless of the reliability measures employed. However, a small but statistically significant decrease over time in the magnitudes of assessed probabilities was observed. This effect was linked to a decrease in subjects overconfidence during the course of the experiment.     

When Equal Chances = Good Chances: Verbal Probabilities and the Equiprobability Effect

When six equally qualified candidates compete for the same position, p = 1/6 for each. People seem to accept this principle more readily for numerical than for verbal probabilities. Equal chances with three to six alternatives are often verbally described in a positive vein as "entirely possible" or "a good chance" and rarely negatively as "doubtful" or "improbable." This equiprobability effect of verbal probabilities is demonstrated in five studies describing job applicants, lottery players, competing athletes, and examination candidates. The equiprobability effect is consistent with a causal (propensity) view of probabilities, where chances are believed to reflect the relative strength of facilitating and preventive causes. If important conditions in support of the target outcome are present (the candidate is qualified for the position), and there is little to prevent it from occurring (no stronger candidates), chances appear to be good. In the presence of obstacles (one stronger candidate), or in the absence of facilitating conditions (the candidate is poorly qualified), chances appear to be poor, even when numerical p values remain constant. The findings indicate that verbal and numerical probability estimates can reflect different intuitions. Copyright 2001 Academic Press.     

Probability Distortions and Outcome Desirability: Experimental Verification of Medical Folklore1

A belief common among medical personnel is that in conveying diagnoses or prognoses to patients, it is always best to emphasize the positive. In order to see if emphasis on the positive does make a difference in one's expectation of the more desirable of two alternative outcomes actually occurring, this laboratory experiment was conducted. College students were led to believe they had a low, moderate, or high probability of being assigned to one of two tasks, which differed in desirability. For some students the instructions focused on the probability of being assigned to the desirable task, whereas for others the instructions focused on the probability of being assigned to the undesirable. The two probabilities were always complementary; that is, the probability of being assigned to the desirable task was equal to one minus the probability of being assigned to the undesirable task. Following an interpolated activity, each subject's expectation of being assigned to the desirable or undesirable task was measured. Across all probability levels, subjects for whom the instructions had focused on the probability of being assigned to the desirable task viewed that assignment as significantly more likely than did subjects for whom the instructions had focused on the complementary probability of being assigned to the undesirable task. The implications of this for communicating with patients, for preventive medicine, and for coping with serious illness are briefly discussed.     

EVALUATION OF ERRORLESS COMPLIANCE TRAINING IN A GENERAL EDUCATION CLASSROOM

Errorless compliance training (ECT) is a success‐based, nonaversive intervention to reduce child noncompliance that has been shown to be effective in both home and special education settings. In the current study, ECT was evaluated in a multiple‐baseline across‐subjects design with three kindergarten students who displayed noncompliant behavior in their general education classrooms. The researcher delivered a range of classroom requests to each student to determine the probability of compliance for each request. Requests were then arranged in a hierarchy, ranging from those initially yielding high compliance probabilities (level 1) to those yielding low compliance (level 4). At the beginning of treatment, students were presented with a high number of level 1 requests and provided verbal praise for compliance. Over several weeks, lower probability requests were faded in. The three students demonstrated considerable improvement in compliance levels during and following treatment. Improved compliance generalized to low‐probability requests not used in treatment. When the teacher delivered requests, results of generalization were mixed. The results provide preliminary support for the use of errorless compliance training in the general education setting. Copyright © 2014 John Wiley & Sons, Ltd.     

You say "probable" and I say "likely": improving interpersonal communication with verbal probability phrases

When forecasters and decision makers describe uncertain events using verbal probability terms, there is a risk of miscommunication because people use different probability phrases and interpret them in different ways. In an effort to facilitate the communication process, the authors investigated various ways of converting the forecasters' verbal probabilities to the decision maker's terms. The authors present 3 studies in which participants judged the probabilities of distinct events using both numerical and verbal probabilities. They define several indexes of interindividual coassignment of phrases to the same events and evaluate the conversion methods by comparing the values of these indexes for the converted and the unconverted judgments. In all the cases studied, the conversion methods significantly reduced the error rates in communicating uncertainties.     

Rarely Occurring Headaches and Rarely Occurring Blindness: Is Rarely=Rarely? The Meaning of Verbal Frequentistic Labels in Specific Medical Contexts

In three experimental studies, factors were examined which might influence the interpretation of verbal frequentistic labels in a specific context (i.e. side effects of medical drugs). In Study 1, we directly assessed subjects' numerical equivalents of three verbal labels (recommended for use by the German Federal Health Agency), which were embedded in stylized leaflets for medical drugs; we compared the estimates with those obtained in a context-free situation. The major findings were that (1) subjects' numerical equivalents for the verbal labels were clearly lower in the context condition than in the context-free situation, (2) subjects'; interpretations appeared to depend on the seriousness of the side effects, but (3) this dependency disappeared when explicit base rates were provided. In Studies 2 and 3, we indirectly examined the influence of the seriousness of the side effects, their frequency, and of the mode of expression (verbally versus numerically) by asking for risk judgments for and choices between drugs. Results of particular importance were that (1) seriousness and frequency of side effects had the same influence on judgments and choices but the mode of expression had no significant effect on either judgments or choices; (2) when subjects’ individual numerical equivalents of verbal labels were used in the leaflets, numerically described drugs were judged equally risky as verbally described drugs but were significantly preferred for consumption. These findings have theoretical relevance for research on the processing of verbal and numerical frequentistic expressions as well as a number of practical implications for the communication of medical information.     

Patterns of Preference for Numerical and Verbal Probabilities

We report results of an experiment designed to test a principle formulated by Budescu and Wallsten (1995), that, when communicating uncertainty information, mode choices are sensitive to sources and degrees of vagueness. In addition, we examined subjects’ efficacy in using such uncertainty information as a function of communication mode, source, and vagueness. In phase one of the experiment, subjects in a dyad used precise (numerical) or imprecise (verbal) expressions to communicate to a remote partner precise or vague uncertainty about the likelihoods of events. Spinner outcomes were used to generate precise uncertainty while answers to almanac questions were used to elicit vague uncertainty. In phase two, subjects saw the events paired with their partners’ estimates of similar events, and were asked to gamble on one event from each pair. Communication mode preferences were measured as the relative frequency that subjects chose the numerical mode to either express or receive uncertainty information regarding the events. Efficacy was measured as the relative frequency that subjects choose from the pair the event associated with the objectively more probable uncertainty expression. Underlying uncertainty interacted with direction of communication to affect preferences for modes of expression of the probabilities. Subjects preferred precise (numerical) information, especially for precise events (spinners). For vague events (questions), their preference for precise (numerical) information was stronger when receiving than when communicating information. Similar preferences were reflected in the efficiency of subsequent gamble decisions based on the probability estimates. Specifically, decisions were more efficacious (i.e. consistent with Expected Utility) when degrees of precision in events and estimates matched. © 1997 by John Wiley & Sons, Ltd.     

Understanding ‘Unlikely (20% Likelihood)’ or ‘20% Likelihood (Unlikely)’ Outcomes: The Robustness of the Extremity Effect

Calls to communicate uncertainty using mixed, verbal‐numerical formats (‘unlikely [0–33%]’) have stemmed from research comparing mixed with solely verbal communications. Research using the new ‘which outcome’ approach to investigate understanding of verbal probability expressions suggests, however, that mixed formats might convey disadvantages compared with purely numerical communications. When asked to indicate an outcome that is ‘unlikely’, participants have been shown to often indicate outcomes with a value exceeding the maximum value shown, equivalent to a 0% probability —an ‘extremity effect’. Recognising the potential consequences of communication recipients expecting an ‘unlikely’ event to never occur, we extend the ‘which outcome’ work across four experiments, using verbal, numerical, and verbal‐numerical communication formats, as well as a previously unconsidered numerical‐verbal format. We examine how robust the effect is in the context of consequential outcomes and over non‐normal distributions. We also investigate whether participants are aware of the inconsistency in their responses from a traditional ‘how likely’ and ‘which outcome’ task. We replicate and extend previous findings, with preference for extreme outcomes (including above maximum values) observed in both verbal and verbal‐numerical formats. Our results suggest caution in blanket usage of recently recommended verbal‐numerical formats for the communication of uncertainty. Copyright © 2018 John Wiley & Sons, Ltd.