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Stability in meanings for quantitative terms: A comparison over 20 Years
... There exist many frequency terms that can be used in rating scales (e.g., Kipfer, 1992, p. 960). In this study, two questionnaire forms based on Simpson (1944Simpson ( , 1963 were used to collect empirical evidence of 20 frequency terms. The first form was exactly the same as the one used in Simpson (1944). ...
... The results from the two forms are presented in Table 1 Simpson (1944) and Simpson (1963) The orderings of the means from the two forms are perfect. The maximum difference between two sets of means is 1.54 (i.e., 'Very seldom'). ...
... The maximum difference between two sets of medians is 2.5 (e.g., 'Frequently', 'Sometimes', etc.). In comparison with results from Simpson (1944Simpson ( , 1963, the Form 1 column in Table 1 shows inflated per cent values for 'Rather often', 'Sometimes', 'Occasionally', 'Now and then', and 'Once in a while'. In Simpson (1944Simpson ( , 1963, the modifier 'Rather' reduced the per cent when used in 'Rather often', whereas it increased the value for the current sample. ...
... Research on how people understand expressions of frequency (e.g., often) and probability (e.g., likely) extends back to the middle of the 20th century (Cliff, 1959;Lichtenstein & Newman, 1967;Simpson, 1944Simpson, , 1963, with several studies investigating what numerical equivalents adults assign to different terms (for reviews, see Clark, 1990;Mosteller & Youtz, 1990;Teigen & Brun, 2003;Wallsten & Budescu, 1995). In these studies, participants are typically asked to map words to numbers by providing quantitative judgments (e.g., percentages or frequencies) for different terms. ...
... Generally, within-subject variation tends to be lower than between-subjects variability, indicating a fairly stable understanding of everyday uncertainty terms at the individual level, although different people may vary in their judgments (Budescu & Wallsten, 1985). On the other hand, between-subjects variation in the interpretation of particular terms notwithstanding, people can also be quite consistent in their quantitative judgments (Simpson, 1963). For instance, Mosteller and Youtz (1990) evaluated 52 expressions across 20 different studies and found that "the studies give similar, though not identical, results for the same expression when sampling and other sources of variability are considered" (p. ...
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.
... Research on how people understand expressions of frequency (e.g., often) and probability (e.g., likely) extends back to the middle of the 20 th century (Cliff, 1959;Lichtenstein & Newman, 1967;Simpson, 1944Simpson, , 1963, with several studies investigating what numerical equivalents adults assign to different terms (for reviews, see Clark, 1990;Mosteller & Youtz, 1990;Teigen & Brun, 2003;Wallsten & Budescu, 1995). In these studies, participants are typically asked to map words to numbers by providing quantitative judgments (e.g., percentages or frequencies) for different terms. ...
... Generally, within-subject variation tends to be lower than between-subjects variability, indicating a fairly stable understanding of everyday uncertainty terms at the individual level, although different people may vary in their judgments (Budescu & Wallsten, 1985). On the other hand, between-subjects variation in the interpretation of particular terms notwithstanding, people can also be surprisingly consistent in their quantitative judgments (Simpson, 1963). For instance, Mosteller and Youtz (1990) evaluated 52 expressions across 20 different studies and found that "the studies give similar, though not identical, results for the same expression when sampling and other sources of variability are considered" (p.3). ...
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 2,856 quantitative judgments, including 2,240 judgments from children. Our findings demonstrate that adult-like intuitions about the interpretation of everyday uncertainty terms emerge surprisingly 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.
... Sporadically over many years, investigators have used scaling methods to obtain psychological scale values for words and phrases that express degrees of frequency and amount (Bass et al., 1974;Lilly, 1968;Pohl, 1981;Schriesheim and Schriesheim, 1978;Simpson, 1944Simpson, , 1963Stone and Johnson, 1959), intensity (Bashaw and Anderson, 1968;Cliff, 1959;Dudek, 1959;Mosier, 1941), evaluation (Jones and Thurstone, 1955;Lodge et al., 1976;Spector, 1976), and probability (Howe, 1963(Howe, , 1969Lichtenstein and Newman, 1967;Reagan et al., 1989). Some of the common findings from these studies provide the impetus for this article and the recommendations made herein. ...
... While some researchers might question the generalizability of psychological scaling studies conducted several years ago, there is ample evidence that the scale values of many verbal phrases are stable over time and across different populations. In 1963 for example, Simpson repeated his 1944 study and found that the scale values of some 20 phrases expressing frequency showed very little change (Simpson, 1944(Simpson, , 1963. For only one phrase, sometimes, was the difference greater than five percentage points, and in over one-third of the phrases the percentages were identical. ...
This is the last in a short series of papers on measurement theory and practice with particular relevance to intervention research in nursing, midwifery, and healthcare. Understanding how it is that people respond to the questions posed by researchers is fundamental to progress in the social and health sciences. For decades methodologists in psychology, marketing, education, and survey research have studied this issue. In this paper I review this diverse empirical literature to synthesize basic principles for creating rating scales which can reduce measurement error and increase the quality of resulting data. After introducing a theoretical framework known as the cognitive aspects of survey methods (CASM), I review the fundamentals of psychological scaling theory and discuss how it has been used to study the meanings of verbal response options and provide an illustration of how the quality of measurements may be influenced by our choice of the verbal phrases we present as response options. Next, I review the research on the optimal number of response options to use in various measurement situations and how verbal and numeric anchors can combine to influence data quality. Finally, I summarize the issues covered and present recommendations for best practice when creating and using rating scales in research.
... Little is known, however, about which phrases to use. stone & Johnson (1959) and Simpson (1963) have scaled a large number of frequentistic phrases (e.g., "often," "seldom"); however, in some contexts (e.g., "what is the likelihood that this patient is psychotic?") such frequentistic phrases are less appropriate than nonfrequentistic expressions of probability (e.g., "likely," "improbable"); this study focuses on the latter. ...
... The first Is discrepancy with other results. Simpson (1963) used three of these phrases, reporting responses within one standard deviation of those reported here ("usually," .85 and .80; "seldom," .10; ...
188 SS GAVE NUMERICAL PROBABILITY ESTIMATES FOR EACH OF 41 PROBABILITY-RELATED WORDS AND PHRASES. WHILE THE RESPONSES WERE REASONABLY CONSISTENT, ASYMMETRY BETWEEN MIRROR-IMAGE PHRASES, E.G., QUITE LIKELY (.79) AND QUITE UNLIKELY (.11) WERE FOUND. THUS VERBAL LABELS ON NUMERICAL PROBABILITY RESPONSE SCALES MAY NOT BE PRACTICABLE. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
... In most of the empirical work to date on the meaning of probability words, subjects have been asked to give numerical equivalents to various probability phrases. The overwhelming result has been that there is great intersubject variability in the numerical values assigned to probability terms and great overlap among terms (Bass, Cascio, & O'Connor, 1974;Beyth-Marom, 1982;Budescu & Wallsten, 1985;Foley, 1959;Johnson, 1973;Lichtenstein & Newman, 1967;Simpson, 1944Simpson, ,1963. Withinsubject variability in the assignment of numbers to probabilistic terms is not minor, but is considerably less than between-subjects variability (Beyth-Marom, 1982;Budescu & Wallsten, 1985;Johnson, 1973). ...
Can the vague meanings of probability terms such as doubtful, probable, or likely be expressed as membership functions over the [0, 1] probability interval? A function for a given term would assign a membership value of zero to probabilities not at all in the vague concept represented by the term, a membership value of one to probabilities definitely in the concept, and intermediate membership values to probabilities represented by the term to some degree. A modified pair-comparison procedure was used in two experiments to empirically establish and assess membership functions for several probability terms. Subjects performed two tasks in both experiments: They judged (a) to what degree one probability rather than another was better described by a given probability term, and (b) to what degree one term rather than another better described a specified probability. Probabilities were displayed as relative areas on spinners. Task a data were analyzed from the perspective of conjoint-measurement theory, and membership function values were obtained for each term according to various scaling models. The conjoint-measurement axioms were well satisfied and goodness-of-fit measures for the scaling procedures were high. Individual differences were large but stable. Furthermore, the derived membership function values satisfactorily predicted the judgments independently obtained in task b. The results support the claim that the scaled values represented the vague meanings of the terms to the individual subjects in the present experimental context. Methodological implications are discussed, as are substantive issues raised by the data regarding the vague meanings of probability terms.
... There is overwhelming evidence that people considerably disagree on the numerical interpretation of most verbal expressions. The numerical values subjects assign to the same verbal expressions display large ranges (see also Simpson, 1944Simpson, , 1963Stone and Johnson, 1959;Lichtenstein and Newman, 1967;Budescu and Wallsten, 1985;Clarke et al., 1992). Verbal expressions may be inadequate for effective communication because the sender of information can have a different interpretation than the receiver. ...
... Even more interesting is that performance was almost indiscernible from performance in a condition in which subjects were provided with matched numerical information. The fact that we took the numerical equivalents from a different study (Bocklisch et al., 2012) supports research showing that the interpretation of linguistic uncertainty terms is relatively stable across populations and contexts (Mosteller & Youtz, 1990;Simpson, 1963; but see Section 6.3 below). This is a promising finding for applying computational models of cognition to verbal reasoning tasks. ...
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.
... Most of the empirical literature on probability expressions has focused on the translation of verbal expressions to point numerical equivalents. The overwhelming result is great variability in the values assigned to words and large overlap among the ranges assigned to the various expressions (e.g., Beyth-Marom, 1982;Budescu & Wallsten, 1985;Foley, 1959;Hakel, 1968;Johnson, 1973;Kenney, 1981;Lichtenstein & Newman, 1967;Nakao & Axelrod, 1983;Simpson, 1944Simpson, , 1963. Some of these studies (Beyth-Marom, 1982;Budescu & Wallsten, 1985;Johnson, 1973) have also shown that the between-subjects variability in assigning numbers to expressions far exceeds the within-subjects variability, which itself is not minor. ...
A two-stage within subjects design was used to compare decisions based on numerically and verbally expressed probabilities. In Stage 1, subjects determined approximate equivalences between vague probability expressions, numerical probabilities, and graphical displays. Subsequently, in Stage 2 they bid for (Experiment 1) or rated (Experiment 2) gambles based on the previously equated verbal, numerical, and graphical descriptors. In Stage 1, numerical and verbal judgments were reliable, internally consistent, and monotonically related to the displayed probabilities. However, the numerical judgments were significantly superior in all respects because they were much less variable within and between subjects. In Stage 2, response times, bids, and ratings were inconsistent with both of two opposing sets of predictions, one assuming that imprecise gambles will be avoided and the other that verbal probabilities will be preferred. The entire pattern of results is explained by means of a general model of decision making with vague probabilities which assumes that in the present task, when presented with a vague probability word, people focus on an implied probability interval and sample values within it to resolve the vagueness prior to forming a bid or a rating. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
... In most of the empirical work to date on the meaning of probability words, subjects have been asked to give numerical equivalents to various probability phrases. The overwhelming result has been that there is great intersubject variability in the numerical values assigned to probability terms and great overlap among terms (Bass, Cascio, & O'Connor, !974;Beyth-Marom, 1982;Budescu & Wallsten, 1985;Foley, 1959;Johnson, 1973;Lichtenstein & Newman, 1967;Simpson, 1944Simpson, , 1963. Withinsubject variability in the assignment of numbers to probabilistic terms is not minor, but is considerably less than between-subjects variability (Beyth-Marom, 1982;Budescu & Wallsten, 1985;Johnson, 1973). ...
Assessed membership functions over the [0,1] probability interval for several vague meanings of probability terms (e.g., doubtful, probable, likely), using a modified pair-comparison procedure in 2 experiments with 20 and 8 graduate business students, respectively. Ss performed 2 tasks in both experiments: They judged (A) to what degree one probability rather than another was better described by a given probability term and (B) to what degree one term rather than another better described a specified probability. Probabilities were displayed as relative areas on spinners. Task A data were analyzed from the perspective of conjoint-measurement theory, and membership function values were obtained for each term according to various scaling models. Findings show that the conjoint-measurement axioms were well satisfied and goodness-of-fit measures for the scaling procedures were high. Individual differences were large but stable, and the derived membership function values satisfactorily predicted the judgments independently obtained in Task B. Results indicated that the scaled values represented the vague meanings of the terms to the individual Ss in the present experimental context. (51 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
People typically use verbal probability phrases when discussing risks (“It is likely that this treatment will work”), both in written and spoken communication. When speakers are uncertain about risks, they can nonverbally signal this uncertainty by using prosodic cues, such as a rising, question‐like intonation or a filled pause (“uh”). We experimentally studied the effects of these two prosodic cues on the listener's perceived speaker certainty and numerical interpretation of spoken verbal probability phrases. Participants ( N = 115) listened to various verbal probability phrases that were uttered with a rising or falling global intonation and with or without a filled pause before the probability phrase. For each phrase, they gave a point estimate of their numerical interpretation in percentages and indicated how certain they thought the speaker was about the correctness of the probability phrase. Speakers were perceived as least certain when the verbal probability phrases were spoken with both prosodic uncertainty cues. Interpretation of verbal probability phrases varied widely across participants, especially when rising intonation was produced by the speaker. Overall, high probability phrases (e.g., “very likely”) were estimated as lower (and low probability phrases, such as “unlikely,” as higher) when they were uttered with a rising intonation. The effects of filled pauses were less pronounced, as were the uncertainty effects for medium probability phrases (e.g., “probable”). These results stress the importance of nonverbal communication when verbally communicating risks and probabilities to people, for example, in the context of doctor–patient communication.
This 2004 book views risk analysis as one important basis for informed debate, policy decisions and governance regarding risk issues within societies. Its twelve chapters provide interdisciplinary insights about the fundamental issues in risk analysis for the beginning of a new century. The chapter authors are some of the leading researchers in the broad fields that provide the basis for the risk analysis, including the social, natural, medical, engineering and physical sciences. They address a wide range of issues, including: new perspectives on uncertainty and variability analysis, exposure analysis and the role of precaution, environmental risk and justice, risk valuation and citizen involvement, extreme events, the role of efficiency in risk management, and the assessment and governance of transboundary and global risks. The book will be used as a starting point for discussions at the 2003 First World Congress on Risk, to be held in Brussels.
This 2004 book views risk analysis as one important basis for informed debate, policy decisions and governance regarding risk issues within societies. Its twelve chapters provide interdisciplinary insights about the fundamental issues in risk analysis for the beginning of a new century. The chapter authors are some of the leading researchers in the broad fields that provide the basis for the risk analysis, including the social, natural, medical, engineering and physical sciences. They address a wide range of issues, including: new perspectives on uncertainty and variability analysis, exposure analysis and the role of precaution, environmental risk and justice, risk valuation and citizen involvement, extreme events, the role of efficiency in risk management, and the assessment and governance of transboundary and global risks. The book will be used as a starting point for discussions at the 2003 First World Congress on Risk, to be held in Brussels.
This 2004 book views risk analysis as one important basis for informed debate, policy decisions and governance regarding risk issues within societies. Its twelve chapters provide interdisciplinary insights about the fundamental issues in risk analysis for the beginning of a new century. The chapter authors are some of the leading researchers in the broad fields that provide the basis for the risk analysis, including the social, natural, medical, engineering and physical sciences. They address a wide range of issues, including: new perspectives on uncertainty and variability analysis, exposure analysis and the role of precaution, environmental risk and justice, risk valuation and citizen involvement, extreme events, the role of efficiency in risk management, and the assessment and governance of transboundary and global risks. The book will be used as a starting point for discussions at the 2003 First World Congress on Risk, to be held in Brussels.
This 2004 book views risk analysis as one important basis for informed debate, policy decisions and governance regarding risk issues within societies. Its twelve chapters provide interdisciplinary insights about the fundamental issues in risk analysis for the beginning of a new century. The chapter authors are some of the leading researchers in the broad fields that provide the basis for the risk analysis, including the social, natural, medical, engineering and physical sciences. They address a wide range of issues, including: new perspectives on uncertainty and variability analysis, exposure analysis and the role of precaution, environmental risk and justice, risk valuation and citizen involvement, extreme events, the role of efficiency in risk management, and the assessment and governance of transboundary and global risks. The book will be used as a starting point for discussions at the 2003 First World Congress on Risk, to be held in Brussels.
This 2004 book views risk analysis as one important basis for informed debate, policy decisions and governance regarding risk issues within societies. Its twelve chapters provide interdisciplinary insights about the fundamental issues in risk analysis for the beginning of a new century. The chapter authors are some of the leading researchers in the broad fields that provide the basis for the risk analysis, including the social, natural, medical, engineering and physical sciences. They address a wide range of issues, including: new perspectives on uncertainty and variability analysis, exposure analysis and the role of precaution, environmental risk and justice, risk valuation and citizen involvement, extreme events, the role of efficiency in risk management, and the assessment and governance of transboundary and global risks. The book will be used as a starting point for discussions at the 2003 First World Congress on Risk, to be held in Brussels.
This 2004 book views risk analysis as one important basis for informed debate, policy decisions and governance regarding risk issues within societies. Its twelve chapters provide interdisciplinary insights about the fundamental issues in risk analysis for the beginning of a new century. The chapter authors are some of the leading researchers in the broad fields that provide the basis for the risk analysis, including the social, natural, medical, engineering and physical sciences. They address a wide range of issues, including: new perspectives on uncertainty and variability analysis, exposure analysis and the role of precaution, environmental risk and justice, risk valuation and citizen involvement, extreme events, the role of efficiency in risk management, and the assessment and governance of transboundary and global risks. The book will be used as a starting point for discussions at the 2003 First World Congress on Risk, to be held in Brussels.
This 2004 book views risk analysis as one important basis for informed debate, policy decisions and governance regarding risk issues within societies. Its twelve chapters provide interdisciplinary insights about the fundamental issues in risk analysis for the beginning of a new century. The chapter authors are some of the leading researchers in the broad fields that provide the basis for the risk analysis, including the social, natural, medical, engineering and physical sciences. They address a wide range of issues, including: new perspectives on uncertainty and variability analysis, exposure analysis and the role of precaution, environmental risk and justice, risk valuation and citizen involvement, extreme events, the role of efficiency in risk management, and the assessment and governance of transboundary and global risks. The book will be used as a starting point for discussions at the 2003 First World Congress on Risk, to be held in Brussels.
This 2004 book views risk analysis as one important basis for informed debate, policy decisions and governance regarding risk issues within societies. Its twelve chapters provide interdisciplinary insights about the fundamental issues in risk analysis for the beginning of a new century. The chapter authors are some of the leading researchers in the broad fields that provide the basis for the risk analysis, including the social, natural, medical, engineering and physical sciences. They address a wide range of issues, including: new perspectives on uncertainty and variability analysis, exposure analysis and the role of precaution, environmental risk and justice, risk valuation and citizen involvement, extreme events, the role of efficiency in risk management, and the assessment and governance of transboundary and global risks. The book will be used as a starting point for discussions at the 2003 First World Congress on Risk, to be held in Brussels.
This study examines the association between world religions and the earnings attribute of conservatism. I group the major world religions into two sub-groups, Western and Eastern. Prior literature documents that followers of Western religions have a lower preference for risk relative to followers of Eastern religions. Prior literature also finds a lower preference for risk is associated with more conservative reporting. Using a large sample of firms listed on exchanges around the world, I find earnings of firms domiciled in countries with larger Western religious presence are more conservative. The results hold after using an indicator for whether the predominant religion in the country is a Western religion, controlling for religiosity, and using a sample of U.S. foreign registrants that file a 20-F reconciliation with the SEC. My study contributes to our understanding of how social norms affect financial reporting.
JEL Classifications: G14; G15; M41.
Streszczenie: Kultura narodowa jest często wymieniana jako jeden z ważniejszych elementów środowiska społeczno-ekonomicznego rachunkowości. Uznaje się, że idee, przekonania i wartości, które są podzielane przez członków społeczeństwa mogą wpływać zarówno na założenia, ramy teoretyczne oraz formalno-prawne podstawy systemu rachunkowości, jak i na sposób stosowania określonych rozwiązań księgowych w praktyce. W artykule podjęto próbę odpowiedzi na pytanie, jaki wpływ może mieć kultura na procesy harmonizacji ra-chunkowości na świecie. Słowa kluczowe: kultura, rachunkowość, harmonizacja rachunkowości.
The study of uncertainty in many fields has been beset by debate and even confusion over the meaning(s) of uncertainty and the words that are used to describe it. Normative debates address questions such as whether there is more than one kind of uncertainty and how verbal descriptions of uncertainty ought to be used. Descriptive research, which we shall deal with in this paper, concerns how people actually use words to describe uncertainty and the distinct meanings they apply to those words. The main reason for what might seem an obvious statement is to clarify the somewhat odd context in which most studies of decision making take place.
Research on juror comprehension is reviewed with special attention to recent studies comparing types of definitions of three levels of the standard of proof (preponderance of the evidence, clear and convincing evidence, and beyond a reasonable doubt). Quantified definitions, (in which the standard of proof was expressed in probability terms, and combined quantified and legal definitions had their intended effect; verdicts favoring the plaintiffs decreased in number as the standard of proof became stricter. Nonquantified definitions did not achieve their intended effect on verdicts. The greater effectiveness of quantified definitions in communicating certainty levels precisely and concisely is attributed to the implicit context provided by their positions on an interval scale with known endpoints (i.e., 0–100%).
The focus of this study is management's communication of uncertainty (attested to by auditors) and the potential for miscommunication due to the communication mode used in accounting disclosures. Two hypotheses are addressed to determine if financial statement users differentiate among three levels of uncertainty (using SFAS No. 5 as a vehicle for study), and whether their judgments differ when numerical probabilities replace the prescribed verbal expressions in communicating these uncertainties. The participants for this study are drawn from commercial loan officers from a major regional bank. Results lend evidence that both the level of uncertainty and the mode of communication are significant factors influencing the level of risk revision in an uncertainty exercise. Support is found that miscommunication may exist between the preparers and users of financial statements. However, support is not found that the "vagueness" of SFAS No. 5 verbal expressions of uncertainty is detrimental to users' decision-making abilities.
This research reports and analyzes for archival purposes surveyed perceptions, use, and access by 259 United States based exemplar Primary and Secondary educators of computer-based games and technology for classroom instruction. Participating respondents were considered exemplary as they each won the Milken Educator Award during the 1996–2009 computer era. Overall perceptions are reported along with trend, differences in perceptions by subject area taught, and differences in perception by Primary and Secondary teacher population categories. Overall game usage is reported along with association of perceptions with game usage as well as usage differences due to grade category. Among other findings, adoption of computer-based games for educational use in the classroom by exemplar Primary teacher populations appeared to be in the Late Majority stage of the Rogers Technology Adoption Curve while adoption in the classroom by exemplar Secondary teacher populations appeared to be in the beginning of the Early Majority stage.
A series of three studies examines potential consumer confusion associated with the advertising copy used to describe cause-related marketing (CRM) campaigns, where money is donated to a charity each time a consumer makes a purchase. The first study assesses the relative frequency of various copy formats in CRM on the Internet. The authors find that the majority of the copy formats (69.9%) are abstract (e.g., a portion of the proceeds will be donated), 25.6% are estimable (e.g., X% of the profits will be donated), and 4.5% are calculable (e.g., X% of the price will be donated). Subsequent studies find that (1) slight variations in abstract wording in advertising copy leads to considerable differences in consumers' estimates of the amount being donated, (2) the amount of the donation estimate for each abstract copy format varies considerably across individuals, and (3) the donation amount can impact choice. Taken together, the three studies demonstrate that the vast majority of advertising copy used to describe CRM donations is abstract, that different but legally equivalent abstract copy formats result in large differences in mean perceived donation level, and that these donation levels can impact consumer choice. Implications for advertising strategy and public policy are discussed.
Judgment of the probable accuracy of intelligence data and products is held as integral to the intelligence rating process. Accurate communication of the probability of uncertainty implicit in such judgment is requisite to the effective production and utilization of intelligence. Twenty-eight subjects, 14 U. S. Army enlisted men and 14 extension college students, numerically encoded on a 0 to 100 scale each of 15 probability phrases in each of three sentence contexts. Subjects were relatively consistent in their own encoding of given phrases, but differed, often radically, from other subjects. Cluster analysis of the numbers assigned by subjects indicated an underlying asymmetric probability scale comprised of a small number of intervals.
Thirty Internal locus of control and 30 External locus of control male Ss were assigned further to one of three treatment conditions (10 each): Skill set (100% contrived reinforcement on a mutilated word task presented as “skill-related”); Chance set (50% contrived reinforcement on the same task presented as “chance-related”); and an Ambiguous control condition (not introduced to task). On the dependent variable of assignment of subjective probabilities (PN) to probability-related words, Internals elevated PN under Skill set; Externals did not respond differentially to Skill and Chance sets and “preferred” the nonevaluative Ambiguous condition. Chance set was not responded to differentially by Internals and Externals.
Subjects judged the attractiveness of student apartments characterized by the attributes of size, standard and travelling time to the university. The information describing the apartments was given either in numerical (e.g., 21 m2) or verbal form (e.g., small). In the first experiment the verbal descriptions were scaled numerically to ensure comparability of the numerical and verbal presentations. In the second experiment, the subjects gave attractiveness judgments of these alternatives described in all different combinations of numerically and verbally presented attributes. In the third experiment, ananlyses of numerical judgments and think aloud protocols were used. The most important attribute was travelling time to the university. In general, numerical representation of the most important attribute tended to have somewhat greater impact on attractiveness judgements than verbal descriptions. This average tendency reflected a substantial difference for poor alternatives and a small or nonexisting effect for the most attractive apartments in the set of decision alternatives. This result was related to findings of different decision processes for choices among positive and negative decision alternatives.
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.
The reported experiment took place in a professional forecasting organization accustomed to giving verbal probability assessments (‘likely’, ‘probable’, etc.). It attempts to highlight the communication problems caused by verbal probability expressions and to offer possible solutions that are compatible with the forecasters overall perspective on their jobs
Experts in the organization were first asked to give a numerical translation to 30 different verbal probability expressions most of which were taken from the organization's own published political forecasts. In a second part of the experiment the experts were given 15 paragraphs selected from the organization's political publications each of which contained at least one verbal expression of probability. Subjects were again asked to give a numerical translation to each verbal probability expression
The results indicate that (a) there is a high variability in the interpretation of verbal probability expressions and (b) the variability is even higher in context. Possible reasons for the context effect are discussed and practical implications are suggested.
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.
Physicians often use verbal expressions of probability to characterize their uncertainty about outcomes and the risks or side effects of proposed therapies. However, there is an extensive literature that documents the inherent vagueness of such expressions. Because of the potential importance of probability terms to physician-patient communication and decision-making, we asked patients to tell us the odds they thought applicable to the term “rare”, as used by their physician to discuss the likelihood of an adverse outcome from surgery. Patients were randomly assigned to one of three outcome groups: death, severe heart attack, or severe pneumonia. Demographic data were elicited from each subject, as were indicators of present health status, medical history for certain diseases and surgery, and life expectancy. Linear regression and ANOVA analyses of the responses indicate that patient age, education level, perceived health status, and recency of experience with disease and medical care influence patients' numeric interpretations. We discuss the implications of these results.
In the Analytic Hierarchy Process (AHP), decision makers make pairwise comparisons of alternatives and criteria. The AHP allows to make these pairwise comparisons verbally or numerically. Although verbal statements are intuitively attractive for preference elicitation, there is overwhelming evidence that people have very different numerical interpretations of the same verbal expressions. This study explores the consequences of these differences for the quality of the AHP analysis. The results of the laboratory study with 180 participants confirm that the 1-to-9 conversion table, as is often used in the AHP, tends to overestimate differences in preference. Concerning the outcome of the AHP analysis the numerical mode shows slightly better results (not significant). Given the preference of many people for the verbal mode we conclude that if accuracy is not of the highest importance, the ease and comfort of verbal expressions may be worth the small loss in decision quality.
This paper offers a fuzzy-set model for interpreting vague frequency expressions, such as “rarely” and “sometimes,” in the context of self-reported marijuana use. This model distinguishes between “intersubject fuzziness,” reflecting differences between persons in the numeric interpretation of frequency expressions; “intrasubject fuzziness,” indicating intervals of possible frequencies that a person refers to with a frequency expression; “conjoint fuzziness,” reflecting differences between persons in the size of these intervals; and “random error.” These types of fuzziness were examined for seven frequency expressions in two reporting conditions (confidential research, job interview). Intrasubject fuzziness consistently accounted for the largest proportion of response variance (approximately 50%); intersubject and conjoint fuzziness accounted for approximately 20% and 15%, respectively; random error accounted for about 15% of the variance. Intersubject, intrasubject, and conjoint fuzziness make the numeric interpretation of frequency expressions problematic. They reflect that different persons apply different frequency expressions to describe the same levels of actual marijuana use and that one person may use different expressions to describe marijuana use in different situations. The validity of self-reports may be enhanced by interpreting and analyzing frequency expression as fuzzy sets.
This paper reviews the state of the art on risk communication to the public, with an emphasis on summarizing relevant empirical findings. In particular, the paper reviews empirical results regarding the format of risk communication messages, the use of risk comparisons, audience differences, and the use of mental models as an aid in crafting effective risk communication messages. Later sections discuss the issue of credibility and trust in risk communication, and the use of stakeholder participation processes — important areas in which not as much rigorous empirical information is available. Due to the breadth of the topic, the paper is not intended to be a comprehensive review, but rather an overview of the voluminous literature in this area.
It is occasionally claimed in both applied decision analysis and in basic research that people can better use and understand probabilistic opinions expressed by nonnumerical phrases, such as “unlikely” or “probably,” than by numbers. It is important for practical and theoretical reasons to evaluate this claim. The available literature indicates that there is large variability in the mapping of phrases to numbers, but provides no indication as to its cause. This study asks (a) whether the variability can be attributed to how people interpret the phrases per se, rather than to how they use the number scale and (b) whether the variability is due primarily to between-subject or to within-subject factors. In order to answer these questions, 32 subjects ranked and compared 19 probability phrases on each of three occasions. The results show that individuals have a relatively stable rank ordering of the phrases over time, but that different individuals have different rank orderings. Practical and methodological implications of these data are discussed.
This paper reviews the state of the art on risk communication to decision-makers, with an emphasis on issues involved in communicating technical results. In particular, the paper discusses the treatment of uncertainty, variability, and dependence. It also reviews suggestions from the literature regarding the appropriate format of risk communication messages to decision-makers. Due to the lack of detailed empirical investigations and definitive results about this topic, the paper is not intended to be a comprehensive review, but rather as an exploration of key issues in this area.
This study investigates the effect of language-culture and linguistic translation on the interpretation of verbal uncertainty expressions found in International Accounting Standards. Data are collected from US Certified Public Accountants and German-speaking Wirtschaftsprüfer (chartered or certified accountants) to test three hypotheses. One group of German speakers evaluated uncertainty terms expressed in German and another group in English. The results indicate significant differences in interpretation across the three groups. Some differences are attributed to a language-culture effect and others to a translation effect, with the language-culture effect being more pervasive. These results raise the question of whether International Accounting Standards can be applied consistently across language-cultures.
The issues of how individuals decide which of two events is more likely and of how they understand probability phrases both involve judging relative likelihoods. In this study, we investigated whether derived scales representing probability phrase meanings could be used within a choice model to predict independently observed binary choices. If they can, this simultaneously provides support for our model and suggests that the phrase meanings are measured meaningfully. The model assumes that, when deciding which of two events is more likely, judges take a single sample from memory regarding each event and respond accordingly. The model predicts choice probabilities by using the scaled meanings of individually selected probability phrases as proxies for confidence distributions associated with sampling from memory. Predictions are sustained for 34 of 41 participants but, nevertheless, are biased slightly low. Sequential sampling models improve the fit. The results have both theoretical and applied implications.
The problem was to identify the effect of context situations on the meaning of frequency words. One hundred college students served in the rating of the materials as well as in the experimental task. Frequency words and sentences without frequency words were rated and then four frequency words and five sentences were selected on the basis of the positive-negative continuum. Each of the four frequency words (and no frequency word) were then placed in the five sentences and rated by 20 subjects each. A two-way analysis of variance with repeated measures showed sentences, frequency words, and sentence and frequency words interaction all significant. The main conclusion is frequency words take on different meanings (positive-negative) when placed in various sentences.
Informed consent litigation provides a forum in which probabilistic evidence is elicited from physicians as parties or as expert witnesses. The authors reviewed over 450 medical informed consent opinions reported by both trial and appellate courts in all 50 states over 40 years to determine 1) the extent to which verbal expressions of probability were used by testifying physicians to characterize the risks of medical procedures; 2) when such expressions were used, whether consistent numeric interpretations of the terms were being applied by the physicians; 3) whether the choice of expression was influenced by the severity of the consequences associated with the particular risk; and 4) whether the use of such terms was correlated with trial outcomes, inasmuch as the duty to disclose a risk is said to increase with the magnitude of the risk and probability is one measure of such magnitude. It was found that subjective verbal expressions of probability are used in the litigation setting, and that such expressions represent broad ranges of numeric probabilities. There was some correlation between the expression and the represented numeric probabilities. In general, expressions such as "extremely low" and "low" corresponded to probabilities lower than those represented by terms such as "high" and "very high." Further, verbal expressions appeared to be influenced by the severity of the consequences associated with the risks, but whether this increases or decreases the ambiguity of verbal expressions in the communication process warrants further research. The authors suggest a syntax of verbal expressions of probability as a means to reduce the numeric ambiguity of these terms.
The objective was to examine the way that cancer patients translate verbal descriptors of probability into numerical estimates. A list of words commonly used on consent forms to describe the likelihood for benefits or risks of therapies was provided to 100 cancer patients. Two formats, paper/pencil or computer, were used to provide the list of words. Two methods, magnitude estimation and linear analogue scaling, were used to obtain probability estimates for each word. In addition, two scenarios were developed to study 'context effects' on numerical interpretations of verbal descriptions of probability. All patients provided numerical values for the words on two occasions, separated by one week, and two interviewers collected the data. Regardless of method or format, each word elicited widely variable numerical interpretations. An ANOVA model, including patient, word, interviewer, time, method and format, indicated that patient and interviewer produced major effects on probability estimates. Agreement between methods and across time was good. Paper/pencil and computer formats yielded similar results. Context effects did not appear to influence the numerical probabilities elicited by the 2 scenarios. It was concluded that, within this group of patients, there was no consensus about numerical meaning of a given word, and that interviewers can systematically influence numerical interpretations. There appears to be a great deal of 'noise' in this particular line of communication between patients and health professionals.
One hundred mothers and 50 medical students and doctors were interviewed to examine their understanding of eight common probability expressions as they are used in statements of the kind that doctors regularly make to mothers of babies. Respondents were asked to translate each term into a number on a scale from 0 to 10. There was a wide range of interpretation of the expressions, and significant differences were found between the mothers and medical group for seven of the expressions. Most mothers expressed a preference for receiving information in numerical terms. We advise that verbal probability expressions should be restricted, and more information presented in numerical terms.
PIP
One of the central elements of genetic counseling is the transmission of quantitative information concerning risks of defects in an unborn child from counselor to client. In order to investigate this subject, the authors studied the understanding of numeric and nonnumeric descriptions of genetic risk by 190 pregnant women. Specifically, 3 risk issues were explored: whether women were able to interpret numeric risks as %s whether shifting denominators affected risk assessment; and the comparative assessment of risk of birth defects in general, and the risk of a neural tube defect, (NTDS) in particular. Respondents were much less likely to assign the correct % equivalent to risk information when the denominator was 1,000 rather than 100. The ability to correctly identify % equivalents affected respondents' quantitative assessment of the frequency of neural tube defects. Shifting the denominator from 100 to 1,000 however, did not affect women's quantitative assessment of the rarity of birth defects. In general, the respondents preserved the relative risk of birth defects and neural tube defects in their choice of descriptive terms. The majority of women evaluated serious birth defects as occurring "often" or "occasionally" and NTDS as occurring "rarely" or "very rarely."
The relationship between cognitive stage and three types of linguistic markers used to convey speaker uncertainty was assessed. Cognitive stage was assessed on the basis of explanations given by 56 subjects on two Piagetian probability tasks. These cognitive interviews also provided context-appropriate verbal data on the production of uncertainty markers, classified referentially as (a) frequency, (b) psychological, and (c) ambiguous. Production of frequency markers was not related to cognitive stage. However, both concrete and formal operational subjects produced more ambiguous markers than preoperational subjects, and formal operational subjects produced more psychological uncertainty markers than concrete and preoperational subjects. The results are discussed in terms of Piaget's hypothesized relationship between language and thought.
To assess the level of involvement patients want in decision making related to the acceptance or rejection of an invasive medical intervention and whether their preference for decision making is related to their preference for qualitative (verbal) or quantitative (numeric) information about the risks of the procedure.
A university-based Department of Veterans Affairs Medical Center.
Cross-sectional study using structured interviews of consecutive patients seen for continuity care visits in a general medicine clinic.
Four hundred and sixty-seven consecutive patients with a mean age of 65.2 years (SD 10.70 years, range 31-88 years) and with a mean of 12.6 years (SD 2.96 years, range 0-24 years) of formal education.
In the context of an invasive diagnostic or therapeutic intervention, patients were asked whether they preferred patient-based, physician-based, or shared patient-physician decision making. Patients were asked to give the ratio of patient-to-physician decision making they preferred, and whether they preferred discussions using words, numbers, or both. Of 467 subjects, 318 (68%) preferred shared decision making; 100 (21.4%) preferred physician-based decision making; and 49 (10.5%) preferred patient-based decision making. In terms of risk disclosure, 436 (93.4%) preferred that their physician disclose risk information to them. Of these 436 patients, 42.7% preferred disclosure of information about the probability of adverse outcomes using qualitative (verbal) expressions of probability; 35.7% preferred disclosure in terms of quantitative (numeric) expressions of probability; and 9.8% preferred disclosure in both qualitative and quantitative terms. Younger patients (odds ratio [OR] 0.96; confidence interval [CI] 0.93, 0.99), patients who had at least one stroke (OR 3.03; CI 1.03, 8.90), and patients who preferred to discuss risk information with their physicians in terms of numbers (OR 2.39; CI 1.40, 4.06) tended to prefer patient-based or shared decision making.
Male veterans consistently preferred shared patient-physician decision making in the context of invasive medical interventions.
A useful starting-point for an overview of human responses to
uncertainty is that people seem to draw upon two primary sources of
heuristics for dealing with uncertainty and commonsense theories about
it. The first one is commonsense realism, and the second is commonsense
sociality. Commonsense realism encompasses lay theories and intuitions
about the physical world and how it works. Commonsense sociality, on the
other hand, refers to lay psychology and sociology-our theories and
intuitions about how the psycho-social world works. From these two
sources spring most, if not all, of our heuristics, devices, formal
methods, abstract theories, and frameworks for coping with an uncertain
world. They overlap and may provide conflicting prescriptions. Perhaps
the strongest and most obvious link between them is vicarious learning
or second-hand knowledge
A group of 158 students taking general and educational psychology courses rated a collection of 48 words or phrases indicating frequency as a 9-point graphic scale from "None of the time" to "All of the time." Scale values and dispersions for the entire list are presented with a recommendation as to one possible selection of terms for a 9-step continuum. From Psyc Abstracts 36:01:1GH24S. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
It was hypothesized that "common adverbs of degree multiply the intensity of the adjectives they modify." This should be reflected by adverb-adjective combinations' psychophysical scale values. Combinations of 9 adverbs and 15 adjectives were rated on a favorable-unfavorable dimension. "The scale values obtained were found to be highly reliable, highly comparable between groups [of raters], and highly correlated with scale values obtained by paired comparisons." The data was in close correspondence to the hypothesis when tested by a matrix method. (16 ref.) From Psyc Abstracts 36:01:1BB27C.
A method of scaling a set of stimuli or objects on a psychological continuum when the relative positions of the same stimuli on a physical continuum are unknown is described here. It possesses the following properties: (1) it requires but a single judgment from each subject for each stimulus, (2) it yields scale values which are linearly related to those obtained by the method of paired comparisons, (3) it provides its own internal consistency check upon the validity of the various assumptions made, and (4) the computations involved are quite simple. (PsycINFO Database Record (c) 2012 APA, all rights reserved)