The Concept of Inductive Probability

The word ‘probability’ in ordinary language has two different senses, here called inductive and physical probability. This paper examines the concept of inductive probability. Attempts to express this concept in other words are shown to be either incorrect or else trivial. In particular, inductive probability is not the same as degree of belief. It is argued that inductive probabilities exist; subjectivist arguments to the contrary are rebutted. Finally, it is argued that inductive probability is an important concept and that it is a mistake to try to replace it with the concept of degree of belief, as is usual today.     

INVOLVEMENT IN COMMUNICATION NETWORKS AS A PREDICTOR OF ORGANIZATIONAL COMMITMENT

This study examines the relationship between involvement in a job-related communication network and organizational commitment. The findings indicate a complex relationship that is moderated by the degree of job involvement. For employees who are not involved in their jobs, involvement in the job-related communication network functions to foster commitment to the organization. Two major conclusions are drawn: (1) the impact of involvement in communication networks on employee attitudes and behaviors may occur only for individuals with certain characteristics; and (2) previous studies that have reported main effects for individual variables on organizational commitment may need reinterpretation in light of the disordinal interaction obtained here. The possibility that different commitment processes operate for different kinds of employees is explored, with special emphasis on those employees for whom communication is a potent factor in determining attitudes. Implications for future research on the relationship between communication network involvement and other employee responses are discussed.     

Non-monotonic Probability Theory and Photon Polarization

A non-monotonic theory of probability is put forward and shown to have applicability in the quantum domain. It is obtained simply by replacing Kolmogorov’s positivity axiom, which places the lower bound for probabilities at zero, with an axiom that reduces that lower bound to minus one. Kolmogorov’s theory of probability is monotonic, meaning that the probability of A is less then or equal to that of B whenever A entails B. The new theory violates monotonicity, as its name suggests; yet, many standard theorems are also theorems of the new theory since Kolmogorov’s other axioms are retained. What is of particular interest is that the new theory can accommodate quantum phenomena (photon polarization experiments) while preserving Boolean operations, unlike Kolmogorov’s theory. Although non-standard notions of probability have been discussed extensively in the physics literature, they have received very little attention in the philosophical literature. One likely explanation for that difference is that their applicability is typically demonstrated in esoteric settings that involve technical complications. That barrier is effectively removed for non-monotonic probability theory by providing it with a homely setting in the quantum domain. Although the initial steps taken in this paper are quite substantial, there is much else to be done, such as demonstrating the applicability of non-monotonic probability theory to other quantum systems and elaborating the interpretive framework that is provisionally put forward here. Such matters will be developed in other works.     

Evidence for a General ADHD Factor from a Longitudinal General School Population Study

Recent factor analytic studies in Attention-Deficit/Hyperactivity Disorder (ADHD) have shown that hierarchical models provide a better fit of ADHD symptoms than correlated models. A hierarchical model includes a general ADHD factor and specific factors for inattention, and hyperactivity/impulsivity. The aim of this 12-month longitudinal study was to test the generalizability of the hierarchical models of ADHD within an elementary school population of 6–9 year old children (250 boys, 260 girls). Examination of differences as a function of informant (parent vs. teacher ratings), sex, and time was conducted. Six potential factor structures for the 18 items of the SWAN (Strengths and Weaknesses of ADHD-symptoms and Normal-behavior) scale were tested using confirmatory and exploratory factor analyses. Hierarchical models with a general ADHD factor and two or three specific factors best accounted for parent and teacher reports of symptoms for both boys and girls and at two time points separated by a 12-month interval. Findings indicate that the 18 SWAN items measure a common latent trait as well as orthogonal factors or dimensions of inattention and hyperactivity/impulsivity.     

A theory of belief

A theory of belief is presented in which uncertainty has two dimensions. The two dimensions have a variety of interpretations. The article focusses on two of these interpretations.The first is that one dimension corresponds to probability and the other to “definiteness,” which itself has a variety of interpretations. One interpretation of definiteness is as the ordinal inverse of an aspect of uncertainty called “ambiguity” that is often considered important in the decision theory literature. (Greater ambiguity produces less definiteness and vice versa.) Another interpretation of definiteness is as a factor that measures the distortion of an individual's probability judgments that is due to specific factors involved in the cognitive processing leading to judgments. This interpretation is used to provide a new foundation for support theories of probability judgments and a new formulation of the “Unpacking Principle” of Tversky and Koehler.The second interpretation of the two dimensions of uncertainty is that one dimension of an event A corresponds to a function that measures the probabilistic strength of A as the focal event in conditional events of the form A|B, and the other dimension corresponds to a function that measures the probabilistic strength of A as the context or conditioning event in conditional events of the form C|A. The second interpretation is used to provide an account of experimental results in which for disjoint events A and B, the judge probabilities of A|(A∪B) and B|(A∪B) do not sum to 1.The theory of belief is axiomatized qualitatively in terms of a primitive binary relation ? on conditional events. (A|B?C|D is interpreted as “the degree of belief of A|B is greater than the degree of belief of C|D.”) It is shown that the axiomatization is a generalization of conditional probability in which a principle of conditional probability that has been repeatedly criticized on normative grounds may fail.Representation and uniqueness theorems for the axiomatization demonstrate that the resulting generalization is comparable in mathematical richness to finitely additive probability theory.     

Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.     

A factor analysis of verbal abilities

A multiple-factor analysis was made of a battery of 42 tests of verbal abilities administered to 119 college adults. Where necessary, the distributions of test scores were normalized before the inter-test correlations were computed. Thurstone'sM (Memory or Rote Learning) factor has been confirmed, but hisV (Verbal Relations) factor seems to have been split into two or possibly three factors,C,J, andG; and hisW (Word Fluency) factor has been split into two factors,A andE. TheC factor seems to represent the richness of the individual's stock of linguistic responses, and theJ factor seems to involve the ability to handle semantic relationships. No satisfactory interpretation can as yet be made of theG factor. TheA factor seems to correspond to the speed of association for common words where there is a high degree of restriction as to appropriate responses. TheE factor is described as an associational facility with verbal material where the only restriction is that the responses must be syntactically coherent. The new factors are:F, facility and fluency in oral speech;H, facility in attaching appropriate names or symbols to stimuli; andD, speed of articulatory movements.This paper is a condensation of the writer's doctoral dissertation, A Factor Analysis of Verbal Abilities, on file at the library of the University of Minnesota.     

Explaining High Conjunction Fallacy Rates: The Probability Theory Plus Noise Account

The conjunction fallacy occurs when people judge the conjunctive probability P(A ∧ B) to be greater than a constituent probability P(A), contrary to the norms of probability theory. This fallacy is a reliable, consistent and systematic part of people's probability judgements, attested in many studies over at least 40 years. For some events, these fallacies occur very frequently in people's judgements (at rates of 80% or more), while for other events, the fallacies are very rare (occurring at rates of 10% or less). This wide range of fallacy rates presents a challenge for current theories of the conjunction fallacy. We show how this wide range of observed fallacy rates can be explained by a simple model where people reason according to probability theory but are subject to random noise in the reasoning process. Copyright © 2016 John Wiley & Sons, Ltd.     

Against Probabilistic Measures of Coherence

It is shown that the probabilistic theories of coherence proposed up to now produce a number of counter-intuitive results. The last section provides some reasons for believing that no probabilistic measure will ever be able to adequately capture coherence. First, there can be no function whose arguments are nothing but tuples of probabilities, and which assigns different values to pairs of propositions {A, B} and {A, C} if A implies both B and C, or their negations, and if P(B)=P(C). But such sets may indeed differ in their degree of coherence. Second, coherence is sensitive to explanatory relations between the propositions in question. Explanation, however, can hardly be captured solely in terms of probability.     

Motivated reasoning and verbal vs. numerical probability assessment: Evidence from an accounting context

A perplexing yet persistent empirical finding is that individuals assess probabilities in words and in numbers nearly equivalently, and theorists have called for future research to search for factors that cause differences. This study uses an accounting context in which individuals are commonly motivated to reach preferred (rather than accurate) conclusions. Within this context, I predict new differences between verbal and numerical probability assessments, as follows: first, individuals will justify an optimistic verbal assessment (e.g., somewhat possible) by retaining the option of re-defining it, in case of negative outcomes, as though the phrase really means something different, and, for that matter, means more things. This re-definition will maintain some connection to the original meaning of the phrase, but de-emphasized relative to the new meaning. Second, based on this behavior, I also predict individuals’ verbal probability assessments to be (1) more biased and yet (2) perceived as more justifiable than their numerical assessments. I find supportive evidence in an experiment designed to test the hypotheses. This study contributes to motivated reasoning and probability assessment theories (1) with new evidence of how individuals can word-smith in multiple attributes of a phrase to justify reaching a preferred conclusion, and (2) with new, reliable differences between verbal and numerical probability assessments. This study has important theoretical and practical implications relevant to organizational contexts in which people assess the likelihoods of uncertainties in words or numbers, and with motivations to reach a preferred conclusion.     

Does More Money Make You Happier? Why so much Debate?

Easterlin’s famous paradox questioned standard economic assumptions about a fundamental relationship in economics: that between happiness and income. In recent years there has been renewed debate about the paradox. In this essay, I highlight some of the methodological issues and challenges underlying that debate. I focus on the sensitivity of the results to the method selected, the choice of micro or macro data, and the way that happiness questions are defined and framed, all of which result in divergent conclusions. I also note the mediating role of the pace and nature of economic growth, institutional frameworks, and inequality. What is most notable is the remarkable consistency in the determinants of individual happiness – including income – within countries of diverse income levels and, at the same time, how happiness is affected by cross-country differences that are related to average per-capita income levels, such as political freedom and public goods. Income clearly plays a role in determining both individual and country level happiness. Still, assessing its role relative to other more difficult to measure factors as countries develop in new ways and at different rates will remain a challenge for the foreseeable future.     

New heterogeneous test statistics for the unbalanced fixed‐effect nested design

When the underlying variances are unknown or/and unequal, using the conventional F test is problematic in the two‐factor hierarchical data structure. Prompted by the approximate test statistics (Welch and Alexander–Govern methods), the authors develop four new heterogeneous test statistics to test factor A and factor B nested within A for the unbalanced fixed‐effect two‐stage nested design under variance heterogeneity. The actual significance levels and statistical power of the test statistics were compared in a simulation study. The results show that the proposed procedures maintain better Type I error rate control and have greater statistical power than those obtained by the conventional F test in various conditions. Therefore, the proposed test statistics are recommended in terms of robustness and easy implementation.     

Alignment in Multimodal Interaction: An Integrative Framework

When people are engaged in social interaction, they can repeat aspects of each other’s communicative behavior, such as words or gestures. This kind of behavioral alignment has been studied across a wide range of disciplines and has been accounted for by diverging theories. In this paper, we review various operationalizations of lexical and gestural alignment. We reveal that scholars have fundamentally different takes on when and how behavior is considered to be aligned, which makes it difficult to compare findings and draw uniform conclusions. Furthermore, we show that scholars tend to focus on one particular dimension of alignment (traditionally, whether two instances of behavior overlap in form), while other dimensions remain understudied. This hampers theory testing and building, which requires a well-defined account of the factors that are central to or might enhance alignment. To capture the complex nature of alignment, we identify five key dimensions to formalize the relationship between any pair of behavior: time, sequence, meaning, form, and modality. We show how assumptions regarding the underlying mechanism of alignment (placed along the continuum of priming vs. grounding) pattern together with operationalizations in terms of the five dimensions. This integrative framework can help researchers in the field of alignment and related phenomena (including behavior matching, mimicry, entrainment, and accommodation) to formulate their hypotheses and operationalizations in a more transparent and systematic manner. The framework also enables us to discover unexplored research avenues and derive new hypotheses regarding alignment.     

Framing experts' (dis)agreements about uncertain environmental events

Agreements and disagreements between expert statements influence lay people's beliefs. But few studies have examined what is perceived as a disagreement. We report six experiments where people rated agreement between pairs of probabilistic statements about environmental events, attributed to two different experts or to the same expert at two different points in time. The statements differed in frame, by focusing on complementary outcomes (45% probability that smog will have negative health effects vs. 55% probability that it will not have such effects), in probability level (45% vs. 55% probability of negative effects), or in both respects. Opposite frames strengthened disagreement when combined with different probability levels. Approximate probabilities can be “framed” in yet another way by indicating reference values they are “over” or “under”. Statements that use different directional verbal terms (over vs. under 50%) indicated greater disagreement than statements with the same directional term but different probability levels (over 50% vs. over 70%). Framing and directional terms similarly affected consistency judgments when both statements were issued by the same expert at different occasions. The effect of framing on perceived agreement was significant for medium (10 and 20 percentage points) differences between probabilities, whereas the effect of directional term was stable for numerical differences up to 40 percentage points. To emphasize agreement between different estimates, they should be framed in the same way. To accentuate disagreements or changes of opinion, opposite framings should be used.     

Verbal interactions of aggressively and nonaggressively predisposed males in a drinking situation

The effects of progressive intoxication were studied in male social drinkers classified from prior histories as either aggressively (A) or nonaggressively (NA) predisposed while intoxicated. Two groups of two A and two NA subjects engaged in videotaped group discussions that were analyzed by Bales interaction process analysis (IPA). At comparable levels of ad libitum alcohol intake in a natural drinking environment, significantly more verbal activity was displayed by the A subjects than by the NA subjects (P <.001), including IPA category D (P <.025). The A subjects tended to address the group as a whole rather than individual members (P <.001) and NA subjects rather than other A subjects (P <.01). Free testosterone levels assessed from saliva were higher among A subjects than among NA subjects (P <.05) with no significant changes related to time and progressive intoxication. The results suggest that the tendency to behave aggressively while intoxicated may be a fairly stable individual trait, possibly related to androgen levels and active or coercive modes of social communication.     

样例类型与解释方式对初中生数学概率问题解决的效果

为考察样例类型与解释方式对初中生数学概率问题解决的促进作用,实验1随机选取初中生90名,比较正确样例组、正误样例组、对照组的学习效果,实验2随机选取另外90名初中生,比较有教学解释、有自我解释与无解释的正误样例组的即时与延时测试学习效果,研究发现:(1)正误样例学习效果显著好于正确样例;(2)有解释的正误样例学习效果显著好于无解释的正误样例;(3)与有教学解释的正误样例学习效果相比,有自我解释的正误样例学习效果显著且更持久。     

The Effects of Vocalics and Nonverbal Sensitivity on Compliance A Replication and Extension

An interaction between receiver ability to decode vocalic cues and speaker vocalic patterns in obtaining compliance was investigated in this study. Expectancy theory was offered as an explanation for this interaction. Because changes in vocalic patterns can violate expectations, receivers make consistent interpretations of these vocalic cues, and evaluations of these interpretations may be affected by decoder predispositions toward communication that, in turn, produce differential perceptions of source reward. Respondents were interviewed by trained encoders who used neutral, pleasant, and hostile vocal patterns. Compliance was assessed by asking for a donation of time to communication research. Follow-up surveys measured perceived relational messages, interviewer credibility, vocal pleasantness, and the degree to which the vocalic pattern was expected. The predicted disordinal interaction between decoding ability and voice condition was found. Decoding ability did not correlate with predispositions, nullifying source reward as a factor in the evaluation of vocalic violations. It was suggested that preferences for vocalic patterns influenced evaluations: Good decoders may have preferred affiliative cues and thus complied more with pleasant voices, whereas poor decoders may have preferred assertive patterns and complied more with hostile voices.     

Maternal attitudes during pregnancy predict mother-infant physical proximity six months after birth

The purpose of this study was to develop an instrument for assessing maternal attitudes. Three photographs representing infants or mother-infant dyads were presented to 26 mothers in the second half of pregnancy and six months after birth. Nine mothers were clinical cases, seventeen mothers were nonpathological controls. Thirty-three semantic categories were used to code the mothers' responses to the pictures. Mothers' responses were coded independently by two researchers. The factor analysis of the codes yielded an ‘attraction to, vs rejection of, children’ factor. Compared with the control group, the mean factor score of the clinical group was significantly lower, i. e. reflected less attraction (p < 0.01). To study the relation between the attraction factor and the physical proximity of mothers and infants, 21 of these mother-infant dyads were videotaped in a semi-structured play interaction six months after birth. Recordings were coded independently by two researchers for various indices of proximity (spatial proximity, kisses, embraces, touches). The factor analysis of the codes yielded a factor contrasting distant vs close and tender interaction. A significant correlation was found between the attraction scores of pregnant women and the proximity scores of mother-infant interaction (r = 0.46; p < 0.05). These results suggest that this instrument is useful in assessing maternal attitudes of psychiatrically disturbed pregnant women and that maternal attitudes of pregnant women are significant predictors of physical proximity in motherinfant interaction at the end of the first semester.     

Investigation of Psychometric Properties of the Georgian Version of Posttraumatic Growth Inventory

This paper reports the analysis of psychometric properties of the Georgian version of the Posttraumatic Growth Inventory (PTGI-Geo). In particular, factor structure, internal consistency of the subscales, gender differences, and relation between traumatic event category and posttraumatic growth (PTG) are examined. The study had 641 participants in two studies (study 1, n = 300; study 2, n = 341 participants). The study revealed that PTGI-Geo consists of four factors, instead of the original five factors; namely, the first three factors (New Possibilities, Relation to Others, and Personal Strength) remained unchanged, while the fourth (Spiritual Change) and the fifth (Appreciation of Life) factors merged and formed a new fourth factor. All four new factors have similar internal consistency as the original inventory. There were also some between-person differences for gender consistent with other research.     

Mental models in word problem-solving: A comparison between American and Korean sixth-grade students

Mental model analysis was conducted in word problem solving using American (n = 42) and Korean (n = 44) sixth-graders. Two levels of mental models–the problem model and the mathematical model–constructed in the process of word problem solving were investigated. Categories for correct and incorrect models were developed to be used in think-aloud protocol analysis. The majority of students who constructed correct problem models classified the problems rapidly according to solution procedures as they read the problems, or restated the problems focusing on the specific words relating them to other statements in the problems. However, significant differences were found between American and Korean sixth-graders' in some categories of problem and mathematical models. While many Korean sixth-graders' problem-solving process steps were proceduralized, this was not the case for American sixth-graders, even for those who had a readily accessible knowledge base of basic mathematical facts.