Tests of randomness for pseudorandom number generators

This study examined the “randomness” of the numbers generated by the VIC-20 computer. Using eight standard tests, it was determined that the numbers provided by the VIC-20 are adequately random for practical purposes. The tests are applicable to other computer systems and provide a general means for evaluating random-number generators.     

Cultural Influences on Number Preferences: Christmas and Grading Systems

People consistently prefer numbers associated with themselves (e.g., birth dates) over other numbers. We argue that such number preferences are also shaped by cultural influences, such as customs regarding the day on which Christmas is celebrated and customs regarding ranking of numerals used in national school’s grading system. Across 6 different countries (N = 657), the day on which Christmas is celebrated had an influence on the preference for the numbers 24 vs. 25, and numbers used for better grades were uniformly rated better than numbers used for poorer grades. If grading did not involve numbers (e.g., letters A to F), then no effect appeared.

     

Consistency in interpretation of probabilistic phrases

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.     

Experimental test of the prospect theory value function: A stochastic dominance approach

According to prospect theory, individuals are risk averse regarding gains but risk seeking regarding losses, implying an S-shaped value function. The S-shaped value function hypothesis is based on experiments in which subjects are asked to choose separately between alternatives with either only positive or only negative outcomes, alternatives which rarely exist in the capital market. In addition, the S-shaped findings may be biased by the “certainty effect” and by probability distortion. In this paper we employ the recently developed prospect stochastic dominance criterion to test the prospect theory S-shaped value function hypothesis with mixed outcomes and with no “certainty effect.” Assuming that subjects do not distort moderate probabilities, we strongly reject the prospect theory S-shaped value function, with at least 76–86% of the choices being inconsistent with such preferences. When possible subjective probability distortions are taken into account, we find that at least 50–66% of the choices are inconsistent with an S-shaped value function.     

Cognitive reference points

Two methods were used to test the hypothesis that natural categories (such as colors, line orientations, and numbers) have reference point stimuli (such as focal colors, vertical and horizontal lines, and numbers that are multiples of 10) in relation to which other stimuli of the category are judged. In Experiment I, subjects placed pairs of stimuli into sentence frames consisting of linguistic “hedges” such as “— is essentially—.” Results were that the supposed reference stimuli were most often placed in the second (reference) slot. In Experiment II, the subject placed a stimulus in physical space to represent his feeling of the psychological distance of that stimulus from another spatially fixed stimulus. Results showed that, when supposed reference stimuli were fixed, other stimuli were placed closer to them than vice versa. The results have substantive implications for the understanding of internal structure of categories and methodological implications for the mapping of reference points, quantification of linguistic intuitions, and the assumption of symmetry in psychological distance judgments.     

Threshold adjustment in response to asymmetric loss functions: The case of auditors’ “substantial doubt” thresholds

Thresholds play a critical role in linking judgments and choices. One way they do so is by dividing a continuous judgment variable, such as probability, into two regions that imply different choices and actions, such as operate/do not operate, admit/do not admit, or invest/do not invest. We examine this link by focusing on the tendency of professional decision makers to adjust their thresholds when the risks associated with negative decision outcomes are elevated. We report two studies involving experienced auditors that investigate thresholds in a “going-concern” setting. In this setting, the auditor assesses the probability that a business firm will be unable to continue in existence for the coming year; if that probability exceeds a “substantial doubt” threshold (also assessed by the auditor), the auditor is required to disclose the relevant information in the firm’s annual report to the public. Our studies use two experimental cases based on actual business firms that differ in their objective likelihoods of not continuing as going concerns. We derive the auditors’ substantial doubt thresholds from the relationship between their probability assessments and their disclosure choices, unlike all prior research which has simply asked auditors to state the probability they believe represents substantial doubt. We find that auditors’ derived thresholds are adjusted downward for the more problematic firm, a result that we attribute to the asymmetric loss functions inherent in going-concern settings. The second study has some of the auditors directly provide their substantial doubt thresholds (SDTs). The downward adjustment is again found for derived thresholds but not for elicited thresholds, suggesting that the method of capturing thresholds may be an important issue in understanding judgment and choice.     

Trait gambling cognitions predict near-miss experiences and persistence in laboratory slot machine gambling

'Near-miss' outcomes (i.e., unsuccessful outcomes close to the jackpot) have been shown to promote gambling persistence. Although there have been recent advances in understanding the neurobiological responses to gambling near-misses, the psychological mechanisms involved in these events remain unclear. The goal of this study was to explore whether trait-related gambling cognitions (e.g., beliefs that certain skills or rituals may help to win in games of chance) influence behavioural and subjective responses during laboratory gambling. Eighty-four individuals, who gambled at least monthly, performed a simplified slot machine task that delivered win, near-miss, and full-miss outcomes across 30 mandatory trials followed by a persistence phase in extinction. Participants completed the Gambling-Related Cognitions Scale (GRCS; Raylu & Oei, 2004), as well as measures of disordered gambling (South Oaks Gambling Screen [SOGS]; Lesieur & Blume, 1987) and social desirability bias (DS-36; Tournois, Mesnil, & Kop, 2000). Skill-oriented gambling cognitions (illusion of control, fostered by internal factors such as reappraisal of losses, or perceived outcome sequences), but not ritual-oriented gambling cognitions (illusion of control fostered by external factors such as luck or superstitions), predicted higher subjective ratings of desire to play after near-miss outcomes. In contrast, perceived lack of self-control predicted persistence on the slot machine task. These data indicate that the motivational impact of near-miss outcomes is related to specific gambling cognitions pertaining to skill acquisition, supporting the idea that gambling near-misses foster the illusion of control.     

Verbal probabilities: Ambiguous, context-dependent, or both?

To investigate the communication value of verbal probabilistic phrases, like “possibly,” “probably,” and “perhaps,” three experiments were conducted. Subjects were asked to judge the degree of probability expressed by such phrases in different contexts: in sentences reflecting opinions on current events, in a medical discussion of treatment effectiveness, and in videotaped news reports. Judgments of degree of probability were performed in the first study on a 0–100% probability scale and in the other two on 7-point rating scales. Results indicated that different contexts influence the interpretation of probability terms and in many cases, but not always, lead to higher between-subject variability than when the terms are judged in isolation, presumably because the interpretation of probability terms tends to be correlated with the judges' personal opinions on the topics. Special communication problems arise from the fact that most people are not fully aware of the ambiguity of these phrases and underestimate the variability of such ratings in the general population. Miscommunication between experts and the general public was illustrated by answers to a questionnaire given to general medical practitioners and to parents of small children. The latter preferred numerical probabilities to words, but thinking from an individual-oriented perspective, they often misunderstood the intended statistical meanings.     

Stimulus Characteristics Determine Processing Approach on Random Array Letter-Cancellation Tasks

Target-to-distractor ratio strongly influences performance on typical random array letter cancellation tasks, suggesting that a “controlled” processing approach is used. This study was designed to determine whether “automatic” processing could be also demonstrated in the random array cancellation paradigm by changing the perceptual characteristics of the stimuli. Thirty-two healthy subjects sequentially performed four random array cancellation tasks with 50 and 100 stimuli. The letters “I” or “O' were targets and “L” served as the distractor. Performance was measured by the number of correctly canceled targets divided by the time to completion, corrected for accuracy. There was a strong effect of the number of stimuli on forms using I targets (p< .00001), but not for O's (p= .15) Performance scores were lower for I target forms than for O targets. These findings demonstrate that performance approximating “automatic” processing can also be elicited on clinically useful, office-based, or bedside tests such as random array cancellation.     

Suppressing natural heuristics by formal instruction: The case of the conjunction fallacy

A basic principle of probability is the conjunction rule, p(B) p(A&B). People violate this rule often, particularly when judgments of probability are based on intensional heuristics such as representativeness and availability. Though other probabilistic rules are obeyed with increasing frequency as people's levels of mathematical talent and training increase, the conjunction rule generally does not show such a correlation. We argue that this recalcitrance is not due to inescapable “natural assessments”; rather, it stems from the absence of generally useful problem-solving designs that bring extensional principles to bear on this class of problem. We predict that when helpful extensional strategies are made available, they should compete well with intensional heuristics. Two experiments were conducted, using as subjects adult women with little mathematical background. In Experiment 1, brief training on concepts of algebra of sets, with examples of their use in solving problems, reduced conjunction-rule violations substantially, compared with a control group. Evidence from similarity judgments suggested that use of the representativeness heuristic was reduced by the training. Experiment 2 confirmed these training effects and also tested the hypothesis that conjunction-rule violations are due to misunderstanding of “B” as “B and not A.” Changes in detailed wording of the propositions to be ranked produced substantial effects on judgment, but the pattern of these effects supported the hypothesis that, for the type of problem used here, most conjunction errors are due to use of representativeness or availability. We conclude that such intensional heuristics can be suppressed when alternative strategies are taught.     

Effect propensity

In a choice between two options, decision makers can often be roughly divided into three groups: those who strongly prefer the first option, those who strongly prefer the second option, and those whose choices are most sensitive to the specific conditions (Switchers). In any reference state, such as the experimental control, Switchers’ choices are unlikely to be exactly equally divided between the options, which potentially creates a ceiling effect among those most susceptible to influence by the particular conditions or experimental manipulations. The limited growth potential of the option favored by Switchers in the reference state can produce “effect propensity,” whereby any condition or manipulation applied to the reference state is more likely to increase the share of the other option. We test this proposition in a series of studies in the context of choices between safe and risky options and between lower-price/quality and higher-price/quality options. The results indicate that a large majority of conceptually unrelated manipulations tend to increase the choice share of risky and higher-price/quality options. This effect propensity can be reversed when the risky and higher-price/quality options are the status quo alternatives or asymmetrically dominating in the reference state. Alternative explanations for effect propensity are examined. We discuss the implications of effect propensity for the interpretation of research findings, the selection of controls, and theory tests.     

Share and Share Alike or Winner Take All?: The Influence of Social Value Orientation upon Choice and Recall of Negotiation Heuristics

Two experiments test the hypothesis that social value orientation influences choice and recall of heuristics in individuals preparing for negotiation. Consistent with predictions, Study 1 shows that in the preparation phase, negotiators with a prosocial value orientation choose more cooperative heuristics (e.g., “equal split is fair”) than competitive heuristics (e.g., “your gain is my loss”) while negotiators with a competitive social value orientation do the reverse. Negotiators with an individualistic social value orientation do not discriminate in their choice between cooperative and competitive heuristics. Study 2 shows that following preparation, prosocial negotiators recall more cooperative than competitive heuristics while individualists and competitors do the reverse. Additional measures suggest that prosocial negotiators prefer cooperative heuristics because these are seen as morally appropriate, whereas individualists and competitors prefer competitive heuristics because these are seen as effective.     

Circadian amplitude reduction is not specific for major depression

Affective disorder has often been associated with disturbances of circadian rhythmicity. The present study addressed the question of the specificity of this relationship. Two groups of subjects, a “depression-prone” and a control group, were selected on the basis of their scores on two widely-used depression questionnaires. For a period of 4 consecutive weeks circadian rhythmicity was recorded by means of log-booklets, which the subjects used to keep daily records of their hours of sleep, subjective sleep quality, and subjective alertness, mood and oral temperature. The results showed significantly lower values of subjective sleep quality and estimated sleep efficiency for the “depression-prone” group. Moreover, for the latter group nonparametric spectral analysis revealed a significantly weaker circadian rhythmicity of subjective alertness, mood, as well as oral temperature. It was concluded that these results argue against the specificity of the amplitude reduction, as often reported to be the most consistent circadian abnormality in affective disorder.     

Environmental enrichment affects suboptimal, risky, gambling-like choice by pigeons

Pigeons prefer a risky option with a low probability of a high payoff over a less risky option that results in more food. This finding is analogous to suboptimal human monetary gambling because in both cases there appears to be an overemphasis of the occurrence of the winning event and an underemphasis of the losing event. In the present research, we found that pigeons that were exposed to an enriched environment (a large cage with three other pigeons for 4 h a day) were less likely to show this suboptimal choice behavior compared with typically housed laboratory pigeons in a control group. These results have implications for the mechanisms underlying suboptimal choice by humans (e.g., problem gamblers), and they suggest that a enriched environment may allow for enhanced self-control.     

Cues to referent gender in randomly constructed names.

50 volunteers' assignments of gender to 32 randomly constructed names confirmed previous findings with respect to the structure of actual names (men's names are shorter, women's names tend to end in vowels, especially the schwa vowel) and with respect to the emotionality of sounds in actual names (men's names sound more Active, Nasty, and Unpleasant; women's names sound softer). Assignment of sex to random names was predictable (R>.8) on the basis of combinations of these variables.     

Social desirability response bias as one source of the discrepancy between subjective weights and regression weights

This study of the judgment process investigated whether social desirability response bias is more closely associated with directly weighted subjective weights than less directly assessed regression weights. Graduating college students indicated their preferences for 11 job characteristics in four different tasks: (a) a statistical weighting task completed honestly, (b) a statistical weighting task completed to “look good” to a recruiter, (c) a subjective weighting task completed honestly, and (d) a subjective weighting task completed to “look good” to a recruiter. Predicted judgments were calculated from the weights obtained in each condition. Pearson correlation coefficients using these predicted judgments were computed between conditions; the relationship between the honest and positive impression predicted judgments derived from subjective weights was significantly greater than the relationship between honest and positive impression predicted judgments derived from regression weights for 19 of 23 participants. It was concluded that social desirability response bias was more closely related to subjective weights than to regression Weights.     

Controlling the uncontrollable: effects of stress on illusory perceptions of controllability.

Individuals' failure to exercise actual control over an event might be compensated for by trying to bolster a generalized, subjective sense of control. Control might then be sought by undertaking acts the effect of which on the environment is illusory. This observation led to the hypothesis that stress, which undermines persons' sense of control, would engender illusory perceptions of controllability. The hypothesis was tested in 3 experiments that required Ss to choose between 2 gambling forms. Although the 2 forms were essentially identical, 1 was designed to instill an illusion of control. The results showed that highly stressed Ss, compared with those who experienced low stress, preferred gambling forms that heightened perceptions of controllability.     

A random support model of the calibration of subjective probabilities

A stochastic model of the calibration of subjective probabilities based on support theory (Rottenstreich and Tversky, 1997, Tversky and Koehler, 1994) is presented. This model extends support theory—a general representation of probability judgment—to the domain of calibration, the analysis of the correspondence between subjective and objective probability. The random support model can account for the common finding of overconfidence, and also predicts the form of the relationship between overconfidence and item difficulty (the “hard–easy effect”). The parameters of the model have natural psychological interpretations, such as discriminability between correct and incorrect hypotheses, and extremity of judgment. The random support model can be distinguished from other stochastic models of calibration by: (a) using fewer parameters, (b) eliminating the use of variable cutoffs by mapping underlying support directly into judged probability, (c) allowing validation of model parameters with independent assessments of support, and (d) applying to a wide variety of tasks by framing probability judgment in the integrative context of support theory.     

Outcome trees and baseball: A study of expertise and list-length effects

When people estimate the probability of an event using a list that includes all or most of the possible events, their estimate of that probability is lower than if the other possible events are not explicitly identified on the list (i.e., are collapsed into an all-other-possibilities category). This list-length (or pruning) effect has been demonstrated to occur even for people who have expertise or considerable knowledge in the event domain. We reasoned that the experts used in previous studies would be unlikely to have probabilistic representations of their problem domains (e.g., auto mechanics, auditors, hospitality managers). We used baseball experts (n= 35) and novices (n = 56) on the assumption that expertise in baseball almost certainly involves mental representations of probability for various baseball events. Subjects estimated the frequency of hits, walks, strikeouts, putouts, and “all other” outcomes for an average major league player in 100 times at bat. Other subjects estimated these event outcome frequencies in a short-list condition (e.g., strikeouts, walks, and “all other”). Strong list-length effects were observed with novices; the frequency estimate for strikeouts, for example, was nearly twice as high in the short-list condition as in the long-list condition. Experts, however, showed no list-length effect and their estimated probabilities were very near the actual (normatively correct) probabilities in all conditions. We argue that the omission effect can be overridden by strong mental representations of the family of possible events and/or a clear knowledge of the probabilities associated with the events. As well, we argue that list-length effects seem to result at least in part from an anchoring-and-adjustment strategy.     

Development of the concept of comparative subjective probability

This study investigates which formal principles govern subjective probability, and whether the validity of these principles depends on age. Two types of tasks were administered to 144 subjects from 3;8 to 19 years: a gambling task (with objective probabilities) and a sporting task (without objective probabilities). Six formal principles of the mathematical concept of qualitative probability (a nonnumerical concept based on ordinal scale properties) were tested. Results indicate that these principles are valid as principles of subjective probability for all age groups. Only the youngest age group (4 years or younger) had a smaller degree of confirmation.